Femap Structural - Verification Guide - Free Download PDF Ebook

Version 8.2 )(0$36WUXFWXUDO Verification Guide Proprietary and Restricted Rights Notice This information product is licensed to the user for the period set forth in the applicable license agreement, subject to termination of the license by Unigraphics Solutions Inc. at any time and at all times remains the property of Unigraphics Solutions Inc. or third parties from whom Unigraphics Solutions Inc. has obtained a licensing right. The information contained within including, but not limited to, the ideas, concepts and know-how, is proprietary, confidential and trade secret to Unigraphics Solutions Inc. or such third parties and the information contained therein shall be maintained as proprietary, confidential and trade secret to Unigraphics Solutions Inc. or to such third parties. The information contained within shall not be copied or reproduced in any form whatsoever, nor is any information to be disclosed to anyone other than an authorized representative of the user’s employer who is contractually obligated not to disclose same, without express prior written consent of Unigraphics Solu- tions Inc. The user of this information and the computer program(s) referred to herein retains full control over and is solely responsible for the mechanical design of the user’s equipment, machinery, systems, and products. Unigraphics Solutions Inc. makes no warranties of any kind, including the warranty of merchantability or fitness for a particular purpose in respect to the equipment, machinery, systems, and products derived or resulting hereunder, and the user assumes all risks and liability for results obtained by the manufacturing, use or implementation of the computer program(s) described herein, whether used singly or in combination with other designs or products. Unigraphics Solutions Inc. shall not be liable for any special or consequential damages. Unigraphics Solutions Inc. makes no warranty that the equipment, machinery, systems, and products derived or resulting hereunder will not infringe the claims of domestic or foreign patents and further does not warrant against infringement by reason of the user thereof in combination with other designs, products, or materials or in the operation of any process. User shall protect, indemnify and hold harmless Unigraphics Solutions Inc. of and from any loss, cost, damage or expense arising from any claim that is in any way associated with the computer program(s) described within. Data presented in examples do not necessarily reflect actual test results and should not be used as design criteria. By acceptance of this product, the user agrees to the above conditions and further agrees that the product will not be exported (or re-exported from a country of installation), directly or indirectly, separately or as part of a system, without user or user’s employer, at its own cost, first obtaining all licenses from the United States Department of Commerce and any other appropriate agency of the United States Government as may be required by law. Copyright © 1986, 1987, 1988, 1989, 1990, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002 Unigraphics Solutions Inc. All rights reserved. Restricted Rights Legend: This commercial computer software, documentation, and related materials are provided with restricted rights. Use, duplication, or disclosure by the U.S. Gov- ernment is subject to the protections and restrictions as set forth in the Unigraphics Solutions Inc. commercial license agreement for the software, documentation, and related material as prescribed in DOD FAR 227-7202-3(a), or for Civilian agencies, in FAR 27.404(b)(2)(i), and any successor or similar regulation, as applicable. Unigraphics Solutions Inc., 10824 Hope Street, Cypress, CA 90630. EDS, SDRC, I-DEAS, FEMAP, Dual Engine Geometry Modeling, FEMAP Professional, FEMAP Enterprise and FEMAP Structural and the EDS logo are trademarks, registered trademarks, or service marks of Electronic Data Systems Corporation or its subsidiaries. All other trademarks, registered trademarks, or service marks belong to their respective holders. The information contained within is subject to change without notice and should not be construed as a commitment by Unigraphics Solutions Inc. Unigraphics Solutions Inc. assumes no responsibility for any errors or omissions that may appear within.. Conventions This manual uses different fonts to highlight command names or input that you must type. Throughout this manual, you will see references to Windows. Windows refers to Microsoft ® Windows NT, Windows 2000, Windows 95, Windows 98, Windows Me, or Windows XP. You will need one of these operating environments to run FEMAP for the PC. This manual assumes that you are familiar with the general use of the operating environment. If you are not, you can refer to the Windows User’s Guide for additional assistance. Similarly, throughout the manual all references to FEMAP, refer to the latest version of our software. EDS PLM Solutions P.O. Box 1172, Exton, PA 19341 Phone: (610) 458-3660 FAX: (610) 458-3665 Web: http://www.femap.com a:setup Shows text that you should type. OK, Cancel Shows a command name or text that you will see in a dialog box. Table of Contents Proprietary and Restricted Rights Notice Overview Linear Statics Verification Using Theoretical Solutions Nodal Loads on a Cantilever Beam .................................................................................... 4 Axial Distributed Load on a Linear Beam .......................................................................... 6 Distributed Loads on a Cantilever Beam ............................................................................ 9 Moment Load on a Cantilever Beam ................................................................................ 12 Thermal Strain, Displacement, and Stress on Heated Beam ............................................ 15 Uniformly Distributed Load on Linear Beam .................................................................. 18 Membrane Loads on a Plate ............................................................................................. 21 Thin Wall Cylinder in Pure Tension ................................................................................. 24 Thin Shell Beam Wall in Pure Bending ........................................................................... 27 Strain Energy of a Truss ................................................................................................... 30 Linear Statics Verification Using Standard NAFEMS Benchmarks Elliptic Membrane ............................................................................................................ 34 Cylindrical Shell Patch Test ............................................................................................. 39 Laminate Strip .................................................................................................................. 42 Hemisphere-Point Loads .................................................................................................. 44 Z–Section Cantilever ........................................................................................................ 47 Skew Plate Normal Pressure ............................................................................................. 49 Thick Plate Pressure ......................................................................................................... 53 Solid Cylinder/Taper/Sphere–Temperature ...................................................................... 58 Normal Modes/Eigenvalue Verification Using Theoretical Solutions Undamped Free Vibration - Single Degree of Freedom ................................................... 65 Two Degrees of Freedom Undamped Free Vibration - Principle Modes ......................... 68 Three Degrees of Freedom Torsional System .................................................................. 71 Two Degrees of Freedom Vehicle Suspension System .................................................... 73 Cantilever Beam Undamped Free Vibrations ...................................................................76 Natural Frequency of a Cantilevered Mass ...................................................................... 78 Normal Modes/Eigenvalue Verification Using Standard NAFEMS Bench- marks Bar Element Test Cases .................................................................................................... 82 Pin-ended Cross - In-plane Vibration ........................................................................ 83 Pin-ended Double Cross - In-plane Vibration ........................................................... 86 Free Square Frame - In-plane Vibration .................................................................... 89 TOC-2 Cantilever with Off-Center Point Masses ................................................................. 92 Deep Simply-Supported Beam .................................................................................. 95 Circular Ring - In-plane and Out-of-plane Vibration ................................................ 98 Cantilevered Beam .................................................................................................. 101 Plate Element Test Cases ................................................................................................ 104 Thin Square Cantilevered Plate -Symmetric Modes ............................................... 105 Thin Square Cantilevered Plate - Anti-symmetric Modes ...................................... 108 Free Thin Square Plate ............................................................................................ 111 Simply-Supported Thin Square Plate ...................................................................... 114 Simply-Supported Thin Annular Plate .................................................................... 117 Clamped Thin Rhombic Plate ................................................................................. 121 Cantilevered Thin Square Plate with Distorted Mesh ............................................. 124 Simply-Supported Thick Square Plate, Test A ....................................................... 129 Simply-Supported Thick Square Plate, Test B ........................................................ 133 Clamped Thick Rhombic Plate ............................................................................... 136 Simply-Supported Thick Annular Plate .................................................................. 140 Cantilevered Square Membrane .............................................................................. 144 Cantilevered Tapered Membrane ............................................................................ 148 Free Annular Membrane ......................................................................................... 152 Cantilevered Thin Square Plate ............................................................................... 156 Cantilevered Thin Square Plate #2 .......................................................................... 161 Axisymmetric Solid and Solid Element Test Cases ....................................................... 164 Free Cylinder - Axisymmetric Vibration ................................................................ 165 Thick Hollow Sphere - Uniform Radial Vibration .................................................. 168 Simply-Supported Annular Plate -Axisymmetric Vibration ................................... 171 Deep Simply-Supported Solid Beam ...................................................................... 174 Simply-Supported Solid Square Plate ..................................................................... 178 Simply-Supported Solid Annular Plate ................................................................... 182 Cantilevered Solid Beam ......................................................................................... 186 Verification Test Cases from the Societe Francaise des Mechaniciens Mechanical Structures - Linear Statics Analysis with Bar or Rod Elements ................. 191 Short Beam on Two Articulated Supports .............................................................. 192 Clamped Beams Linked by a Rigid Element .......................................................... 194 Transverse Bending of a Curved Pipe ..................................................................... 196 Plane Bending Load on a Thin Arc ......................................................................... 199 Nodal Load on an Articulated Rod Truss ................................................................ 201 Articulated Plane Truss ........................................................................................... 203 Beam on an Elastic Foundation ............................................................................... 206 Mechanical Structures - Linear Statics Analysis with Plate Elements ........................... 209 Plane Shear and Bending Load on a Plate ............................................................... 210 Infinite Plate with a Circular Hole .......................................................................... 212 Uniformly Distributed Load on a Circular Plate ..................................................... 215 Torque Loading on a Square Tube .......................................................................... 218 Cylindrical Shell with Internal Pressure .................................................................. 221 TOC- 3 Uniform Axial Load on a Thin Wall Cylinder ........................................................ 225 Hydrostatic Pressure on a Thin Wall Cylinder ........................................................ 229 Gravity Loading on a Thin Wall Cylinder .............................................................. 232 Pinched Cylindrical Shell ........................................................................................236 Spherical Shell with a Hole ..................................................................................... 239 Uniformly Distributed Load on a Simply-Supported Rectangular Plate ................. 242 Uniformly Distributed Load on a Simply-Supported Rhomboid Plate ................... 247 Shear Loading on a Plate ......................................................................................... 251 Mechanical Structures - Linear Statics Analysis with Solid Elements ........................... 254 Solid Cylinder in Pure Tension ............................................................................... 255 Internal Pressure on a Thick-Walled Spherical Container ...................................... 261 Internal Pressure on a Thick-Walled Infinite Cylinder ...........................................268 Prismatic Rod in Pure Bending ............................................................................... 274 Thick Plate Clamped at Edges ................................................................................. 279 Mechanical Structures - Normal Modes/Eigenvalue Analysis ....................................... 284 Lumped Mass-Spring System ..................................................................................285 Short Beam on Simple Supports .............................................................................. 288 Axial Loading on a Rod .......................................................................................... 291 Cantilever Beam with a Variable Rectangular Section ...........................................294 Thin Circular Ring ...................................................................................................297 Thin Circular Ring Clamped at Two Points ............................................................300 Vibration Modes of a Thin Pipe Elbow ................................................................... 303 Cantilever Beam with Eccentric Lumped Mass ......................................................307 Thin Square Plate (Clamped or Free) ...................................................................... 311 Simply-Supported Rectangular Plate ...................................................................... 314 Thin Ring Plate Clamped on a Hub ......................................................................... 317 Vane of a Compressor - Clamped-free Thin Shell .................................................. 320 Bending of a Symmetric Truss ................................................................................ 323 Hovgaard’s Problem - Pipes with Flexible Elbows ................................................. 326 Rectangular Plates ...................................................................................................328 Stationary Thermal Tests - Steady State Heat Transfer Analysis ................................... 330 Hollow Cylinder - Fixed Temperatures ................................................................... 331 Hollow Cylinder - Convection ................................................................................ 334 Cylindrical Rod - Flux Density ............................................................................... 337 Hollow Cylinder with Two Materials - Convection ................................................340 Wall - Convection .................................................................................................... 344 Wall - Fixed Temperatures ...................................................................................... 347 L-Plate ..................................................................................................................... 350 Hollow Sphere - Fixed Temperatures, Convection ................................................. 353 Hollow Sphere with Two Materials -Convection .................................................... 356 Thermo-mechanical Test - Linear Statics Analysis ........................................................ 360 Thermal Gradient on a Thin Pipe ............................................................................ 361 Index ...............................................................................................................................365 Overview This guide contains verification test cases for the FEMAP Structural solver. These test cases verify the function of the different FEMAP Structural analysis types using theoretical and benchmark solutions from well–known engineering test cases. Each test case contains test case data and information, such as element type and material properties, results, and references. The guide contains test cases for: • Linear Statics verification using theoretical solutions • Linear Statics verification using standard NAFEMS benchmarks • Normal Modes/Eigenvalue verification using theoretical solutions • Normal Modes/Eigenvalue verification using standard NAFEMS benchmarks • Verification Test Cases from the Societe Francaise des Mechaniciens Linear Statics Verification Using Theoretical Solutions The purpose of these linear statics test cases is to verify the function of the FEMAP Structural Statics Analysis software using theoretical solutions. The test cases are relatively simple in form and most of them have closed–form theoretical solutions. The theoretical solutions shown in these examples are from well–known engineering texts. For each test case, a specific reference is cited. All theoretical reference texts are listed at the end of this topic. The finite element method is very flexible in the types of physical problems represented. The verification tests provided are not exhaustive in exploring all possible problems, but represent common types of applications. This overview provides information on the following: • understanding the test case format • understanding comparisons with theoretical solutions • references Understanding the Test Case Format Each test case is structured with the following information: • test case data and information - physical and material properties - finite element modeling (modeling procedure or hints) - units - solution type - element type - boundary conditions (loads, constraints) • results • references (text from which a closed–form or theoretical solution was taken) Note: . The node numbers listed in each case refer to the node numbers in the neutral (.neu) files associated with this guide. If you remesh a model, or rebuild that model from scratch, your node numbering may differ. 3 In addition to these example problems, test cases from NAFEMS (National Agency for Finite Element Methods and Standards, National Engineering Laboratory, Glasgow, U.K.) have been executed. Results for these test cases can be found in the next section, Linear Stat- ics Analysis Verification Using NAFEMS Standard Benchmarks. Understanding Comparisons with Theoretical Solutions While differences in finite element and theoretical results are, in most cases, negligible, some tests would require an infinite number of elements to achieve the exact solution. Ele- ments are chosen to achieve reasonable engineering accuracy with reasonable computing times. Results reported here are results which you can compare to the referenced theoretical solution. Other results available from the analyses are not reported here. Results for both theoretical and finite element solutions are carried out with the same significant digits of accuracy. The closed–form theoretical solution may have restrictions, such as rigid connections, that do not exist in the real world. These limiting restrictions are not necessary for the finite element model, but are used for comparison purposes. Verification to real world problems is more difficult but should be done when possible. The actual results from the FEMAP Structural software may vary insignificantly from the results presented in this document. This variation is due to different methods of performing real numerical arithmetic on different systems. In addition, it is due to changes in element formulations which SDRC has made to improve results under certain circumstances. References The following references have been used in the Linear Statics Analysis verification problems presented: 1. Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill, Inc., 1992.) 2. Harris, C. O., Introduction to Stress Analysis, (1959.) 3. Roark, R. and Young, W., Formulas for Stress and Strain, 5th Edition, (New York: McGraw–Hill Book Company, 1975.) 4. Shigley, J. and Mitchel L., Mechanical Engineering Design, 4th Edition, (New York: McGraw–Hill Book Company, 1983.) 5. Timoshenko, S., Strength of Materials, Part I, Elementary Theory and Problems, (New YorK: Van Norstrand Reinhold Company, 1955.) Nodal Loads on a Cantilever Beam The complete model and results for this test case are in file mstvl001.neu. Determine the deflection of a beam at the free end. Determine the stress at the end of the beam. Test Case Data and Information Element Types bar Units Inch Model Geometry Length=480 in Cross Sectional Properties • Area = 30 x 30 in • I y =I z = 67500 in 4 Material Properties • E = 30 E+06 psi Finite Element Modeling • 5 nodes • 4 successive bar elements along the X axis 5 Boundary Conditions Constraints Constrain the left end (node 1) of the beam in all six degrees. Loads Set nodal force to 50,000 lb. in the negative Y direction. Solution Type Statics Results Reference • Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill, Inc., 1992.) p. 716. Beam End A1 Z Shear Force Stress (Node 1) T2 Translation (Node 5) Bench Value 5333.3 0.91022 FEMAP Structural 5333.3 0.913 Difference 0% 0.30% Axial Distributed Load on a Linear Beam The complete model and results for this test case are in file mstvl002.neu. Determine the stress, elongation, and constraint force due to an axial loading along a linear beam. Test Case Data and Information Element Type bar Units Inch Model Geometry Length = 300 in Cross Sectional Properties • Area = 9 in 2 • square cross section (3 in x 3 in) • I = 6.75 in 4 Material Properties E = 30E+6 psi Finite Element Modeling • 31 nodes 7 • 30 bar elements along the X axis, each 10 inches long. Boundary Conditions Constraints Constrain one end of the beam (node 1) in all translations and rotations. Loads Set the axial distributed load (force per unit length) to 1000lb/in for the 10–inch long element (element 30) furthest from the constrained end. Solution Type Statics 8 Results Reference • Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill, Inc., 1992.) p. 76. Beam End A1 Axial Stress (Node 1) T1 Translation (Node 2) T1 Constraint Force (Node 1) Bench value 1111.1 0.0111111 -10,000 FEMAP Structural 1111.1 0.0109258 -10,000 Difference 0 1.6% 0 Distributed Loads on a Cantilever Beam The complete model and results for this test case are in file mstvl003.neu. Determine the deflection of a beam at the free end. Determine the stress at the midpoint of the beam and the reaction force at the restrained end. Test Case Data and Information Element Type bar Units Inch Model Geometry • Length = 480 in Cross Sectional Properties • Area = 900 in 2 • square cross section (30 in x 30 in) • I y = I z = 67500 in 4 Material Properties E = 30 E+06 psi Finite Element Modeling • 9 nodes 10 • 8 successive bar elements along the X axis Boundary Conditions Constraints Constrain the left end of the beam (node 1) in all translations and rotations. Loads Define a distributed load on the elements of 250 lb/in in the negative Y direction. Solution Type Statics Results Beam End A1Z Bend Stress (node 1) Total Translation (node 5) Total Constraint Force (lb) Bench Value 6,400.0 0.8190 120,000 FEMAP Structural 6,400.0 0.8225* 120,000 Difference 0.0% 0.43% 0 11 * Includes shear deformation which is neglected in theoretical value. Reference • Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill, Inc., 1992.) p. 716. Moment Load on a Cantilever Beam The complete model and results for this test case are in file mstvl004.neu. Determine the deflection of a beam at the free end. Determine the bending stress of the beam and the reaction force at the restrained end. Test Case Data and Information Element Type bar Units Inch Model Geometry Length = 480 in Cross Sectional Properties • Area = 900 in 2 • square cross section (30 in x 30 in) • I y = I z = 67500 in 4 Material Properties E = 30 E+06 psi Finite Element Modeling • 9 nodes 13 • 8 successive bar elements along the X axis. Boundary Conditions Constraints Constrain the left end of the beam (node 1) in all translations and rotations. Loads Set the Z–moment of the end node (node 5) to 2.5e+6 in–lb. Solution Type Statics 14 Results Reference • Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill Inc., 1992.) p. 716. Beam End A1 Z Bend Stress (psi) (node 1) Total Translation (in) (node 5) Total Constraint Moment (lb.) (node 1) Bench Value 555.6 0.1422 2.5E+06 FEMAP Structural 555.6 0.1422 2.5E+06 Difference 0 0 0 Thermal Strain, Displacement, and Stress on Heated Beam The complete model and results for this test case are in file mstvl007.neu. A beam originally 1 meter long and at -50° C is heated to 25° C. Determine the displacement and thermal strain on a cantilever beam. In case 1, fix the beam at the free end. In case 2, fix the beam at both ends. In both cases, determine the displacement, constraint forces, and stresses along the beam. Test Case Data and Information Element Type bar Units SI - meter Model Geometry Length = 1 m Cross Sectional Properties Area = 0.01 m 2 Material Properties • E = 2.068E+11 PA • Coeff. of thermal expansion = 1.2E-05 m/(m-C) • v = 0.3 Finite Element Modeling • 11 nodes 16 • 10 bar elements on the X axis. Boundary Conditions Constraints • Case 1: Constrain the node on one end (node 1) of the beam in all translations and rotations. • Case 2: Constrain the nodes on both ends (nodes 1 and 11) of the beam in all translations and rotations. Loads Set the temperature on all nodes to 25°C. Set the reference temperature to -50°C. Solution Type Statics 17 Results Case: One Fixed End Case: Both Ends Fixed Reference • Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill, Inc., 1992.) p. 65. Total Translation (Node 11) (m) Beam End A1 Axial Strain Bench Value 9E-04 9E-04 FEMAP Structural 9E-04 9E-04 Difference 0 0 Total Translation (m) Total Constraint Force(N) (node 1) Beam End A1 Axial Stress (Pa) Bench Value 0 1.86+06 –1.86E+08 FEMAP Structural 0 1.86+06 –1.86E+08 Difference 0 0 0 Uniformly Distributed Load on Lin- ear Beam The complete model and results for this test case are in file mstvl008.neu. A beam 40 feet long is restrained and loaded with a distributed load of –833 lb. Determine the beam end torque stress and the deflection at the middle of the beam. Test Case Data and Information Element Type bar Units Inch Model Geometry Length = 480 in Cross Sectional Properties • Rectangular cross section (1.17 in x 43.24 in) • I z = 7892 in 4 Material Properties • E = 30E6 psi Finite Element Modeling • 5 nodes 19 • 4 successive bar elements that are each 10 feet long Boundary Conditions Constraints Constrain nodes 2 and 4 in five degrees of freedom. Do not constrain rotation about Z. Loads Define a distributed load (force per unit length) of -833 lb. (global negative Y direction) on the elements 1 and 4. Solution Type Statics 20 Results Reference • Timoshenko, S., Strength of Materials, Part I, Elementary Theory and Problems, (New York: Van Norstrand Reinhold Company, 1955.) p. 98. Total Translation (in) (node 3) Beam End A1 Z Bend Stress (psi) (node 3) Bench Value 0.182 16,439 FEMAP Structural 0.182 16,439 Difference 0 0 Membrane Loads on a Plate The complete model and results for this test case are in file mstvl009.neu. A circle is scribed on an unstressed aluminum plate. Forces acting in the plane of the plate cause normal stresses. Determine the change in the length of diameter AB and of diameter CD. Test Case Data and Information Element Types plate Units Inch Model Geometry • Length = 15 in • Diameter = 9 in • Thickness = 3/4 in Material Properties • E = 10 E+06 psi • Poisson’s ratio = 1/3 • F(x)/l = 9,000 lb./in • F(z)/l = 15,000 lb./in 22 Finite Element Modeling Create 1/4 of the model and apply symmetry boundary conditions. Then multiply the answer by 2 for correct results. Remember to account for the ratio of the circle diameter to plate length. Boundary Conditions Constraints Constrain nodes along adjacent sides of the plate to allow only translation along the corresponding axis. • Node 1: Fully constrain in all translations and rotation. • Nodes 2-6: Constrain in the Y and Z translations and the X and Z rotations. • Nodes 12, 13, 19, 25, 31: Constrain in the X and Y translations and the X and Z rotations. Loads Set the elemental edge load to 9,000 lb./in in the X direction and 15,000 lb/in in the Z direction. 23 Solution Type Statics Results Post Processing • (T1 translation at node 7 - T1 translation at node 10) x2 = (.004-.0016) x2 = .0048 • (T3 translation at node 7 - T3 translation at node 24) x2 = (.012-.0048) x2 = .0144 Reference • Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill, Inc., 1992.) p. 85. T1 Translation (in) T3 Translation (in) Bench Value 4.8E-03 14.4E-03 FEMAP Structural 4.8E-03 14.4E-03 Difference 0 0 Thin Wall Cylinder in Pure Tension The complete model and results for this test care are in file mstvl014.neu. Determine the stress and deflection of a thin wall cylinder with a uniform axial load. Test Case Data and Information Element Type linear quadrilateral plate Units Inch Model Geometry • R = 0.5 in • Thickness = 0.01 in • y = 1.0 in Material Properties • E = 10000 psi • v = 0.3 Finite Element Modeling • 25 nodes • Create 1/4 model of the cylinder with 16 linear quadrilateral plate elements and symmetry boundary conditions. 25 Boundary Conditions Constraints • Constrain node 1 in the X and Z translation and the Z rotation. • Constrain nodes 2-4 in the Z translation. • Constrain node 5 in the Y and Z translation and Z rotation. • Constrain nodes 6, 11, 16, and 21 in the X translation and Z rotation. • Constrain nodes 10, 15, 20, and 25 in the Y translation and Z rotation. Loads • Nodal forces of p/(pi)D = 3.1831 where p = 10 psi; Apply the following nodal forces: • Nodes 21, 25: .9757 pounds • Nodes 22, 23, 24: 1.9509 pounds Solution Type Statics Results Top Y Normal Stress (psi) T3 Translation (in) T1 Translation (in) Bench Value 1000.0 0.1 -0.015 FEMAP Structural 1000.0 0.1 -0.015 Difference 0 0 0 26 Reference • Roark, R. and Young, W., Formulas for Stress and Strain, 6th Edition, (New York: McGraw–Hill Book Company, 1989.) p. 518, Case 1a. Thin Shell Beam Wall in Pure Bend- ing The complete model and results for this test case are in file mstvl015.neu. Determine the maximum stress, maximum deflection, and strain energy of a thin shell beam wall with a uniform bending load. Test Case Data and Information Element Type linear quadrilateral plate Units Inch Model Geometry • Length = 30 in • Width = 5 in • Thickness = 0.1 in Material Properties • E = 30E6 psi • v = 0.03 Finite Element Modeling • 14 nodes 28 • 6 linear quadrilateral plate elements Boundary Conditions Constraints Constrain the nodes at one end (nodes 7 and 14) in all translations and rotations. Out–of–plane Loads Apply nodal forces (nodes 1 and 8) of p/w = 1.2 lbs/in. where p = 6.0 lb Solution Type Statics 29 Results Reference • Shigley, J. and Mitchel L., Mechanical Engineering Design, 4th Edition, (New York: McGraw–Hill, Inc., 1983.) pp. 134, 804. T3 Translation (in) Node 1 Plate Bottom Major Stress (psi) Node 7 Total Strain Energy (lb in) Bench Value 4.320 21600 12.96 FEMAP Structural 4.242 20983 12.73 Difference 2.17% 1.39% 2.16% Strain Energy of a Truss The complete model and results for this test case are in file mstvl016.neu. Determine the strain energy of a truss. The cross–sectional area of the diagonal members is twice the cross–sectional area of the horizontal and vertical members. Test Case Data and Information Element Type rod Units Inch Model Geometry • Length = 10 in Cross Sectional Properties Cross sectional area (A) = 0.01 in 2 Material Properties E = 30E6 psi Finite Element Modeling • 4 nodes • 5 rod elements 31 Boundary Conditions Constraints • Constrain node 1 in the X, Y, and Z translations and the X and Y rotations. • Constrain node 3 in the Y and Z translations and the X and Y rotations. Loads • Apply nodal force in Y direction on node 2; p = 300 lb Solution Type Statics Results Reference • Beer and Johnston, Mechanics of Materials, (New York: McGraw–Hill, Inc., 1992.) p. 588. Total Strain Energy (lb in) Bench Value 5.846 FEMAP Structural 5.846 Difference 0 Linear Statics Verification Using Standard NAFEMS Benchmarks The purpose of these linear statics test cases is to verify the function of the FEMAP Structural Statics Analysis software using standard benchmarks published by NAFEMS (National Agency for Finite Element Methods and Standards, National Engineering Laboratory, Glas- gow, U.K.). These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elements in commercial software. All results obtained using the FEMAP Structural Statics Analysis software compare favorably with other commercial finite element analysis software. Results of these test cases using other commercial finite element analysis software programs are available from NAFEMS. A detailed discussion of the linear statics NAFEMS benchmarks can be found in the NAFEMS publication Background to Benchmarks, cited below. The results for all of these test cases illustrate the need for adequate mesh refinement for obtaining accurate stresses, especially when using linear elements. The linear triangular and linear tetrahedral elements are particularly poor performers for stress analysis and are not generally recommended. Understanding the Test Case Format Each test case is structured with the following information: • test case data and information - physical and material properties - finite element modeling (modeling procedure or hints) - units - finite element modeling information - boundary conditions (loads and constraints) - solution type • results • reference References The following references have been used in these test cases: Note: The node numbers listed in each case refer to the node numbers in the neutral (.neu) files associated with this guide. If you remesh a model, or rebuild that model from scratch, your node numbering may differ. 33 • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993). Elliptic Membrane The complete model and results for this test case are in the following files: • le101.neu (quadrilateral plane strain) • le102.neu (triangular plane strain) • le103.neu (quadrilateral plate) This test is a linear elastic analysis of an elliptic membrane (shown below) using coarse and fine meshes of plane strain elements and plate elements. The plane strain elements use a plane stress element formulation. It provides the input data and results for NAFEMS Standard Benchmark Test LE1. Ellipses: Test Case Data and Information Physical and Material Properties • Thickness = 0.1 m • Isotropic material • E = 210 x 10 3 MPa A B C D X Y Ellipse AC: x 2 ---     2 y 2 + 1 = Ellipse BD: x 3.25 ----------     2 y 2.75 ----------     2 + 1 = 35 • v = 0.3 Units SI Finite Element Modeling • plane strain (with plane stress element formulation) - linear and parabolic quadrilaterals - coarse and fine mesh • plane strain (with plane stress element formulation) - linear and parabolic triangles - coarse and fine mesh • plate - linear and parabolic quadrilaterals - coarse and fine mesh 36 The fine mesh is created by approximately halving the coarse mesh. Boundary Conditions Constraints • Constrain the nodes along edge AB in the X translation. • Constrain the nodes along edge CD in the Y translation. Linear Triangle Parabolic Triangle Fine Mesh Coarse Mesh Linear Quadrilateral Parabolic Quadrilateral Fine Mesh Coarse Mesh A B C D A B C D A B C D A B C D A B C D A B C D A B C D A B C D 37 Loads • Uniform outward pressure on the elements on outer edge BD = 10MPa • Inner curved edge AC is unloaded Solution Type Statics Results Output - Plate Mid Y Normal Stress at point D Node # Element Type & Mesh NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) Plane Strain Elements with a Plane Strain Formulation (le101): Node 4 linear quad - coarse mesh 92.7 62.8 Node 204 linear quad - fine mesh 92.7 80.3 Node 104 parabolic quad - coarse mesh 92.7 88.3 Node 304 parabolic quad - fine mesh 92.7 90.7 Plane Strain Elements with a Plane Strain Formulation (le102): Node 4 linear triangle - coarse mesh 92.7 54.2 Node 204 linear triangle - fine mesh 92.7 72.0 Node 104 parabolic triangle - coarse mesh 92.7 93.0 Node 304 parabolic triangle – fine mesh 92.7 94.0 38 References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE1. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993). Plate Elements (le 103): Node 4 linear quad - coarse mesh 92.7 66.4 Node 204 linear quad - fine mesh 92.7 82.3 Node 104 parabolic quad - coarse mesh 92.7 88.6 Node 304 parabolic quad - fine mesh 92.7 91.7 Cylindrical Shell Patch Test The complete model and results for this test case are in the following files: • le201a.neu (linear plate, case 1) • le201b.neu (parabolic plate, case 1) • le202a.neu (linear plate, case 2) • le202b.neu (parabolic plate, case 2) This test is a linear elastic analysis of a cylindrical shell (shown below) using plate elements and two different loadings. It provides the input data and results for NAFEMS Standard Benchmark Test LE2. Test Case Data and Information Physical and Material Properties • Thickness = 0.01 m • Isotropic material • E = 210 x 10 3 MPa • v = 0.3 Units SI Finite Element Modeling • le201a and le202a: 9 nodes, 4 linear quadrilateral plates • le201b and le202b: 21 nodes, 4 parabolic quadrilateral plates Linear Quadrilaterals Parabolic Quadrilaterals A B E D C A B E D C 40 Boundary Conditions Constraints Fully constrain the nodes on edge AB in all translations and rotations. Constrain the nodes on edge AD and edge BC in the Z translation and X and Y rotations. Case 1 Loading: • Nodal moments along DC = 1.0 kNm/m: Node 3 = -125 Node 4 = -250 Node 9 = -125 Case 2 Loading: • Nodal forces: Nodes 3, and 9 = 75,000N Node 4 = 150,000N 41 • Apply an elemental pressure on elements 1-4 = 600,000Pa Solution Type Statics Results Output - Plate Top Major Stress at point E (node 2) *Since the shapes of the plates are an approximation to a cylindrical surface, an edge load will not be in the correct direction. To get this result, the edge load must be input as nodal loads in the tangential direction. References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE2. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993). Plate Element & Loading NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) linear plate - case 1 (le201a) 60.0 57.9 linear plate - case 2 (le202a) 60.0 66.0 * parabolic plate - case 1 (le201b) 60.0 54.8 parabolic plate - case 2 (le202b) 60.0 55.7 * Laminate Strip The complete model and results for this test case are in the following file: • r0031.neu This test is a linear statics analysis of plate using plate elements with a laminate material. It provides the input data and results for NAFEMS Report R0031. Test Case Data and Information Geometry Material Properties Laminate material: 0° fiber direction 10 15 15 10 X Y X Z 1 E 10N/mm A B 0° 90° 0° 90° 0° 90° 0° 0.1 0.1 0.1 0.4 0.1 0.1 0.1 C E D F E 1.0E5 MPa = ν 12 0.4 = E 2 5.0E3 MPa = ν 12 E 1 -------- ν 21 E 2 -------- = G 12 3.0E3 MPa = ν 23 0.3 = G 33 2.0E3 MPa = 43 Units SI Finite Element Modeling 8 x 40 4-noded shells (quarter model) Boundary Conditions Constraints The one quarter model is: • simply supported at A (Z=0) • reflective symmetry about X=25 and Y=5 Loads Line load of 10N/mm at C (X=25, Z=1). Solution Type Statics Results *Value extrapolated from FEMAP Structural results at F. (FEMAP Structural calculates stress at the center of the ply (F)). **Recovered from post-processing. Reference • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. R0031. Results NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) Z deflection at E -1.06 -1.06 Bending stress at E 683.9 *668 Bending stress at F - 601 Interlaminar shear stress at D -4.1 **-4.1 Shear stress at F - -2.2 Hemisphere-Point Loads The complete model and results for this test care are in the following files: • le301.neu (linear quadrilateral plate, coarse mesh) • le302.neu (linear quadrilateral plate, fine mesh) • le303.neu (parabolic quadrilateral plate, coarse mesh) • le304.neu (parabolic quadrilateral plate, fine mesh) This test is a linear elastic analysis of hemisphere point loads (shown below) using coarse and fine meshes of plate elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE3. Test Case Data and Information Physical and Material Properties • Thickness = 0.04 m • Isotropic material • E = 68.25 x 10 3 MPa • v = 0.3 Units SI Finite Element Modeling plate - linear & parabolic quadrilaterals - coarse & fine mesh equally spaced nodes on AC, CE, EA Point G at X = Y = Z = 10 3 1 2 --- ------         Node 7 45 Boundary Conditions Constraints • Fully constrain point E in all translations and rotations. • Constrain the nodes along edge AE (symmetry about X–Z plane) in the Y translation, and X and Z rotations. • Constrain the nodes along edge CE (symmetry about Y–Z plane) in the X translation, and Y and Z rotations. Loads • Concentrated radial load outward at A = 2KN Coarse Mesh Fine Mesh A C E A C E F G D B F G D B 46 • Concentrated radial load inward at C = 2KN Solution Type Statics Results References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE3. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993). Test Case Number Plate Element & Mesh NAFEMS Bench Value(m) FEMAP Structural Result at node 1 (point A) T1 Translation (m) le301 linear quadrilateral plate - coarse mesh 0.185 0.113 le302 linear quadrilateral plate - fine mesh 0.185 0.185 le303 parabolic quadrilateral plate - coarse mesh 0.185 0.0861 le304 parabolic quadrilateral plate - fine mesh 0.185 0.171 Z–Section Cantilever The complete model and results for this test case are in the following files: • le501.neu (linear quadrilateral plate) • le502.neu (parabolic quadrilateral plate) This test is a linear elastic analysis of a Z–section cantilever (shown below) using plate elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE5. Test Case Data and Information Physical and Material Properties • Thickness = 0.1 m • Isotropic material • E = 210 x 10 3 MPa • v = 0.3 Units SI Finite Element Modeling • Test 1: 36 nodes, 24 linear quadrilateral plate elements • Test 2: 95 nodes, 24 parabolic quadrilateral plate elements Boundary Conditions Constraints • Fully constrain the nodes on edges B1, B2, B3 in all translations and rotations. 48 Loads • Torque of 1.2MN applied at end C by two nodal forces (at nodes 9 and 27) of 0.6MN Solution Type Statics Results Output - Plate Top Von Mises Stress (σ xx ), point A, node 30 (compression) References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE5. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993). Plate Element & Loading NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) linear quad - point A/node 30 -108 -117.3 parabolic quad - point A/node 30 -108 -109.2 B1 B2 B3 C Skew Plate Normal Pressure The complete model and results for this test case are in the following files: • le601.neu (linear and parabolic quadrilateral) • le602.neu (linear and parabolic triangle) This test is a linear elastic analysis of a plate (shown below) using plate elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE6. Test Case Data and Information Physical and Material Properties • Thickness = 0.01m • Isotropic material • E = 210 x 10 3 MPa • v = 0.3 Units SI A B C D E 150 o 30 o 10m 50 Finite Element Modeling • plate - linear and parabolic quadrilaterals - coarse and fine mesh • plate - linear and parabolic triangles - coarse and fine mesh Boundary Conditions Constraints (le601) • Constrain nodes 1, 10, 35, and 44 in the X, Y, and Z translations. • Constrain nodes 4, 13, 38, 47 in the X and Z translations. 51 • Constrain all other nodes in the Z translation. Constraints (le602) • Fully constrain nodes 1, 10, 35, 44 in all directions and rotations. • Constrain all other nodes in the Z translation. Loads • Elemental pressure = -0.7KPa in the Z–direction 52 Solution Type Statics Results Output - Plate Bottom Major Stress on the bottom surface at the plate center. References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE6. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993). Test Case Name Node # Plate Element & Mesh NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) le601 Node 9 linear quad - coarse mesh 0.802 0.365 le601 Node 18 linear quad - fine mesh 0.802 0.714 le601 Node 43 parabolic quad - coarse mesh 0.802 1.055 le601 Node 52 parabolic quad - fine mesh 0.802 0.791 le602 Node 9 linear triangle - coarse mesh 0.802 0.390 le602 Node 18 linear triangle - fine mesh 0.802 0.709 le602 Node 43 parabolic triangle - coarse mesh 0.802 0.847 le602 Node 52 parabolic triangle - fine mesh 0.802 0.822 Thick Plate Pressure The complete model and results for this test case are in the following files: • le1001.neu (linear and parabolic brick) • le1002.neu (linear and parabolic wedge) • le1003.neu (linear and parabolic tetrahedron) This article provides the input data and results for NAFEMS Standard Benchmark Test LE10. This test is a linear elastic analysis of a thick (shown below) using coarse and fine meshes of solid elements. Ellipses: Test Case Data and Information Physical and Material Properties • Isotropic material • E=210x10 3 MPa • v = 0.3 A B C D A B C D A’ B’ C’ D’ Ellipse AD: x 2 ---     2 y 2 + 1 = Ellipse BC: x 3.25 ----------     2 y 2.75 ----------     2 + 1 = 54 Units SI Finite Element Modeling • Solid brick • Solid wedge • Solid tetrahedron Solid Brick Linear and parabolic, coarse and fine mesh. Solid Wedge Linear and parabolic, coarse and fine mesh. 55 Solid Tetrahdron Linear and parabolic, fine mesh. 56 Boundary Conditions Constraints • Constrain the nodes on faces DCD’C’ and ABA’B’ in the X and Y translations. • Constrain the nodes on face BCB’C’ in the X and Y translation. • Constrain the nodes along the mid–plane in the Z translation. Loads • Uniform normal elemental pressure on the elements on the upper surface of the plate = 1MPa • Inner curved edge AD unloaded Solution Type Statics 57 Results Output - Solid Y normal stress at point D 3 σ yy References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE10. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993) Test Case Name Node # Element Type & Mesh NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) le1001 N4 linear brick - coarse mesh -5.38 -6.31 le1001 N204 linear brick - fine mesh -5.38 -6.01 le1001 N104 parabolic brick - coarse mesh -5.38 -5.73 le1001 N304 parabolic brick - fine mesh -5.38 -5.84 le1002 N4 linear wedge - coarse mesh -5.38 -3.52 le1002 N204 linear wedge - fine mesh -5.38 -4.97 le1002 N104 parab wedge - coarse mesh -5.38 -5.53 le1002 N304 parab wedge - fine mesh -5.38 -6.10 le1003 N40 linear tetra - fine mesh -5.38 -2.41 le1003 N171 parabolic tetra - fine mesh -5.38 -5.29 Solid Cylinder/Taper/Sphere–Tem- perature The complete model and results for this test case are in the following files: • le1101a.neu (linear brick, coarse mesh) • le1101b.neu (linear brick, fine mesh) • le1102a.neu (parabolic brick, coarse mesh) • le1102b.neu (parabolic brick, fine mesh) • le1103a.neu (linear wedge, coarse mesh) • le1103b.neu (linear wedge, fine mesh) • le1104a.neu (parabolic wedge, coarse mesh) • le1104b.neu (parabolic wedge, fine mesh) • le1105a.neu (linear tetrahedron, coarse mesh) • le1105b.neu (linear tetrahedron, fine mesh) • le1106a.neu (parabolic tetrahedron, coarse mesh) • le1106b.neu (parabolic tetrahedron, fine mesh) This test is a linear elastic analysis of a solid cylinder with a temperature gradient (shown below) using coarse and fine meshes of solid elements. It provides the input data and results for NAFEMS Standard Benchmark Test LE11. Test Case Data and Information Physical and Material Properties • Isotropic material • E = 210 x 10 3 MPa • v = 0.3 • a = 2.3 x 10 -4 / o C Units SI 59 Finite Element Modeling • Solid brick - linear (8–noded) and parabolic (20–noded) - coarse and fine mesh • Solid tetrahedron - linear (4–noded) and parabolic (10–noded) - coarse and fine mesh • Solid wedge - linear (6–nodes) and parabolic (15–noded) - coarse and fine mesh Solid Brick Coarse and fine mesh: Coarse and fine mesh: Boundary Conditions Constraints • Constrain the nodes on the XZ plane and on the opposite face in the Y translation. • Constrain the nodes on the YZ plane in the Z translation. • Constrain the nodes on the XY plane in the X translation. 60 Loads • Nodal temperatures: linear temperature gradient in the radial and axial direction T°C X 2 Y 2 + ( ) 1 2 --- Z + = 61 Solution Type Statics Results Output - Solid Y Normal Stress at point A. Note that the Y direction in the models corresponds to the Z direction in NAFEMS. References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE11. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glas- gow: NAFEMS, 1993). Case Node # at Point A Element Type & Mesh NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) le1101a 30 linear brick - coarse mesh -105 -95.7 le1101b 71 linear brick - fine mesh -105 -99.5 le1102a 67 parabolic brick - coarse mesh -105 -93.9 le1102b 159 parabolic brick - fine mesh -105 -105.9 le1103a 33 linear wedge - coarse mesh -105 -9.49 le1103b 74 linear wedge - fine mesh -105 -46.9 le1104a 71 parabolic wedge - coarse mesh -105 -88.5 le1104b 187 parabolic wedge - fine mesh -105 -96.8 le1105a 8 linear tetra - coarse mesh -105 -31.4 le1105b 8 linear tetra - fine mesh -105 -65.2 le1106a 8 parabolic tetra - coarse mesh -105 -89.6 le1106b 8 parabolic tetra - fine mesh -105 -97.2 62 Normal Modes/Eigenvalue Verifica- tion Using Theoretical Solutions The purpose of these normal mode dynamics test cases is to verify the function of the FEMAP Structural Normal Modes/Eigenvalue Analysis software using theoretical solutions. The test cases are relatively simple in form and most of them have closed–form theoretical solutions. The theoretical solutions shown in these examples are from well known engineering texts. For each test case, a specific reference is cited. All theoretical reference texts are listed at the end of this topic. The finite element method is very flexible in the types of physical problems represented. The verification tests provided are not exhaustive in exploring all possible problems, but represent common types of applications. This overview provides information on the following: • understanding the test case format • understanding comparisons with theoretical solutions • references Understanding the Test Case Format Each test case is structured with the following information: • test case data and information - physical and material properties - finite element modeling (modeling procedure or hints) - units - solution type - element type - boundary conditions (loads and constraints) • results • references (text from which a closed–form or theoretical solution was taken) Note: The node numbers listed in each case refer to the node numbers in the neutral (.neu) files associated with this guide. If you remesh a model, or rebuild that model from scratch, your node numbering may differ. 64 Understanding Comparisons with Theoretical Solutions While differences in finite element and theoretical results are, in most cases, negligible, some tests would require an infinite number of elements to achieve the exact solution. Ele- ments are chosen to achieve reasonable engineering accuracy with reasonable computing times. Results reported here are results which you can compare to the referenced theoretical solution. Other results available from the analyses are not reported here. Results for both theoretical and finite element solutions are carried out with the same significant digits of accuracy. The closed–form theoretical solution may have restrictions, such as rigid connections, that do not exist in the real world. These limiting restrictions are not necessary for the finite element model, but are used for comparison purposes. Verification to real world problems is more difficult but should be done when possible. The actual results from the FEMAP Structural software may vary insignificantly from the results presented in this document. This variation is due to different methods of performing real numerical arithmetic on different systems. In addition, it is due to changes in element formulations which SDRC has made to improve results under certain circumstances. References The following references have been used in the Normal Mode Dynamics Analysis verification problems presented: • Blevins, R., Formulas For Natural Frequency and Mode Shape, 1st Edition, (New York: Van Norstrand Reinhold Company, 1979.) • Timoshenko and Young, Vibration Problems in Engineering, (New York: Van Norstrand Reinhold Company, 1955.) • Tse, F., Morse, I., and Hinkle, R., Mechanical Vibrations, Theory and Applications, (Boston: Allyn and Bacon, Inc., 1978.) • Tse, F., Morse, I., and Hinkle, R., Mechanical Vibrations, 2nd Edition, (Boston: Allyn and Bacon, Inc., 1978.) Undamped Free Vibration - Single Degree of Freedom The complete model and results for this test case are in file mstvn002.neu. Determine the natural frequency of the system. Test Case Data and Information Element Types • rigid • mass • DOF springs Units SI - meter Model Geometry • Length = 0.5 m • a = 0.3 m Physical Properties • mass = 20 Kg • k = 8 KN/m Finite Element Modeling • Create 5 rigid elements along the X axis. Each rigid should be 0.1m long. • Create a mass element on the end node. 66 • Create 3 DOF spring elements 0.2m from the mass element. Boundary Conditions Constraints Constrain node 6 in all directions except the Z rotation. Constrain all other nodes in the X and Y translations and in the Z rotation. Solution Type Normal Modes/Eigenvalue – Guyan method Results Frequency (Hz) Bench Value 1.90985 FEMAP Structural 1.90986 Difference 0.0% 67 Reference • Tse, F., Morse, I., and Hinkle, R., Mechanical Vibrations, Theory and Applications, (Boston: Allyn and Bacon, Inc., 1978.) p. 75. Two Degrees of Freedom Undamped Free Vibration - Princi- ple Modes The complete model and results for this test case are in file mstvn003.neu. Determine the natural frequencies of a dynamic system with two degrees of freedom. Test Case Data and Information Element Types • DOF springs • mass Units SI- meter Physical Properties • mass = 1 kg • k = 1 N/m Finite Element Modeling • Create four nodes on the Y axis. • Create DOF three springs with stiffness of 1 N/m and with a stiffness reference coordinate system being uniaxial. 69 • Create mass elements with a mass of 1 kg. Boundary Conditions Constraints • Constraint Set 1: Constrain nodes 1 and 4 in all DOF. On the other nodes, constrain all DOF except the Y translation. • Constraint Set 2: On the inner nodes, constrain the Y translation. Use this set as the Mas- ter (ASET) DOF set. Solution Type Normal Modes/Eigenvalue – Guyan method 70 Results Reference • Tse, F., Morse, I., and Hinkle, R., Mechanical Vibrations, 2nd Edition, (Boston: Allyn and Bacon, Inc., 1978.) pp. 145-149. Frequency of Mode 1 (Hz) Frequency of Mode 2 (Hz) Bench Value 0.159155 0.2756644 FEMAP Structural 0.159155 0.2756644 Difference 0.00% 0.00% Three Degrees of Freedom Tor- sional System The complete model and results for this test case are in file mstvn004.neu. Determine the natural frequencies of a dynamic system with three degrees of freedom. Test Case Data and Information Element Types • DOF springs • mass Units SI - meter Physical Properties • J = J1 = J2 = J3 = 0.1 (mass) • k = k1 = k2 = k3 = 1 N*m (stiffness) Finite Element Modeling • Create four nodes on the X axis. • Create three DOF springs with stiffness of 1 N*m and with a stiffness reference coordinate system being uniaxial. • Create three mass elements with a mass coordinate system = 1 and with mass inertia system of: 0.1, 0.0, 0.0, 0.0, 0.0, 0.0. 72 Boundary Conditions Constraints • Constraint Set 1: On one end node (node 1), constrain all DOF. On the other nodes, constrain all DOF except RX. • Constraint Set 2: On the other nodes (nodes 2-4), constrain the DOF in RX. Use this set as the Master (ASET) DOF set. Solution Type Normal Modes/Eigenvalue – Guyan method Results Reference • Tse, F., Morse, I., and Hinkle, R., Mechanical Vibrations, 2nd Edition, (Boston: Allyn and Bacon, Inc., 1978.) pp. 153–155 Frequency of Mode 1 (Hz) Frequency of Mode 2 (Hz) Frequency of Mode 3 (Hz) Bench Value 0.223986 0.627595 0.906901 FEMAP Structural 0.223986 0.627595 0.906901 Difference 0.00% 0.00% 0.00% Two Degrees of Freedom Vehicle Suspension System The complete model and results for this test case are in file mstvn005.neu. Determine the natural frequencies of dynamic system with two degrees of freedom. Degrees of freedom are one translational and one rotational. Test Case Data and Information Element Types 5 nodes, 4 elements: • 2 DOF springs • 1 mass element • 1 rigid element Units SI - meter Model Geometry • Length1 = 1.6 m • Length2 = 2.0 m • r = 1.4 m (radius of gyration; J=m*r*r) Physical Properties • mass = 1800 kg • K1 = 42000 N/m • K2 = 48000 N/m Finite Element Modeling • Create five nodes in the X–Y plane with coordinates: N1 = (0, 0) N2 = (L2, 0) N3 = (-L1, 0) 74 N4 = (L2, -1) N5 = (-L1, -1) • Create a DOF spring with stiffness of k1 between nodes 3 and 5. • Create a DOF spring with stiffness of k2 between nodes 2 and 4. • Create a mass element with a mass coordinate system = 1 and with mass inertia system of: 0.0, 0.0, 3528, 0.0, 0.0, 0.0. • Create a three–noded rigid element using node 1 as the master node and nodes 2 and 3 as the slave nodes. Boundary Conditions Constraints • Constraint Set 1: Constrain nodes 1-3 in the X and Z translation and X and Y rotations. Constrain nodes 4-5 in the X, Y, and Z translations. • Constraint Set 2 (Master (ASET) DOF Set): Constrain nodes 1-3 in the Y translation and Z rotation. 75 Solution Type Normal Modes/Eigenvalue – Guyan method Results Reference • Tse, F., Morse, I., and Hinkle, R., Mechanical Vibrations, 2nd Edition, (Boston: Allyn and Bacon, Inc., 1978.) pp. 150-153. Frequency of Mode 1 (Hz) Frequency of Mode 2 (Hz) Bench Value 1.086347 1.495612 FEMAP Structural 1.086347 1.495612 Difference 0.00% 0.00% Cantilever Beam Undamped Free Vibrations The complete model and results for this test case are in file mstvn006.neu. Determine the natural frequencies of a cantilever beam. Test Case Data and Information Element Type bar Units Inch Model Geometry • Length = 100 in • Height = 2 in Physical and Material Properties • w = 1 lb/in • J = .10 • Poisson’s ratio = .3 Calculated Data • A = h 2 = 4 in 2 • I = h 4 /12 = 1.33333 • G = E/2 x 1/1+nu = 11538461.54 • m = w/g = 2.59067375E-3 • Ip = Ixx + Iyy = 2.66666 Finite Element Modeling • Create 11 nodes on X axis. 77 • Create 10 bars between the nodes. Boundary Conditions Constraints • Fully constrain one end node (node 1) in all directions and rotations. Solution Type Normal Modes/Eigenvalue – SVI method Results Reference • Blevins, R., Formulas For Natural Frequency and Mode Shape, 1st Edition, (New York: Van Norstrand Reinhold Company, 1979) pp. 108,193. Mode Bench Values (Hz) FEMAP Structural (Hz) Difference 1 & 2 6.9533571 6.951037 -0.033% 3 & 4 43.575945 43.54267 -0.076% 5 64.684410 64.66795 -0.254% 6 & 7 122.01391 121.8567 -0.128% 8 193.85388 195.6024 0.901% 9 & 10 238.75784 238.6964 -0.026% Natural Frequency of a Cantilevered Mass The complete model and results for this test case are in file mstvn007.neu. Determine the natural frequencies of a dynamic system consisting of a massless bar element and a mass element at the end. Test Case Data and Information Element Types • bar • mass Units Inch Model Geometry • Length = 30 in Physical and Material Properties • Mass = 0.5 lbm • E = 30E6 psi • Density = 1.0E-06 • I = 1.5 in 4 Finite Element Modeling • Create 2 nodes on the X axis with coordinates (0,0,0) and (30,0,0). • Create a bar between nodes with shear area ratio=0. 79 • Create a mass on one node with mass of 0.5 lbm. Boundary Conditions Constraints • −Constraint Set 1: On the wall end (at node 1), constrain all DOF. On the mass end, constrain the DOF in Z, RX, and RY. • Constraint Set 2: On the mass end node, constrain the DOF in Z, Y, and RZ. Use this set as the Master (ASET) DOF set. Solution Type Normal Modes/Eigenvalue – Guyan method Results Natural Frequency (Hz) Bench Value 15.9155 FEMAP Structural 15.9154 Difference 0.00% 80 Reference • Tse, F., Morse, I., and Hinkle, R., Mechanical Vibrations, 2nd Edition, (Boston: Allyn and Bacon, Inc., 1978.) p. 72 Normal Modes/Eigenvalue Verifica- tion Using Standard NAFEMS Benchmarks The purpose of these normal mode dynamics test cases is to verify the function of the FEMAP Structural Normal Modes/Eigenvalue solver using standard benchmarks published by NAFEMS (National Agency for Finite Element Methods and Standards, National Engineer- ing Laboratory, Glasgow, U.K.). These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elements in commercial software. All results obtained using the FEMAP Structural software compare favorably with other commercial finite element analysis software. Results of these test cases using other commercial finite element analysis software programs are available from NAFEMS. Understanding the Test Case Format Each test case is structured with the following information: • test case data and information - units - material properties - finite element modeling information - boundary conditions (loads and constraints) - solution type • results • reference Reference The following reference has been used in these test cases: • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Note: The node numbers listed in each case refer to the node numbers in the neutral (.neu) files associated with this guide. If you remesh a model, or rebuild that model from scratch, your node numbering may differ. Bar Element Test Cases The normal mode dynamics test cases using the standard NAFEMS benchmarks include these bar element test cases: • "Pin-ended Cross - In-plane Vibration" • "Pin-ended Double Cross - In-plane Vibration" • "Free Square Frame - In-plane Vibration" • "Cantilever with Off-Center Point Masses" • "Deep Simply-Supported Beam" • "Circular Ring - In-plane and Out-of-plane Vibration" • "Cantilevered Beam" Pin-ended Cross - In-plane Vibra- tion The complete model and results for this test case are in file nf001ac.neu. This test is a normal modes/eigenvalue analysis of a pin–ended cross (shown below) using bar elements. This document provides the input data and results for NAFEMS Selected Bench- marks for Natural Frequency Analysis, Test 1. Attributes of this test are: • coupling between flexural and extensional behavior • repeated and close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Key–in section: • Area = .015625 m 2 Shear ratio: A B C D 5.0 m .125 m .125 m 84 • Y = 0 • Z = 0 Material Properties Finite Element Modeling • 17 nodes • 16 bar elements; four elements per arm Boundary Conditions Constraints • Constrain points A, B, C, D (nodes 2, 3, 4, 5) in all directions except for the Z rotation. • Constrain node point Z (node 1) in the Z translation and X rotation. E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = η 0.29 Poissons ratio ( ) = G 8.01x10 10 = 85 • Constrain all other nodes (6-17) in the Z translation and X and Y rotations. Solution Type Normal Modes/Eigenvalue – SVI method Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 1. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural (Hz) 1 11.336 linear 11.336 11.336 2, 3 17.709 linear 17.687 17.687 4 17.709 linear 17.715 17.715 5 45.345 linear 45.477 45.477 6, 7 57.390 linear 57.364 57.364 8 57.390 linear 57.683 57.683 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Pin-ended Double Cross - In-plane Vibration The complete model and results for this test case are in file nf002ac.neu. This test is a normal modes/eigenvalue analysis of a pin–ended double cross (shown below) using bar elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 2. Attributes of this test are: • coupling between flexural and extensional behavior • repeated and close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Key–in section: • Area = .015625 m 2 Shear ratio: A B C D E F G H 5.0 m 5.0m .125 m .125 m 87 • Y = 0 • Z = 0 Material Properties Finite Element Modeling • 33 nodes • 32 bar elements; four elements per arm Boundary Conditions Constraints • Constrain points A, B, C, D, E, F, G, H (nodes 2-9) in all directions except for the Z rotation. • Constrain all other nodes 1, (10-33) in the Z translation and X and Y rotations. E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = 88 The following figure shows the boundary conditions. Solution Type Normal Modes/Eigenvalue – SVI method Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 2. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (Hz) 1 11.336 linear 11.336 11.336 2, 3 17.709 linear 17.687 17.687 4,5, 6,7,8 17.709 linear 17.715 17.715 9 45.345 linear 45.477 45.477 10, 11 57.390 linear 57.364 57.364 12,13, 14,15, 16 57.390 linear 57.683 57.683 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Free Square Frame - In-plane Vibra- tion The complete model and results for this test are in file nf003ac.neu. This test is a normal modes/eigenvalue analysis of a free square frame (shown below) using bar elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 3. Attributes of this test are: • coupling between flexural and extensional behavior • rigid body modes (3 modes) • repeated and close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear ratio: • Y = 1.0 • Z = 1.0 10.0 m 10.0m .125 m .125 m 90 Material Properties Finite Element Modeling • 16 nodes • 16 bar elements; four elements per arm Boundary Conditions Constraints • Constraint Set 1: Constrain all nodes in the Z translation and X and Y rotations. E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = 91 • Constraint Set 2 (Kinematic DOF): Constrain nodes 1 and 3 in the X and Y translation and the Z rotation. Solution Type Normal Modes/Eigenvalue – SVI method Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 3. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural (Hz) 4 3.261 linear 3.262 3.259 5 5.668 linear 5.665 5.662 6, 7 11.136 linear 11.145 11.127 8 12.849 linear 12.833 12.793 9 24.570 linear 24.664 24.611 10, 11 28.695 linear 28.813 28.700 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilever with Off-Center Point Masses The complete model and results for this test is in file nf004a.neu. This test is a normal modes/eigenvalue analysis of a cantilever with off–center point masses (shown below) using bar elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 4. Attributes of this test are: • coupling between torsional and flexural behavior • inertial axis non–coincident with flexibility axis • discrete mass, rigid links • close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear ratio: • Y = 1.128 • Z = 1.128 Material Properties Finite Element Modeling • 8 nodes • 9 elements E 200x10 9 N m 2 ------- = ρ 8000k g m 3 ------- = ν 0.3 = 93 five bar elements along cantilever two mass elements two rigid elements Boundary Conditions Constraints • Fully constrain point A (node 1) in all directions. Solution Type Normal Modes/Eigenvalue – SVI method 94 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 4 Mode # Ref. Value (Hz) NAFEMS Target Value (Hz) FEMAP Structural Result (Hz) 1 1.723 1.723 1.722 2 1.727 1.727 1.726 3 7.413 7.413 7.410 4 9.972 9.972 9.947 5 18.155 18.160 18.051 6 26.957 26.972 26.712 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Deep Simply-Supported Beam The complete model and results for this test are in file nf005ac.neu. This test is a normal mode dynamic analysis of a deep simply–supported beam. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Fre- quency Analysis, Test 5. Attributes of this test are: • shear deformation and rotary inertial (Timoshenko beam) • possibility of missing extensional modes when using iteration solution methods • repeated eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear Ratio • Y = 1.176923 • Z = 1.176923 Material Properties Finite Element Modeling • 6 nodes E 200x10 9 N m 2 ------- = ρ 8000k g m 3 ------- = ν 0.3 = 96 • 5 bar elements Boundary Conditions Constraints • Constrain the X, Y, Z translation an X rotation at point A (node 1) • Constrain the Y and Z translation at point B (node 10) The boundary conditions are shown in the following diagram. Solution Type Normal Modes/Eigenvalues – SVI method Results Mode # Ref. Value (Hz) NAFEMS Target Value (Hz) FEMAP Structural Result (Hz) 1, 2 42.649 42.568 42.710 3 77.542 77.841 77.841 4 125.00 125.51 125.52 5, 6 148.31 145.46 150.76 7 233.10 241.24 241.24 8, 9 284.55 267.01 301.08 97 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 5. Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Circular Ring - In-plane and Out-of- plane Vibration The complete model and results for this test are in file nf006ac.neu. This test is a normal modes/eigenvalue analysis of a circular ring using bar elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 6. Attributes of this test are: • rigid body modes (six modes) • repeated eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear ratio: • Y = 1.128205 • Z = 1.128205 Material Properties Finite Element Modeling • 20 nodes E 200x10 9 N m 2 ------- = ρ 8000k g m 3 ------- = ν 0.3 = 99 • 20 bar elements Boundary Conditions Constraints • Constraint Set 1 (Kinematic DOF): Constrain nodes 10 and 11 in all directions and rotations. Solution Type Normal Modes/Eigenvalue – SVI method 100 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 6. Mode # Ref. Value (Hz) NAFEMS Target Value (Hz) FEMAP Structural Result (Hz) 7, 8 (out of plane) 51.849 52.290 52.211 9, 10 (in plane) 53.382 53.971 53.775 11, 12 (out of plane) 148.77 149.70 148.92 13, 14 (in plane) 150.99 152.44 151.25 15 (out of plane) 286.98 288.25 285.33 16 (in plane) 289.51 288.25 285.33 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilevered Beam The complete model and results for this test case are in the following files: • nf071a.neu (Test 1) • nf071b.neu (Test 2) • nf071c.neu (Test 3) This test is a normal modes/eigenvalue analysis of a cantilevered beam. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 71. Attributes of this test are: • ill–conditioned stiffness matrix Test Case Data and Information Units SI Material Properties Finite Element Modeling Three tests - all use 8 bar elements and 9 nodes • Test 1: a=b • Test 2: a = 10b E 200x10 9 N m 2 ------- = ρ 8000k g m 3 ------- = 102 • Test3: a = 100b Boundary Conditions Constraints • Fully constrain point A (node 1) in all directions and rotations. • Constrain all other nodes in the Z translation and X and Y rotations. Solution Type Normal Modes/Eigenvalue – SVI method Bar elements always use a consistent mass formulation. 103 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 71. Mode # Ref. Value (Hz) Mesh FEMAP Structural Result (Hz) 1 1.010 a = b a = 10b a = 100b 1.0095 1.0095 1.0095 2 6.327 a = b a = 10b a = 100b 6.3223 6.3260 6.3289 3 17.716 a = b a = 10b a = 100b 17.693 17.791 17.819 4 34.717 a = b a = 10b a = 100b 34.675 34.854 35.061 5 57.390 a = b a = 10b a = 100b 57.422 60.595 64.751 6 85.730 a = b a = 10b a = 100b 86.135 101.673 104.654 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Plate Element Test Cases The normal mode dynamics test cases using the standard NAFEMS benchmarks include these plate element test cases: • "Thin Square Cantilevered Plate -Symmetric Modes" • "Thin Square Cantilevered Plate - Anti-symmetric Modes" • "Free Thin Square Plate" • "Simply-Supported Thin Square Plate" • "Simply-Supported Thin Annular Plate" • "Clamped Thin Rhombic Plate" • "Cantilevered Thin Square Plate with Distorted Mesh" • "Simply-Supported Thick Square Plate, Test A" • "Clamped Thick Rhombic Plate" • "Simply-Supported Thick Square Plate, Test B" • "Simply-Supported Thick Annular Plate" • "Cantilevered Square Membrane" • "Cantilevered Tapered Membrane" • "Free Annular Membrane" • "Cantilevered Thin Square Plate" • "Cantilevered Thin Square Plate #2" Thin Square Cantilevered Plate - Symmetric Modes The complete model and results for this test case are in the following files: • nf011alc.neu (linear quadrilateral plate, consistent mass) • nf011all.neu (linear quadrilateral plate, lumped mass) • nf011apc.neu (parabolic quadrilateral plate, consistent mass) • nf011apl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a thin, square, cantilevered plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 11a. Attributes of this test are: • symmetric modes, symmetric boundary conditions along the cutting plane Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 and Test 2 (nf011alc and nf011all) • 45 nodes • 32 linear quadrilateral plate elements - thickness = 0.05m Test 2 and Test 3 (nf011apc and nf011apl) • 37 nodes E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 106 • 8 parabolic quadrilateral plate elements - thickness = 0.05m Mesh only half the plate (10m x 5m). Boundary Conditions • Constraints (all tests) • Fully constrain nodes 1-5 in all translations and rotations. • Constrain nodes 6, 11, 16, 21, 26, 31, 36, 41 in the X and Y translations and X and Z rotations. • Constrain all other nodes in the X and Y translations and Z rotation. Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Linear Quadrilateral Plates Parabolic Quadrilateral Plates 107 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 11a. Mode # Ref. Value (Hz) Mesh FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 0.421 linear parabolic 0.415 0.414 0.418 0.418 2 2.582 linear parabolic 2.507 2.444 2.623 2.569 3 3.306 linear parabolic 3.117 3.081 3.315 3.281 4 6.555 linear parabolic 5.984 6.018 6.573 6.551 5 7.381 linear parabolic 7.241 6.954 7.979 7.525 6 11.402 linear parabolic 10.387 10.493 12.112 11.950 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Thin Square Cantilevered Plate - Anti-symmetric Modes The complete model and results for this test case are the in following files: • nf011blc.neu (linear quadrilateral plate, consistent mass) • nf011bll.neu (linear quadrilateral plate, lumped mass) • nf011bpc.neu (parabolic quadrilateral plate, consistent mass) • nf011bpl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a thin, square, cantilevered plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 11b. Attributes of this test are: • anti–symmetric modes Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf011blc.neu and nf011bll.neu) • 45 nodes, 32 linear quadrilateral plate elements - thickness = 0.05m Tests 3 and 4 (nf011bpc.neu and nf011bpl.neu) • 37 nodes, 8 parabolic quadrilateral plate elements - thickness = 0.05m E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 109 Mesh only half the plate (10m x 5m). Boundary Conditions Constraints (all tests) • Fully constrain nodes 1-5 in all directions. • Constrain nodes 6, 11, 16, 21, 26, 31, 36, 41 in the X, Y, Z translations and Z rotation. • Constrain all other nodes in the X and Y translations and Z rotation. Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 110 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 11b. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 1.029 linear parabolic 1.019 1.018 0.993 0.999 1.012 1.024 2 3.753 linear parabolic 3.839 3.710 3.553 3.541 3.750 3.728 3 7.730 linear parabolic 8.313 7.768 7.130 6.847 8.162 7.846 4 8.561 linear parabolic 9.424 8.483 8.082 7.894 9.079 8.693 5 not available linear parabolic 11.728 11.185 9.805 9.954 11.526 11.451 6 not available linear parabolic 17.818 15.755 13.087 13.724 17.192 16.918 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Free Thin Square Plate The complete model and results for this test case are in the following files: • nf012lc.neu (linear quadrilateral plate, consistent mass) • nf012ll.neu (linear quadrilateral plate, lumped mass) • nf012pc.neu (parabolic quadrilateral plate, consistent mass) • nf012pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a free thin square plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Bench- marks for Natural Frequency Analysis, Test 12. Attributes of this test are: • rigid body modes (three modes) • repeated eigenvalues • use of kinematic DOF for the rigid body mode calculation with the SVI eigensolver Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf012lc.neu and nf012ll.neu) • 81 nodes, 64 linear quadrilateral plate elements - thickness = 0.05m Tests 3 and 4 (nf012pc.neu and nf012pl.neu) • 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 0.05m E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 112 Boundary Conditions Constraints • Constraint Set 1: Constrain all the nodes in the X and Y translations and Z rotation. • Constraint Set 2 (Kinematic DOF): Constrain nodes 1 and 3 in all directions and rotations. Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 113 Results Reference NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 12. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 4 1.622 linear parabolic 1.632 1.532 1.570 1.567 1.615 1.619 5 2.360 linear parabolic 2.402 2.356 2.246 2.183 2.394 2.364 6 2.922 linear parabolic 3.006 2.861 2.815 2.750 2.990 2.930 7, 8 4.233 linear parabolic 4.251 4.122 3.912 3.879 4.218 4.186 9 7.416 linear parabolic 7.859 7.363 6.902 6.586 7.751 7.494 10 not available linear parabolic 8.027 7.392 6.903 6.586 7.884 7.494 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Thin Square Plate The complete model and results for this test case are in the following files: • nf013lc.neu (linear quadrilateral plate, consistent mass) • nf013ll.neu (linear quadrilateral plate, lumped mass) • nf013pc.neu (parabolic quadrilateral plate, consistent mass) • nf013pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thin square plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 13. Attributes of this test are: • well established • repeated eigenvalues Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf013lc.neu and nf013ll.neu) • 81 nodes, 64 linear quadrilateral plate elements - thickness = 0.05m Tests 3 and 4 (nf013pc.neu and nf013pl.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 115 • 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 0.05m Boundary Conditions Constraints • Constrain all nodes in the X and Y translations and Z rotation. • Constrain the nodes along edges X = 0 and X = 10m in the Z translation and X rotation. • Constrain the nodes along edges Y = 0 and Y = 10m in the Z translation and Y rotation. • Fully constrain the DOF on the four corner nodes (9, 13, 41, 68). Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: 116 • using lumped mass • using consistent mass Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 13. Mode # Ref. Value (Hz) Mesh FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 2.377 4–noded 8–noded 2.338 2.375 2.399 2.383 2, 3 5.942 4–noded 8–noded 5.820 5.932 6.206 6.034 4 9.507 4–noded 8–noded 8.909 9.392 9.873 9.831 5, 6 11.884 4–noded 8–noded 11.770 11.879 13.375 12.590 7, 8 15.449 4–noded 8–noded 14.215 15.033 16.786 16.734 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Thin Annular Plate The complete model and results for this test case are in the following files: • nf014lc.neu (linear quadrilateral plate, consistent mass) • nf014ll.neu (linear quadrilateral plate, lumped mass) • nf014pc.neu (parabolic quadrilateral plate, consistent mass) • nf014pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thin annular plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 14. Attributes of this test are: • curved boundary (skewed coordinate system) • repeated eigenvalues Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf014lc and nf014ll): • 192 nodes, 160 linear quadrilateral plate elements - thickness = 0.06m Tests 3 and 4 (nf014pc and nf014pl) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 118 • 176 nodes, 48 parabolic quadrilateral plate elements - thickness = 0.06m Boundary Conditions • Constraint Set 1 (All Tests): Constrain all nodes in in the X and Y translation and Z rotation. Additionally constrain all nodes around the model’s circumference in the Z translation and X rotation. • Constraint Set 2 (Kinematic DOF): Tests 1 and 2: Constrain nodes 258 and 290 in the X and Y translations. 119 Tests 3 and 4: Constrain nodes 21 and 133 in the X and Y translations. Solution Type Normal Mode Dynamics - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) Mesh FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 1.870 linear parabolic 1.859 1.840 1.877 1.873 2, 3 5.137 linear parabolic 5.175 5.111 5.249 5.151 4, 5 9.673 linear parabolic 9.686 9.672 9.983 9.713 6 14.850 linear parabolic 14.188 13.946 15.412 14.924 7, 8 15.573 linear parabolic 15.326 15.547 16.176 15.708 9 18.382 linear parabolic 17.594 17.380 19.088 18.521 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. 120 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 14. Clamped Thin Rhombic Plate The complete model and results for this test case are in the following files: • nf015lc.neu (linear quadrilateral plate, consistent mass) • nf015ll.neu (linear quadrilateral plate, lumped mass) • nf015pl.neu (parabolic quadrilateral plate, lumped mass) • nf015pc.neu (parabolic quadrilateral plate, consistent mass) This test is a normal modes/eigenvalue analysis of a clamped thin rhombic plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 15. Attributes of this test are: • distorted elements Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf015lc.neu and nf015ll.neu): • 169 nodes, 144 linear quadrilateral plate elements - thickness = 0.05m E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 122 Tests 3 and 4 (nf015pc.neu and nf015pl.neu): • 133 nodes, 36 parabolic quadrilateral plate elements - thickness = 0.05m Boundary Conditions Constraints • Completely constrain the nodes along all four edges of the part in all directions and rotations. • Constrain all other nodes in the X and Y translation and Z rotation. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 123 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 15. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 7.938 linear parabolic 8.142 7.873 7.818 7.902 7.955 7.929 2 12.835 linear parabolic 13.891 12.480 12.831 12.851 13.388 13.008 3 17.941 linear parabolic 20.036 17.312 17.807 17.952 19.072 18.472 4 19.133 linear parabolic 20.165 18.738 18.554 18.964 19.239 19.168 5 24.009 linear parabolic 27.704 27.950 23.665 23.879 26.185 25.226 6 27.922 linear parabolic 32.046 25.883 27.698 27.910 29.816 28.810 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilevered Thin Square Plate with Distorted Mesh The complete model and results for this test case are in the following files: • nf016a1.neu (16 parabolic quadrilateral plate, lumped mass) • nf016a2.neu (16 parabolic quadrilateral plate, consistent mass) • nf016b1.neu (16 parabolic quadrilateral plate, lumped mass) • nf016b2.neu (16 parabolic quadrilateral plate, consistent mass) • nf016c1.neu (4 parabolic quadrilateral plate, lumped mass) • nf016c2.neu (4 parabolic quadrilateral plate, consistent mass) • nf016d1.neu (4 parabolic quadrilateral plate, lumped mass) • nf016d2.neu (4 parabolic quadrilateral plate, consistent mass) This test is a normal modes/eigenvalue analysis of a cantilevered thin square plate meshed with distorted plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 16. Attributes of this test are: • distorted meshes Test Case Data and Information Units SI Material Properties Finite Element Modeling All tests - parabolic quadrilateral plate elements - thickness = 0.05m E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 125 Four tests: • Test 1 (nf016a1, nf016a2) - 65 nodes, 16 elements • Test 2 (nf016b1, nf016b2) - 65 nodes, 16 elements with specified nodes at the following XY coordinates: X Coordinate Y Coordinate 4.0 4.0 2.25 2.25 4.75 2.5 7.25 2.75 7.5 4.75 7.75 7.25 5.25 7.25 2.25 7.25 2.5 4.75 126 • Test 3 (nf016c1, nf016c2) - 21 nodes, 4 elements • Test 4 (nf016d1, nf016d2) - 21 nodes, 4 elements with a specified node at X=4.0, Y=4.0. Boundary Conditions 127 Constraints (nf016a1 and nf016a2) • Constrain the nodes along the model’s Y axis in the X, Y, and Z translations and in the Y and Z rotations. • Constrain all other nodes in the Z rotation only. Constraints (nf016b1 and nf016b2) • Fully constrain the nodes along the model’s Y axis in all directions. • Constrain all other nodes in the Z rotation only. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 128 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 16. Mode # Ref. Value (Hz) Test NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 0.421 1 2 3 4 0.4174 0.4174 0.4144 0.4145 0.4139 0.4135 0.4021 0.3999 0.4181 0.4182 0.4189 0.4192 2 1.029 1 2 3 4 1.020 1.020 0.999 1.002 0.9985 0.9967 0.9347 0.9202 1.024 1.024 1.021 1.025 3 2.582 1 2 3 4 2.564 2.571 2.554 2.565 2.444 2.445 2.132 2.112 2.569 2.566 2.708 2.698 4 3.306 1 2 3 4 3.302 3.317 3.401 3.424 3.082 3.072 2.707 2.697 3.281 3.280 3.449 3.430 5 3.753 1 2 3 4 3.769 3.780 3.697 3.714 3.540 3.535 3.136 3.077 3.728 3.731 3.913 3.881 6 6.555 1 2 3 4 6.805 6.883 5.455 5.133 6.018 5.994 5.458 5.459 6.551 6.552 7.108 6.858 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Thick Square Plate, Test A The complete model and results for this test case are in the following files: • nf021alc.neu (linear quadrilateral plate, consistent mass) • nf021all.neu (linear quadrilateral plate, lumped mass) • nf021apc.neu (parabolic quadrilateral plate, consistent mass) • nf021apl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thick square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 21a. Attributes of this test are: • well–established • repeated eigenvalues • effect of secondary restraints Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf021alc.neu and nf021all.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 130 • 81 nodes, 64 linear quadrilateral plate elements - thickness = 1.0m Tests 3 and 4 (nf021apc.neu and nf021apl.neu) • 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 1.0m Boundary Conditions Constraints • Fully constrain the corner nodes in all directions and rotations. • Constrain the nodes along edges X=0 and X=10m in all directions, except the Y rotation. • Constrain the nodes along edges Y=0 and Y=10m in all directions, except the X rotation. 131 • Constrain all other nodes in the X and Y translation and Z rotation. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) Mesh NAFEMSTar get Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 45.897 linear parabolic 46.659 45.936 45.50 46.165 46.35 45.830 2, 3 109.44 linear parabolic 115.84 110.41 108.70 110.32 114.12 109.38 4 167.89 linear parabolic 177.53 170.38 160.63 167.30 174.29 169.75 5, 6 204.51 linear parabolic 233.40 212.81 204.75 204.59 227.05 208.20 132 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 21a. 7, 8 256.50 linear parabolic 283.60 269.96 240.84 249.26 276.88 268.40 9 336.62 linear parabolic 371.11 344.77 298.18 311.32 364.30 319.40 10 336.62 linear parabolic 371.11 344.77 320.41 347.63 385.84 319.40 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Thick Square Plate, Test B The complete model and results for this test case are in the following files: • nf021blc.neu (linear quadrilateral plate elements, consistent mass) • nf021bll.neu (linear quadrilateral plate elements, lumped mass) • nf021bpc.neu (parabolic quadrilateral plate elements, consistent mass) • nf021bpl.neu (parabolic quadrilateral plate elements, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thick square plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 21b. Attributes of this test are: • well–established • repeated eigenvalues • effect of secondary restraints Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf021blc.neu and nf021bll.neu) • 81 nodes, 64 linear quadrilateral plate elements - thickness = 1.0m E 200X10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 134 Tests 3 and 4 (nf021plc.neu and nf021pll.neu) • 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 1.0m Boundary Conditions Constraints • Constrain the nodes along all edges in the X,Y, and Z translations and Z rotation. • Constrain all other nodes in the X and Y translation and Z rotation. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass 135 • using consistent mass Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 21b. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 45.897 linear parabolic 44.745 44.134 44.14 44.815 44.96 44.493 2, 3 109.44 linear parabolic 112.94 107.85 106.96 108.52 112.25 107.57 4 167.89 linear parabolic 170.28 164.19 156.96 163.57 170.17 165.70 5, 6 204.51 linear parabolic 230.23 20.07 203.40 203.12 225.51 206.46 7, 8 256.50 linear parabolic 274.19 260.32 237.31 245.71 272.47 263.61 9 336.62 linear parabolic 355.98 342.80 293.95 307.16 358.43 318.56 10 336.62 linear parabolic 355.98 342.80 319.64 346.85 384.78 318.58 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Clamped Thick Rhombic Plate The complete model and results for this test case are in the following files: • nf022lc.neu (linear quadrilateral plate, consistent mass) • nf022ll.neu (linear quadrilateral plate, lumped mass) • nf022pc.neu (parabolic quadrilateral plate, consistent mass) • nf022pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a thick clamped thick rhombic plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 22. Attributes of this test are: • distorted elements Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf022lc.neu and nf022ll.neu) E 200X10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 137 • 121 nodes, 100 linear quadrilateral plate elements - thickness = 1.0m Tests 3 and 4 (nf022pc.neu and nf022pl.neu) • 133 nodes, 36 parabolic quadrilateral plate elements - thickness = 1.0m Boundary Conditions Constraints • Fully constrain the nodes along all four edges in all directions and rotations. 138 • Constrain all other nodes in the X and Y translations and Z rotation. Solution Type Normal Mode Dynamics - SVI Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 133.95 linear parabolic 137.80 133.86 133.33 134.51 135.17 132.48 2 201.41 linear parabolic 218.48 203.34 204.42 204.30 213.06 200.28 3 265.81 linear parabolic 295.42 271.38 269.23 270.17 288.08 266.06 4 282.74 linear parabolic 296.83 283.68 279.75 283.95 289.05 273.65 5 334.45 linear parabolic 383.56 346.41 337.92 338.90 377.05 338.88 6 not available linear parabolic 426.59 386.62 381.87 381.90 411.28 369.79 139 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 22 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Thick Annular Plate The complete model and results for this test case are in the following files: • nf023lc.neu (linear quadrilateral plate, consistent mass) • nf023ll.neu (linear quadrilateral plate, lumped mass) • nf023pc.neu (parabolic quadrilateral plate, consistent mass) • nf023pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thick annular plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 23. Attributes of this test are: • curved boundary (skewed coordinate system) • repeated eigenvalues Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf023lc.neu and nf023ll.neu) E 200X10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 141 • 192 nodes, 160 linear quadrilateral plate elements - thickness = 0.6m Tests 3 and 4 (nf023pc.neu and nf023pl.neu) • 176 nodes, 48 parabolic quadrilateral plate elements - thickness = 0.6m Boundary Conditions Constraints • Constrain the nodes around the circumference in the X, Y, and Z translations and X and Z rotations. 142 • Constrain all other nodes in the X and Y translation and Z rotation. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 18.58 linear parabolic 18.82 18.59 18.49 18.32 18.61 18.59 2, 3 48.92 linear parabolic 49.82 49.02 49.89 48.99 50.35 49.13 4, 5 92.59 linear parabolic 96.06 92.90 93.43 93.19 95.44 92.42 143 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 23. 6 140.15 linear parabolic 148.34 140.86 136.71 134.27 145.39 139.41 7, 8 not available linear parabolic 153.68 146.63 145.21 146.87 151.28 145.37 9 166.36 linear parabolic 174.52 167.31 163.74 160.43 174.10 166.11 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilevered Square Membrane The complete model and results for this test case are in the following files: • nf031lc.neu (linear quadrilateral plate, consistent mass) • nf031ll.neu (linear quadrilateral plate, lumped mass) • nf031pc.neu (parabolic quadrilateral plate, consistent mass) • nf031pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered square membrane meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 31. Attributes of this test are well established. Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf031lc.neu and nf031ll.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 145 • 81 nodes, 64 linear quadrilateral plate elements - thickness = 0.05m Tests 3 and 4 (nf031pc.neu and nf031pl.neu) • 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 0.05m Boundary Conditions Constraints • Fully constrain the nodes along the Y axis in all directions and rotations. 146 • Constrain all other nodes in the Z translation and X, Y, and Z rotations. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 52.404 linear parabolic 52.905 52.635 52.47 52.16 52.77 52.39 2 125.69 linear parabolic 126.11 125.87 125.59 125.18 126.06 122.48 3 140.78 linear parabolic 143.20 141.47 139.54 138.28 142.83 138.02 4 222.54 linear parabolic 228.85 224.59 214.61 209.01 227.04 214.95 5 241.41 linear parabolic 247.90 243.26 239.84 239.16 247.25 227.48 6 255.74 linear parabolic 260.61 256.76 252.06 251.31 259.46 236.73 147 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 31. Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilevered Tapered Membrane The complete model and results for this test case are in the following files: • nf032lc.neu (linear quadrilateral plate, consistent mass) • nf032ll.neu (linear quadrilateral plate, lumped mass) • nf032pc.neu (parabolic quadrilateral plate, consistent mass) • nf032pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered tapered membrane meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 32. Attributes of this test are: • shear behavior • irregular mesh • symmetry Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf032lc.neu and nf032ll.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 149 • 153 nodes, 128 linear quadrilateral plate elements - thickness = 0.1m Tests 3 and 4 (nf032pc.neu and nf032pl.neu) • 153 nodes, 32 parabolic quadrilateral plate elements - thickness = 0.1m Boundary Conditions Constraints • Fully constrain the nodes along the Y axis in all directions and rotations. 150 • Constrain all other nodes in the Z translation and the X, Y, and Z rotations. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 44.623 linear parabolic 44.905 44.636 44.73 44.84 44.82 45.14 2 130.03 linear parabolic 132.12 130.14 129.92 129.05 131.28 130.50 3 162.70 linear parabolic 162.83 162.72 162.61 162.37 162.80 161.37 4 246.05 linear parabolic 252.99 246.63 244.62 241.80 250.56 245.00 5 379.90 linear parabolic 393.31 382.02 375.09 369.61 391.79 374.78 6 391.44 linear parabolic 396.26 391.55 389.81 388.11 393.11 375.77 151 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 32 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Free Annular Membrane The complete model and results for this test case are in the following files: • nf033lc.neu (linear quadrilateral plate, consistent mass) • nf033ll.neu (linear quadrilateral plate, lumped mass) • nf033pc.neu (parabolic quadrilateral plate, consistent mass) • nf033pl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a free annular membrane meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 33. Attributes of this test are: • repeated eigenvalues • rigid body modes (three modes) • kinematically incomplete suppressions Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf033lc.neu and nf033ll.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 153 • 192 nodes, 160 linear quadrilateral plate elements - thickness = 0.06m Tests 3 and 4 (nf033pc.neu and nf033pl.neu) • 176 nodes, 48 parabolic quadrilateral plate elements - thickness = 0.06m Boundary Conditions Constraints • Constraint Set 1 (DOF set): Tests 1 and 2: Constrain nodes 254 and 286 in the X and Y translations. 154 Tests 3 and 4: Constrain nodes 7 and 19 in the X and Y translations. • Constraint Set 2: Constrain all other nodes in the Z translation and X, Y, and Z rotations. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 155 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 33. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 4, 5 129.24 linear parabolic 129.51 126.48 127.71 126.66 128.70 126.15 6 226.17 linear parabolic 225.46 224.27 224.52 222.82 225.22 218.17 7, 8 234.74 linear parabolic 234.92 232.95 229.67 230.12 234.94 225.14 9, 10 264.66 linear parabolic 272.13 264.81 263.86 262.45 270.83 257.67 11, 12 336.61 linear parabolic 340.34 335.70 328.44 329.09 339.93 311.38 13, 14 376.79 linear parabolic 391.98 378.60 368.15 368.48 389.38 361.52 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilevered Thin Square Plate The complete model and results for this test case are in the following files: • nf073ac.neu (Test 1 - parabolic quadrilateral plate, consistent mass) • nf073al.neu (Test 2 - parabolic quadrilateral plate, lumped mass) • nf073bc.neu (Test 3 - parabolic quadrilateral plate, consistent mass) • nf073bl.neu (Test 4 - parabolic quadrilateral plate, lumped mass) • nf073cc.neu (Test 5 - parabolic quadrilateral plate, consistent mass) • nf073cl.neu (Test 6 - parabolic quadrilateral plate, lumped mass) • nf073dc.neu (Test 7 - parabolic quadrilateral plate, consistent mass) • nf073dl.neu (Test 8 - parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered thin square plate. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Fre- quency Analysis, Test 73. Attributes of this test are: • effect of master DOF selection on frequencies Test Case Data and Information Units SI 157 Material Properties Finite Element Modeling 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 0.05m Boundary Conditions Constraints • Constraint Set 1: Constrain the nodes along the Y axis in the X, Y, and Z translations and Y rotation. • Constraint Set (DOF set) 2: Create a constraint set to define a Master (ASET) DOF set (in Z direction) - four different placements: E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 158 Tests 1 and 2: Tests 3 and 4: Tests 5 and 6: 159 Tests 7 and 8: Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) DOF Set NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 0.421 test 1 test 2 test 3 test 4 0.4174 0.4174 0.4175 0.4184 0.4139 0.4139 0.4140 0.4147 0.4182 0.4182 0.4183 0.4191 2 1.029 test 1 test 2 test 3 test 4 1.020 1.020 1.021 1.032 0.999 1.000 1.001 1.009 1.025 1.026 1.027 1.036 3 2.582 test 1 test 2 test 3 test 4 2.564 2.597 2.677 2.850 2.449 2.476 2.524 2.670 2.580 2.610 2.675 2.844 160 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 73. 4 3.306 test 1 test 2 test 3 test 4 3.302 3.345 3.365 3.571 3.095 3.126 3.140 3.325 3.314 3.352 3.362 3.555 5 3.753 test 1 test 2 test 3 test 4 3.769 3.888 4.035 5.466 3.563 3.663 3.765 4.816 3.781 3.891 4.023 5.414 6 6.555 test 1 test 2 test 3 test 4 6.805 7.517 7.495 ----- 6.126 6.694 6.675 ------ 6.798 7.498 7.479 ------ Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilevered Thin Square Plate #2 The complete model and results for this test case are in the following files: • nf074c.neu (parabolic quadrilateral plate, consistent mass) • nf074l.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered thin square plate. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Fre- quency Analysis, Test 74. Test Case Data and Information Units SI Material Properties Finite Element Modeling 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 0.05m E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 162 Boundary Conditions Constraints Constrain the nodes along the Y axis in the X, Y, and Z translations and the Y rotation. Solution Type Normal Modes/Eigenvalues - SVI Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 0.471 0.4139 0.4181 2 1.029 0.999 1.024 3 2.582 2.444 2.569 4 3.306 3.082 3.281 5 3.753 3.540 3.728 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. 163 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 74. Axisymmetric Solid and Solid Ele- ment Test Cases The normal mode dynamics test cases using the standard NAFEMS benchmarks include these axisymmetric solid and solid element test cases: • "Free Cylinder - Axisymmetric Vibration" • "Simply-Supported Annular Plate -Axisymmetric Vibration" • "Thick Hollow Sphere - Uniform Radial Vibration" • "Simply-Supported Solid Square Plate" • "Simply-Supported Solid Annular Plate" • "Deep Simply-Supported Solid Beam" • "Cantilevered Solid Beam" Free Cylinder - Axisymmetric Vibra- tion The complete model and results for this test case are in the following files: • nf041lc.neu (linear axisymmetric solid quadrilateral, consistent mass) • nf041ll.neu (linear axisymmetric solid quadrilateral, lumped mass) • nf041pc.neu (parabolic axisymmetric solid quadrilateral, consistent mass) • nf041pl.neu (parabolic axisymmetric solid quadrilateral, lumped mass) This test is a normal modes/eigenvalue analysis of a free cylinder meshed with axisymmetric elements. This document provides the input data and results for NAFEMS Selected Bench- marks for Natural Frequency Analysis, Test 41. Attributes of this test are: • rigid body modes (one mode) • coupling between axial, radial, and circumferential behavior • close eigenvalues Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf041lc.neu and nf041ll.neu): E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 166 • 68 nodes, 48 linear axisymmetric quadrilateral solid elements Tests 3 and 4 (nf041pc.neu and nf041pl.neu): • 43 nodes, 8 parabolic axisymmetric quadrilateral solid elements Boundary Conditions Constraints • Tests 1 and 2: Create a constraint set (Kinematic DOF set) to constrain nodes 1 and 68 in the X and Z translations. • Tests 3 and 4: Create a constraint set (Kinematic DOF set) to constrain nodes 1 and 51 in the X and Z translations. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 167 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 41. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 2 243.53 linear parabolic 244.01 243.50 243.18 243.24 243.96 243.50 3 377.41 linear parabolic 379.41 377.46 370.86 356.49 378.15 377.46 4 394.11 linear parabolic 395.41 394.28 379.31 356.88 394.42 394.30 5 397.72 linear parabolic 401.35 397.94 385.92 375.85 398.00 397.97 6 405.28 linear parabolic 421.87 406.41 389.56 393.65 406.85 406.44 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Thick Hollow Sphere - Uniform Radial Vibration The complete model and results for this test case are in the following files: • nf042lc.neu (linear axisymmetric solid quadrilateral, consistent mass) • nf042ll.neu (linear axisymmetric solid quadrilateral, lumped mass) • nf042pc.neu (parabolic axisymmetric solid quadrilateral, consistent mass) • nf042pl.neu (parabolic axisymmetric solid quadrilateral, lumped mass) This test is a normal modes/eigenvalue analysis of a thick, hollow sphere using axisymmetric solid elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 42. Attributes of this test are: • curved boundary (skewed coordinate system) • constraint equations Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf042lc.neu and nf042ll.neu) • 22 nodes, 10 linear axisymmetric solid quadrilateral elements - α = 5° Tests 3 and 4 (nf042pc.neu and nf042pl.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 169 • 53 nodes, 10 parabolic axisymmetric solid quadrilateral elements Boundary Conditions Constraints • Constraint Set 1: Constrain all nodes in the Z translation. • Constraint Equations: Constrain all nodes at the same R’ are constrained to have same r’ displacement Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 170 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 42. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 369.91 linear parabolic 370.64 370.01 369.91 369.49 370.08 369.83 2 838.03 linear parabolic 841.20 838.08 831.80 832.72 839.49 837.77 3 1451.2 linear parabolic 1473.1 1453.0 1421.3 1433.7 1470.5 1450.85 4 2117.0 linear parabolic 2192.2 2131.7 2030.5 2072.9 2188.6 2117.3 5 2795.8 linear parabolic 2975.7 2852.8 2604.2 2706.3 2970.9 2799.5 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Annular Plate - Axisymmetric Vibration The complete model and results for this test case are in the following files: • nf043lc.neu (linear axisymmetric solid quadrilateral, consistent mass) • nf043ll.neu (linear axisymmetric solid quadrilateral, lumped mass) • nf043pc.neu (parabolic axisymmetric solid quadrilateral, consistent mass) • nf043pl.neu (parabolic axisymmetric solid quadrilateral, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported annular plate meshed with axisymmetric elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 43. Attributes of this test are: • well established Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf043lc.neu and nf043ll.neu): E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 172 • 80 nodes, 60 linear axisymmetric solid quadrilateral elements Tests 3 and 4 (nf043pc.neu and nf043pl.neu) • 28 nodes, 5 parabolic axisymmetric solid quadrilateral elements Boundary Conditions Constraints Constrain point A (node 1) in the Z translation Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 173 Results Reference NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 43. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 18.543 linear parabolic 18.711 18.582 18.542 18.429 18.570 18.582 2 150.15 linear parabolic 145.46 145.56 138.66 135.97 140.24 140.56 3 224.16 linear parabolic 224.22 224.18 224.20 224.00 224.20 224.18 4 358.29 linear parabolic 385.59 374.05 361.50 353.62 371.48 374.05 5 629.19 linear parabolic 689.34 686.04 643.34 633.16 673.79 686.05 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Deep Simply-Supported Solid Beam The complete model and results for this test case are in the following files: • nf051lc.neu (linear solid brick, consistent mass) • nf051ll.neu (linear solid brick, lumped mass) • nf051pc.neu (parabolic solid brick, consistent mass) • nf051pl.neu (parabolic solid brick, lumped mass) This test is a normal mode dynamic analysis of a deep, solid beam meshed with bricks. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 51. Attributes of this test are: • skewed coordinate system • skewed restraints Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf051lc.neu, nf051ll.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 175 • 88 nodes, 30 linear solid brick elements Tests 3 and 4 (nf051pc.neu, nf051pl.neu) • 68 nodes, 5 parabolic solid brick elements Boundary Conditions Constraints, Tests 1 and 2: • Constrain node 7 in the X, Y, and Z translations. • Constrain node 8 in the X and Z translations. • Constrain node 87 in the Y and Z translations. • Constrain node 88 in the Z translation. 176 • Constrain all other nodes along the plane Y’ in the Y translation. Constraints, Tests 3 and 4: • Constrain node 10 in the X, Y, and Z translations • Constrain nodes 12 and 35 in the X and Z translations. • Constrain node 30 in the Y and Z translations. • Constrain node 71 in the Z translation. • Constrain all other nodes along the plane Y’ in the Y translation. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 177 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 51. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 38.200 linear parabolic 42.881 38.821 37.964 37.788 38.282 38.269 2 85.210 linear parabolic 93.817 88.451 83.407 87.027 83.977 87.659 3 152.23 linear parabolic 170.67 159.34 152.84 150.53 157.63 157.49 4 245.53 linear parabolic 286.12 259.20 251.76 243.10 265.02 259.00 5 297.05 linear parabolic 318.86 307.92 288.20 281.27 298.43 306.02 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Solid Square Plate The complete model and results for this test case are in the following files: • nf052lc.neu (linear solid brick, consistent mass) • nf052ll.neu (linear solid brick, lumped mass) • nf052pc.neu (parabolic solid brick, consistent mass) • nf052pl.neu (parabolic solid brick, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported solid square plate meshed with bricks. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 52. Attributes of this test are: • well established • rigid body modes (three modes) • kinematically incomplete suppressions Test Case Data and Information Units SI Material Properties Finite Element Modeling Tests 1 and 2 (nf052lc.neu, nf052ll.neu) E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 179 • 324 nodes, 192 linear solid brick elements Tests 3 and 4 (nf052pc.neu, nf052pl.neu) • 155 nodes, 16 parabolic solid brick elements Boundary Conditions Constraints • Constraint Set 1: Constrain all the nodes along the four edges on the plane ZS = -0.5m in the Z translation. 180 • Constraint Set 2 (Kinematic DOF): Tests 1 and 2: Constrain nodes 36 and 264 in the X, Y, and Z translations. Tests 3 and 4: Constrain nodes 27 and 219 in the X and Y translation. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass Results Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 4 45.897 linear parabolic 51.654 44.762 44.115 44.502 45.318 44.796 5, 6 109.44 linear parabolic 132.73 110.52 106.73 107.94 113.96 110.54 7 167.89 linear parabolic 194.37 169.08 156.48 161.44 173.30 169.11 8 193.59 linear parabolic 197.18 193.93 193.58 193.16 196.77 193.92 9, 10 206.19 linear parabolic 210.55 206.64 200.14 185.60 209.56 206.65 181 Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 52. Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Simply-Supported Solid Annular Plate The complete model and results for this test case are in the following files: • nf053lc.neu (linear solid brick, consistent mass) • nf053ll.neu (linear solid brick, lumped mass) • nf053pc.neu (parabolic solid brick, consistent mass) • nf053pl.neu (parabolic solid brick, lumped mass) This test is a normal modes/eigenvalue analysis of a solid annular plate using solid elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 53. Attributes of this test are: • curved boundary (skewed coordinate system) • constraint equations Test Case Data and Information Units SI Material Properties Finite Element Modeling • 160 nodes, 60 linear solid bricks: E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = α 5° = 183 • 68 nodes, 5 solid parabolic bricks Boundary Conditions Constraints, Tests 1 and 2: • Constrain nodes 76-80 and 156-160 in the Y and Z translations. • Constrain all other nodes in the Y translation. α 10° = 184 • Constraint equations: Constrain nodes at same R and Z are constrained to have same z displacement. Constraints, Tests 3 and 4: • Constrain nodes 11, 22, 33, 44, 66, 77, 88, and 99 in the Y and Z translations and X, Y, and Z rotations. • Constrain all other nodes in the Y translation and X, Y, and Z rotations. • Constraint equations: Constrain nodes at same R and Z are constrained to have same z displacement Solution Type Normal Modes/Eigenvalues - SVI method Results were obtained two different ways: • using lumped mass • using consistent mass 185 Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 53. Mode # Ref. Value (Hz) Mesh NAFEMS Target Value (Hz) FEMAP Structural Result (lumped mass) (Hz) FEMAP Structural Result (consistent mass) (Hz) 1 18.583 linear parabolic 19.659 18.582 18.612 18.409 18.641 18.629 2 140.15 linear parabolic 146.42 140.42 140.13 134.21 141.78 141.44 3 224.16 linear parabolic 224.25 224.18 224.34 223.62 224.48 224.33 4 358.29 linear parabolic 386.70 374.04 369.74 345.98 380.74 380.03 5 629.19 linear parabolic 689.47 686.02 668.73 616.01 690.09 688.59 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Cantilevered Solid Beam The complete model and results for this test case are in the following files: • nf072ac.neu (conventional numbering, consistent mass) • nf072al.neu (conventional numbering, lumped mass) • nf072bc.neu (unconventional numbering, consistent mass) • nf072bl.neu (unconventional numbering, lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered solid beam. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 72. Attributes of this test are: • highly populated stiffness matrix Test Case Data and Information Units SI Material Properties Finite Element Modeling Two tests - both use solid parabolic brick elements E 200x10 9 N m 2 ------- = ρ 8000 kg m 3 ------- = ν 0.3 = 187 • Test 1: conventional node numbering • Test 2: unconventional node numbering Boundary Conditions Constraints • Constrain all nodes on the X=0 plane in the X, Y, and Z translations. 188 • Constrain all nodes on the Y=1m plane in the Y translation. Solution Type Normal Modes/Eigenvalue – SVI Method Results Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 72. Mode # Mesh NAFEMS Target Value (Hz) FEMAP Structural (lumped mass) (Hz) FEMAP Structural (consistent mass) (Hz) 1 Test 1 Test 2 16.007 16.007 15.800 15.800 16.007 16.007 2 Test 1 Test 2 87.226 87.226 82.235 82.235 87.226 87.226 3 Test 1 Test 2 125.96 125.96 125.03 125.03 125.96 125.96 4 Test 1 Test 2 209.56 209.56 189.33 189.33 209.56 209.56 5 Test 1 Test 2 351.11 351.11 299.30 299.32 351.11 351.11 6 Test 1 Test 2 375.81 375.81 352.39 352.40 375.82 375.81 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Verification Test Cases from the Societe Francaise des Mech- aniciens The purpose of these test cases is to verify the function of the FEMAP Structural software using standard benchmarks published by SFM (Societe Francaise des Mecaniciens, Paris, France) in “Guide de validation des progiciels de calcul de structures.” Included here are: • test cases on mechanical structures using linear statics analysis and normal modes/eigenvalue analysis • stationary thermal test cases using heat transfer analysis • a thermo–mechanical test case using linear statics analysis Results published in “Guide de validation des progiciels de calcul de structures” are compared with those computed using the FEMAP Structural software. Understanding the Test Case Format Each test case is structured with the following information: • test case data and information - units - material properties - finite element modeling information - boundary conditions (loads and constraints) - solution type • results • reference Reference The following reference has been used in these test cases: Note: The node numbers listed in each case refer to the node numbers in the neutral (.neu) files associated with this guide. If you remesh a model, or rebuild that model from scratch, your node numbering may differ. 190 • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Mechanical Structures - Linear Stat- ics Analysis with Bar or Rod Ele- ments The linear statics analysis test cases from the Societe Francaise des Mecaniciens include these bar and rod element test cases: • "Short Beam on Two Articulated Supports" • "Clamped Beams Linked by a Rigid Element" • "Transverse Bending of a Curved Pipe" • "Plane Bending Load on a Thin Arc" • "Nodal Load on an Articulated Rod Truss" • "Articulated Plane Truss" • "Beam on an Elastic Foundation" Short Beam on Two Articulated Supports The complete model and results for this test case are in file ssll02.neu. This test is a linear statics analysis of a short, straight beam with plane bending and shear loading. It provides the input data and results for benchmark test SSLL02/89 from “Guide de validation des progiciels de calcul de structures.” • area = 31E-4m 2 • inertia = 2810E-8m 4 • Shear area ratio = 2.42 Test Case Data and Information Units SI Material Properties Finite Element Modeling • 10 bar elements • 11 nodes The mesh is shown in the following figure: E 2E11 Pa = ν 0.3 = 193 Boundary Conditions Constraints • Constrain the nodes at both free ends of the beam (nodes 1 and 2) in all directions except for the Z rotation. Loads • On nodes 1-10, apply a load = 1E5 N/m in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLL02/89. Total Translation at point B (Node 7) Bench Value -1.25926E-3 FEMAP Structural Value -1.25926E-3 Difference 0.00% Clamped Beams Linked by a Rigid Element The complete model and results for this test case are in file ssll05.neu. This test is a linear statics analysis of a straight, cantilever beam with plane bending and a rigid element. It provides the input data and results for benchmark test SSLL05/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties • E = 2E11 Pa • I = (4/3)E-8m 4 Finite Element Modeling • 20 bar elements • 1 rigid element • 26 nodes The mesh is shown in the following figure: Boundary Conditions Constraints • Nodes 1 and 4: Fully constrained in all directions. 195 Loads • Node 3: Set nodal force = 1000 N in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLL05/89. Node # Displacement Reaction Force Bench Value FEMAP Structural Difference Node 6 Displacement Y (T2 Translation) -0.125 -0.125 0.00% Node 3 Displacement Y (T2 Translation) -0.125 -0.125 0.00% Node 1 Force Y (N) (T2 Constraint Force) 500 500 0.00% Node 1 Moment R z (Nm) (R3 Constraint Moment) 500 500 0.00% Node 4 Force Y (N) (T2 Constraint Force) 500 500 0.00% Node 4 R z moment (Nm) (R3 Con- straint Moment) 500 500 0.00% Transverse Bending of a Curved Pipe The complete model and results for this test case are the following files: • ssll07a.neu (linear beam) • ssll07b.neu (curved beam) This test is a linear statics analysis (three–dimensional problem) of a curved pipe with transverse bending and bending–torque loading. It provides the input data and results for benchmark test SSLL07/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (ssll07a) • 90 bar elements • 91 nodes Test 2 (ssll07b) • 90 curved beam elements • 91 nodes E 2E11 Pa = ν 0.3 = 197 The mesh for Test 1 is shown in the following figure: Boundary Conditions Constraints • Fully constrain node 91 in all translations and rotations. Loads • Create a nodal force at node 1 = 100 N in Z direction The boundary conditions are shown in the following figure: 198 Solution Type Statics Results Mf = bending moment Mt = torsional moment *See “Post Processing” below Post Processing Bar Element (ssll07a) List beam forces on element 167, second end • Mf=Bar End BX2 Moment • Mt=Bar End BX1 Moment Curved Beam Element (ssll07b) List beam forces on element 166, second end • Mf=Bar End BX2 Moment • Mt=Bar End BX1 Moment Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLL07/89. Node # Point Displacement Moment Bench Value Test Number FEMAP Structural Difference Node 1 Displacement Z (T3 Translation) 0.13462 1 0.13465 0.02% Node 1 Displacement Z (T3 Translation) 2 0.13464 0.01% θ=15° Mt (Nm)* 74.1180 1 76.6709 3.44% Mt (Nm)* 2 75.8109 1.02% Mf (Nm) -96.5925 1 -96.3680 0.23% Mf (Nm) 2 -95.2869 1.35% Plane Bending Load on a Thin Arc The complete model and results for this test case are in file ssll08.neu. This test is a linear statics analysis (plane problem) of a thin arc with plane bending. It provides the input data and results for benchmark test SSLL08/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 11 nodes • 10 bar elements The mesh is shown in the following figure: Boundary Conditions Constraints • Node 2: Constrain the X, Y, and Z translations. • Node 1: Constrain the Y and Z translation only. E 2E11 Pa = ν 0.3 = 200 • Nodes 3-11: Constrain in the Z translation only. Loads • Force=100N in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLL08/89. Node # Displacement Bench Value FEMAP Structural Difference Node 2 R z (rad) (R3 Rotation) -3.0774E-2 -3.1097E-2 1.05% Node 1 R z (rad) (R3 Rotation) 3.0774E-2 3.1097E-2 1.05% Node 7 Y (m) (T2 Translation) -1.9206E-2 -1.9342E-2 0.71% Node 1 X (m) (T1 Translation) 5.3913E-2 5.3735E-2 0.33% Nodal Load on an Articulated Rod Truss The complete model and results for this test case are in file ssll11.neu. This test is a linear statics analysis of a plane truss with an articulated rod. It provides the input data and results for benchmark test SSLL11/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties • E = 1.962E11 Pa Finite Element Modeling • 4 nodes • 4 rod elements The mesh is shown in the following figure: Boundary Conditions Constraints • Nodes 3 and 17: Constrained in the X, Y, and Z translations only. 202 • Nodes 2 and 18: Constrained in the Z translation only. Loads • Node 2: Set Nodal force = 9.81E3 N in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLL11/89. Node # Displacement Bench Value FEMAP Structural Difference Node 18 X (m) (T1 Translation) 0.26517E-3 0.26517E-3 0.00% Node 18 Y (m) (T2 Translation) 0.08839E-3 0.08839E-3 0.00% Node 2 X (m) (T1 Translation) 3.47902E-3 3.47903E-3 ~0.00% Node 2 Y (m) (T2 Translation) -5.60084E-3 -5.6004E-3 ~0.00% Articulated Plane Truss The complete model and results for this test case are in the following files: • ssll14a.neu (4 bar elements) • ssll14b.neu (10 bar elements) This test is a linear statics analysis of a straight cantilever beam with plane bending and tension–compression. It provides the input data and results for benchmark test SSLL14/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties • E = 2.1E11 Pa Finite Element Modeling Test 1 (ssll14a) • 4 bar elements • 5 nodes Test 2 (ssll14b) • 10 linear beam elements • 11 nodes The mesh for Test 1 is shown in the following figure: 204 Boundary Conditions Test 1 (ssll14a) • Constraints Nodes 1 and 4: Constrain in the X, Y, and Z translations. Nodes 2, 3, 8: Constrain in the Z translation only. • Loads Set forces and moments to the following numeric values: p = -3,000N/m (on element 4); F1 = -20,000N (on node 8); F2 = -10,000N (on node 2); M = -100,000Nm (on node 2) Test 2 (ssll14b) • Constraints Nodes 1 and 4: Constrain in the X, Y, and Z translations. Nodes 2, 3, 5-13: Constrain in the Z translation only. • Loads (ssll14b) Set forces and moments to the following numeric values: p = -3,000N/m (on elements 5-7); F1 = -20,000N (on node 8); F2 = -10,000N (on node 2); M = -100,000Nm (on node 2) The boundary conditions are shown in the following figure: Solution Type Statics 205 Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLL14/89. Node # Displacement Reaction Force Bench Value Test Number FEMAP Structural Difference 1 V vertical (Y) reaction (N) (T2 Constraint Force) 31500.0 1 2 33233.1 33233.1 5.50% 5.50% 1 horizontal (x) reaction (N) (T1 Constraint Force) 20239.4 1 2 20609.2 20609.3 1.82% 1.83% 8 Y (m) (T2 Translation) -0.03072 1 2 -0.03106 -0.03161 1.10% 2.90% Note: The software takes shear effect into account. Beam on an Elastic Foundation The complete model and results for this test case are in file ssll16.neu. This test is a linear statics analysis (plane problem) of a straight beam with plane bending and an elastic support. It provides the input data and results for benchmark test SSLL16/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties • E = 2.1E11 Pa • K = 8.4E5 N/m 2 • Each spring stiffness is set to: K*L/ (number of DOF spring elements). Finite Element Modeling • 50 bar elements • 49 DOF spring elements • 51 nodes The mesh is shown in the following figure: 207 Boundary Conditions Constraints • Nodes 1 and 51: Constrain in the X, Y, and Z translations. • Nodes 2-49: Constrain in the Z translation and X and Y rotations only. Loads • Set forces, moments, and distributed loads on element to the following numeric values: F = -10000 N (node 26) ; p = -5000 N/m (elements 1-50) ; M = 15000 Nm (node 51); M= -15000 Nm (node 1). The distributed loads are shown below: 208 The forces and moments are shown below: Solution Type Statics Results *On element 26, second end Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLL16/89. Node Displacement Force, Moment Bench Value FEMAP Structural Difference 51 rotation(rad) R z (R3 rotation) -0.003045 -0.003041 0.36% reaction force (N) Y (T2 Constraint Force) 11674 11646 0.78% 26 disp. Y (m) (T2 Translation) -0.423326E-2 -0.42270E-2 0.41% 26 M moment (Nm)* (Bar End BX3 Moment) 33840 33286 1.63% Mechanical Structures - Linear Stat- ics Analysis with Plate Elements The linear statics analysis test cases from the Societe Francaise des Mecaniciens include these plate element test cases: • "Plane Shear and Bending Load on a Plate" • "Infinite Plate with a Circular Hole" • "Uniformly Distributed Load on a Circular Plate" • "Torque Loading on a Square Tube" • "Cylindrical Shell with Internal Pressure" • "Uniform Axial Load on a Thin Wall Cylinder" • "Hydrostatic Pressure on a Thin Wall Cylinder" • "Gravity Loading on a Thin Wall Cylinder" • "Pinched Cylindrical Shell" • "Spherical Shell with a Hole" • "Uniformly Distributed Load on a Simply-Supported Rectangular Plate" • "Shear Loading on a Plate" • "Uniformly Distributed Load on a Simply-Supported Rhomboid Plate" Plane Shear and Bending Load on a Plate The complete model and results for this test case are in file sslp01.neu. This test is a linear statics analysis (plane problem) of a plate with plane bending. It provides the input data and results for benchmark test SSLP01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 100 linear quadrilateral plate elements • 126 nodes The mesh is shown in the following figure: Boundary Conditions Constraints • Nodes 121-126: Fully constrain in all translations and rotations. E 3E10 Pa = ν 0.25 = 211 Loads • Set a shear force with parabolic distribution on width and constant distribution on thickness • Resultant force: p = 40 N. The boundary conditions are shown in the following figure: Solution Type Statics Results The displacements are shown in the following figure: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLP01/89. Node # Point Coordinates Centerline Displacement Bench Value FEMAP Structural Difference 3 (L,y) Y (mm) (T2 Translation) 0.3413 0.3408 0.15% Infinite Plate with a Circular Hole The complete model and results for this test case are in file sslp02.neu. This test is a linear statics analysis (plane problem) of a plate with tension–compression and a membrane effect. It provides the input data and results for benchmark test SSLP02/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Mapped meshing (with biasing) • 100 linear quadrilateral plate elements • 121 nodes The mesh is shown in the following figure: E 3E10 Pa = ν 0.25 = 213 Boundary Conditions Constraints • Nodes 1-11: Constrain in Y translation and X and Z rotations only. • Nodes 12-110: Constrain in Z translation only. • Nodes 111-121: Constrain in X translation and Y and Z rotations only. Loads • Tension force P = 2.5 N/mm**2 (in plane force of 2500 N/m) The boundary conditions are shown in the following figure: Solution Type Statics 214 Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLP02/89. Point Coordinates Node # Stress Bench Value FEMAP Structural Difference (a,0) 1 Plate Top Y Normal Stress 7.5 7.52 0.26% 56 (N/mm**2) Plate Top Y Normal Stress 2.5 2.61 4.40% 111 Plate Top Y Normal Stress -2.5 -2.38 4.80% σ θ a π 4 --- ,     a π 2 --- ,     Uniformly Distributed Load on a Cir- cular Plate The complete model and results for this test case are in the following files: • ssls03a.neu (linear quadrilateral) • ssls03b.neu (linear triangle) This test is a linear statics analysis (three–dimensional problem) of a circular plate fixed at the edge with transverse bending and a uniform load. It provides the input data and results for benchmark test SSLS03/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (ssl03a) - Free meshing: • 38 linear quadrilateral plate elements • 50 nodes E 2.1 11 ×10 Pa = ν 0.3 = 216 Test 2 (ssl03a) - Free meshing: • 53 linear triangular plate elements • 38 nodes Only 1/4 of the plate is meshed. Boundary Conditions Constraints • Constrain node 1 in all directions except for the Z translation. • Fully constrain nodes 2-3 and nodes 15-21 in all directions. • Constrain nodes 4-8 in the X translation and Y and Z rotations. • Constrain nodes 9-13 in the Y translation and X and Z rotations. Loads • Uniform elemental pressure p = -1000 Pa. Note: Symmetric conditions are applied to the sides. 217 Test 1 boundary conditions: Solution Type Statics Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS03/89. Node # Point T3 Translation (Displacement Z) Bench Value Test Number FEMAP Structural Difference Node 1 Center O w (m) -0.0065 1 -0.0065 0.00% Node 1 Center O -0.0065 2 -0.0065 0.00% Torque Loading on a Square Tube The complete model and results for this test case are in file ssls05.neu. This test is a linear statics analysis (three–dimensional problem) of a thin–walled tube loaded in torsion by pure shear at the free end. It provides the input data and results for benchmark test SSLS05/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Mapped meshing • 160 linear quadrilateral plate elements • 176 nodes The mesh is shown in the following figure: E 2.1 11 ×10 Pa = ν 0.3 = 219 Boundary Conditions Constraints • Completely constrain nodes 1-5, 57-60, 112-115, and 167-169 in all translations and rotations. Loads • Torque equal to 10 Nm on the free end. The boundary conditions are shown in the following figure: Solution Type Statics Results Note: This translates into an equivalent nodal force of ±12.5N. Node # Displacement and Stress Bench Value FEMAP Structural Difference 193 T2 Translation (m) -0.617E-7 -0.617E-7 0.00% 193 R1 Rotation (rad) 0.123E-4 0.123E-4 0.00% 193 Plate Bottom Minor Stress (Pa) -0.11E6 -0.11E6 0.00% 208 T2 Translation (m) -0.987E-7 -0.988E-7 0.10% 208 R1 Rotation (rad) 0.197E-4 0.197E-4 0.00% 208 Plate Bottom Minor Stress (Pa) -0.11E6 -0.11E6 0.00% 220 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS05/89. Cylindrical Shell with Internal Pres- sure The complete model and results for this test are in the following files: • ssls06a.neu (linear quadrilateral, test 1) • ssls06b.neu (linear quadrilateral, test 2) This test is a linear statics analysis of the thin cylinder loaded by internal pressure. It provides the input data and results for benchmark test SSLS06/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (ssls06a) - Mapped meshing • 100 linear quadrilateral plate elements • 121 nodes E 2.1 11 ×10 Pa = ν 0.3 = 222 Test 2 (ssls06b) - Mapped meshing • 400 linear quadrilateral plate elements • 441 nodes Boundary Conditions Constraints for Test 1 (ssls06a) • Constrain node 1 in all directions except for the Y translation. • Constrain nodes 2-10 in the Z translation and X and Y rotations. • Constrain node 11 in all directions except for the X translation. • Constrain nodes 12, 23, 34, 45, 56, 67, 78, 89, 100, and 111 in the X translation and Y and Z rotations only. • Constrain nodes 22, 33, 44, 55, 66, 77, 88, 99, 110, 121 in the Y translation and X and Z rotations. Constraints for Test 2 (ssls06b) • Constrain node 1 in all directions except for the Y translation. • Constrain nodes 2-20 in the Z translation and X and Y rotations. • Constrain node 21 in all directions except for the X translation. • Constrain nodes 22, 43, 64, 85, 106, 127, 148, 169, 190, 211, 232, 253, 274, 295, 316, 337, 358, 379, 400, and 421 in the X translation and Y and Z rotations only. • Constrain nodes 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441 in the Y translation and X and Z rotations only. Loads for Test 1 and Test 2 • Internal pressure on the elements = 10000 Pa. 223 The boundary conditions are shown in the following figure: Solution Type Statics Results Node # Displacement and Stress Bench Value Test Number FEMAP Structural Difference 11 Plate Top Y Normal Stress 0.0 1 1.32 21 Plate Top Y Normal Stress 2 -0.139 111 Plate Top X Normal Stress 5.00E5 1 4.98E5 0.40% 421 σ22(Pa) Plate Top X Normal Stress 2 4.99E5 0.20% σ11 Pa ) ( ) σ11 Pa ) ( ) σ22 Pa ) ( ) σ22 Pa ) ( ) 224 All results are averages. Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS06/89. 121 T1 Translation 2.38E-6 1 2.37E-6 0.42% 441 T1 Translation 2 2.38E-6 0.00% 121 T3 Translation -1.43E-6 1 -1.42E-6 0.70% 441 T3 Translation 2 -1.43E-6 0.00% ∆R m ( ) ∆R m ( ) ∆L m ( ) ∆L m ( ) Uniform Axial Load on a Thin Wall Cylinder The complete model and results for this test are in the following files: • ssls07a.neu (parabolic quadrilateral plate, test 1) • ssls07b.neu (parabolic triangle plate, test 2) This test is a linear static analysis of a thin cylinder loaded axially. It provides the input data and results for benchmark test SSLS07/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 • Meshed by revolving a meshed beam • 200 parabolic quadrilateral plate elements E 2.1 11 ×10 Pa = ν 0.3 = 226 • 661 nodes Test 2 • Meshed by free meshing on 1/8 of a cylinder • 400 parabolic triangular plate elements Boundary Conditions Constraints • Constrain the nodes along one long edge in the Y translation and X and Z rotations. • Constrain the nodes along the other long edge in the X translation and the Y and Z rotations. • Constrain the nodes along the top short edge in the Z translation only. • Constrain node 1 in the Y and Z translations and the X and Z rotations. 227 • Constrain node 21 in the X and Z translations and Y and Z rotations. Loads • Uniform axial elemental pressures, q = 10000 N/m The boundary conditions are shown in the following figure: Solution Type Statics Results Node # Displacement and Stress Bench Value Test Number FEMAP Structural Difference 641 Plate Top Y Normal Stress 5.00E5 1 5.00E5 0.00% 641 Plate Top Y Normal Stress 5.00E5 2 5.00E5 0.00% σ11 Pa ( ) σ11 Pa ( ) 228 All results are averages. Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS07/89. 641 Plate Top X Normal Stress 0.0 1 0.0 641 Plate Top X Normal Stress 0.0 2 0.0 641 T1 Translation -7.14E-7 1 -7.14E-7 0.0% 641 T1 Translation -7.14E-7 2 -7.14E-7 0.0% 641 T3 Translation 9.52E-6 1 9.52E-6 0.0% 641 T3 Translation 9.52E-6 2 9.52E-6 0.0% σ22 Pa ( ) σ22 Pa ( ) ∆R m ( ) ∆R m ( ) ∆L m ( ) ∆L m ( ) Hydrostatic Pressure on a Thin Wall Cylinder The complete model and results for this test case are in file ssls08.neu. This test is a linear statics analysis of a thin cylinder loaded by hydrostatic pressure. It provides the input data and results for benchmark test SSLS08/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 200 parabolic quadrilateral plate elements • 661 nodes Cylinder is meshed by revolving a meshed beam. The mesh is shown in the following figure: E 2.1 11 ×10 Pa = ν 0.3 = 230 Boundary Conditions Constraints • Constrain the nodes on side A (from node 21 to node 661) in the X translation and Y and Z rotations. • Constrain the nodes on side B (from node 1 to node 641) in the Y translation,and X and Z rotation. Loads • Internal elemental pressures, p = p 0 *Z/L with p 0 =20000 Pa The boundary conditions are shown in the following figure: Solution Type Statics 231 Results ψ represents the rotation of a generator Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS08/89. Node Point Displacement and Stress Bench Value FEMAP Structural Difference Node 321 Any Plate Top Y Normal Stress 0.0 -0.0054E5 Node 321 x=L/2 Plate Top X Normal Stress 5.0E5 4.98E5 0.40% Node 321 x=L/2 T1 Translation 2.38E-6 2.38E-6 0.00% Node 1 x=L T3 Translation -2.86E-6 1.486E-6 0.00% Node 321 R2 Rotation 1.19E-6 1.19E-6 0.00% σ11 Pa ( ) σ22 Pa ( ) ∆R m ( ) ∆L m ( ) ψ rad ( ) Gravity Loading on a Thin Wall Cyl- inder The complete model and results for this test case are in file ssls09.neu. This test is a linear statics analysis of a thin cylinder loaded by its own weight. It provides the input data and results for benchmark test SSLS09/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 65 linear quadrilateral plate elements (mapped meshing) • 84 nodes E 2.1 11 ×10 Pa = ν 0.3 = γ 7.85 11 ×10 Pa = mass 8002 kg m 3 ------- = 233 The mesh is shown in the following figure: Boundary Conditions Constraints • Nodes 1, 5-16: Constrain in the Y translation and X and Z rotations. • Node 2: Constrain in all directions except for the X translation and Y rotation. • Nodes 3, 21-32: Constrain the X translation and Y and Z rotations. • Node 4: Constrain in the X and Z translations and the Y and Z rotations. • Nodes 33-36: Constrain in the Z translation only. Loads • Body load: Translational acceleration in the Z direction 234 The boundary conditions are shown in the following figure: Solution Type Statics Results Node # Point Displacement and Stress Bench Value FEMAP Structural Difference Node 2 x=0 Plate Top X Normal Stress 3.14E5 3.02E5 3.82% Node 1 Any Plate Top Y Normal Stress 0.0 -1578 to 1578 σ11 Pa ( ) σ22 Pa ( ) 235 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS09/89. Node 2 x=0 T1 Translation -4.49E-7 -4.39E-7 2.00% Node 1 x=L T3 Translation 2.99E-6 2.99E-6 0.00% Node 10 x-L R2 Rotation -1.12E-7 -1.12E-7 0.00 ∆R m ( ) z∆ m ( ) ψ rad ( ) Pinched Cylindrical Shell The complete model and results for this test case are in the following files: • ssls20a.neu (linear triangle plate) • ssls20b.neu (linear quadrilateral plate) This test is a linear statics analysis of a cylindrical shell with nodal forces, F, pinching as shown. It provides the input data and results for benchmark test SSLS20/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (ssls20a) - Free meshing • 296 linear triangle plate elements • 173 nodes E 10.5x10 6 Pa = ν 0.315 = 237 Test 2 (ssls20b) - Mapped meshing • 140 linear quadrilateral plate elements • 165 nodes Boundary Conditions Constraints • Free conditions. To set free boundary conditions, use symmetry about XY, XZ and YZ planes. • Node 1: Fully constrain except for the X translation. • Node 2, 5-13: Constrain in the Y translation and the X and Z rotations. • Node 3: Fully constrain except for the Y translation. • Node 4, 27-35: Constrain in the X translation and the Y and Z rotations. • Nodes 14-26: Constrain the Z translation and the X and Y rotations. Loads • Nodal forces F y = -25 N at point D 238 The boundary conditions are shown in the following figure: Solution Type Statics Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS20/89. Point Displacement Bench Value Test Number FEMAP Structural Difference D Displacement Y (Node 3) (T2 Translation) -113.9E-3 1 -114.4E-3 0.44% D Displacement Y (Node 3) (T2 Translation) -113.9E-3 2 -113.3E-3 0.53% Spherical Shell with a Hole The complete model and results for this test case are in the following files: • ssls21a.neu (Test 1, linear quadrilateral plate) • ssls21b.neu (Test 2, linear triangular plate) • ssls21c.neu (Test 3, parabolic quadrilateral plate) This test is a linear statics analysis of a spherical shell with a hole with nodal forces. It provides the input data and results for benchmark test SSLS21/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (ssls21a) • 100 linear quadrilateral plate elements • 121 nodes E 6.285x10 7 Pa = ν 0.3 = 240 Test 2 (ssls21b) • 200 linear triangular plate elements • 121 nodes Test 3 (ssls21c) • 100 parabolic quadrilateral plate elements • 341 nodes All tests are executed with mapped meshing. Boundary Conditions Constraints • Constrain nodes 1-11 in the X translation and Y and Z rotations. • Constrain nodes 111-121 in the Z translation and X and Y rotations. • Free condition 241 s Loads • Nodal forces F = 2 Newtons Due to the symmetric boundary conditions, only half of the load is applied. The boundary conditions are shown in the following figure: Solution Type Statics Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS21/89. Note: To set free boundary conditions, use symmetry about XY and YZ planes. Point T1 Translation u (m) Bench Value Test Number FEMAP Structural Difference A(R,0,0) node 111 94.0E-3 1 103.3E-3 9.91% node 111 94.0E-3 2 103.7E-3 10.32% node 421 94.0E-3 3 98.6E-3 4.89% Uniformly Distributed Load on a Simply-Supported Rectangular Plate The complete model and results for this test case are in the following files: • ssls24a.neu (Test 1, coarse mesh) • ssls24b.neu (Test 2, fine mesh) • ssls24c.neu (Test 3, very fine mesh) This test is a linear statics analysis of a plate with pressure loading and simple supports. It provides the input data and results for benchmark test SSLS24/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (ssls24a): length/thickness=1 • 100 linear quadrilateral plate elements E 1.0x10 7 Pa = ν 0.3 = 243 • 121 nodes Test 2 (ssls24b): length/thickness=2 • 200 linear quadrilateral plate elements • 231 nodes Test 3 (ssls24c): length/thickness=5 • 500 linear quadrilateral plate elements 244 • 561 nodes Boundary Conditions Constraints • Fully constrain node 1 in all translations and rotations. • Constrain the nodes on all edges in the Z translation only. Loads • Set pressure = 1 N/m**2 in the -Z direction 245 The boundary conditions are shown in the following figure: Solution Type Statics Results Center Node Length/ Thickne ss Parameter Bench Value Test FEMAP Structural Difference 61z direction (T3 Translation) 1.0 0.00444 1 0.00453 2.03% 116z direction (T3 Translation) 2.0 0.01110 2 0.01110 0.0% 281z direction (T3 Translation) 5.0 0.1417 3 0.01402 1.06% α α α 246 Where: q= distributed load b = dimension t = thickness E = elastic modules β values of reference from the “Guide de Validation” are incorrect. The correct values are extracted from “Formulas for Stress and Strain (Roark/Young)”. Note that the plate top surface corresponds to the side of the plate with negative global z coordinates. Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS24/89. 61x component top surface (Plate Top X Normal Stress) 1.0 2874 1 2905 1.00% 116x component top surface (Plate Top Y Normal Stress) 2.0 6102 2 6065 0.61% 281x component top surface (Plate Top Y Normal Stress) 5.0 7476 3 7332 1.93% β β α Max σ σ b βqb 2 t 2 ------------ = = Max y αqb 4 – Et 3 ---------------- = Uniformly Distributed Load on a Simply-Supported Rhomboid Plate The complete model and results for this test case are in the following files: • ssls25a.neu (Test 1) • ssls25b.neu (Test 2) This test is a linear statics analysis (three–dimensional problem) of a plate with pressure and transverse bending. It provides the input data and results for a test similar to benchmark test SSLS25/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • Length/thickness=2 • linear quadrilateral plate elements Test 1 (ssls25a) E 36.0x10 6 Pa = ν 0.3 = θ 30° = 248 Test 2 (ssls25b) Boundary Conditions Constraints • Fully constrain node 231 in all translations and rotations. • Constrain the nodes along the edges of the mesh in the Z translation. θ 45° = 249 Loads • Elemental pressure = 1 N/m**2 in the -Z direction Solution Type Statics Results Test Case Parameters Bench Center location Value FEMAP Structural Difference Test 1 ssls25a Z displacement -3.277x10E-3m Z displacement (T3 Trans- lation) at node 116 -3.137x10E-3m 4.27% ssls25a Y stress -5.70x10E3N/m 2 Y stress (Plate Top Y Nor- mal Stress) at node 116 -5.761x10E3N/m 2 1.07% Test 2 ssls25b Z displacement -3.0x10E-3m Z displacement (T3 Trans- lation) at node 116 -2.894x10E-3m 3.53% ssls25b Y stress -5.39x10E3N/m 2 Y stress (Plate Top Y Nor- mal Stress) at node 116 -5.349x10E3N/m 2 0.76% α 0.118 = θ 30° = β 0.570 = α 0.108 = θ 45° = β 0.539 = 250 Where: q= distributed load b = dimension t = thickness E = elastic modules Values of reference from the “Guide de validation” are incorrect. The correct values are extracted from “Formulas for Stress and Strain (Roark/Young),” table 26, case number 14a. Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS25/89. Max σ =βqb 2 Max y αqb 4 Et 3 ------------- = Shear Loading on a Plate The complete model and results for this test case are in the following files: • ssls27a.neu (Test 1) • ssls27b.neu (Test 2) • ssls27c.neu (Test 3) This test is a linear statics analysis of a thin plate with torque and shear loading. It provides the input data and results for benchmark test SSLS27/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (ssls27a) - Mindlin (element formulation) • 6 linear quadrilateral plate elements • 14 nodes Test 2 (ssls27b) - Kirchhoff (element formulation) • 6 linear quadrilateral plate elements E 1.0x10 7 Pa = ν 0.25 = 252 • 14 nodes Test 3 (ssls27c) - Mindlin (element formulation) • 48 linear quadrilateral plate elements • 75 nodes All tests are executed with mapped meshing. Boundary Conditions Constraints • Fully constrain the nodes on side AD in all translations and rotations. Loads • Create a nodal force Fz = -1N at point B. • Create a nodal force -Fz = 1N at point C. The boundary conditions are shown in the following figure: Solution Type Statics D A C D 253 Results at Location C Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLS27/89. Displacement Node (Total T3 Translation) Bench Value Test Number FEMAP Structural Difference 14 3.537E-2 1 5.335E-2 50.83% 14 3.537E-2 2 3.382E-2 4.38% 75 3.537E-2 3 3.750E-2 6.02% Mechanical Structures - Linear Stat- ics Analysis with Solid Elements The linear statics analysis test cases from the Societe Francaise des Mecaniciens include these solid element test cases: • "Solid Cylinder in Pure Tension" • "Internal Pressure on a Thick-Walled Spherical Container" • "Internal Pressure on a Thick-Walled Infinite Cylinder" • "Prismatic Rod in Pure Bending" • "Thick Plate Clamped at Edges" Solid Cylinder in Pure Tension The complete model and results for this test case are in the following files: • sslv01a.neu (parabolic tetrahedron, free meshing) • sslv01b.neu (linar brick, mapped meshing) • sslv01c.neu (linear quadrilateral axisymmetric solid, mapped meshing) • sslv01d.neu (linear triangular axisymmetric solid, free meshing) This test is a linear statics analysis of a solid cylinder with tension–compression. It provides the input data and results for benchmark test SSLV01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (sslv01a) - Free meshing • 155 parabolic tetrahedron elements • 342 nodes E 2.0x10 11 Pa = ν 0.30 = 256 Test 2 (sslv01b) - Mapped meshing • 192 linear brick elements • 259 nodes Test 3 (sslv01c) - Mapped meshing • 48 linear quadrilateral axisymmetric solid elements • 65 nodes Test 4 (sslv01d) - Free meshing • 28 linear triangular axisymmetric solid elements • 24 nodes 257 Boundary Conditions Constraints • Uniaxial deformation of the cylinder section Constraints (sslv01a) • Nodes 1, 17-19: Constrain in the Y and Z translations. • Nodes 2, 14-16: Constrain in the X and Z translations. • Node 3: Constrain in the X, Y, and Z translations. • Nodes 4, 59-63: Constrain in the X and Y translations. • Nodes 5, 20-22, 33-45, 200-226: Constrain in the Y translation. • Nodes 6, 23-25, 46-58, 173-199: Constrain in the X translation. • Nodes 7-13, 64-72: Constrain in the Z translation. Constraints (sslv01b) • Constrain node 1, 10,19, and 28 in the Y and Z translation. • Constrain nodes 2-8, 11-17, 20-26, and 29-35 in the Z translation. • Constrain nodes 9, 18, 27, and 36 in the X and Z translation. • Constrain node 37 in the X, Y, and Z translations. • Constrain nodes 54, 63, 72, 81, 99, 108, 117, 126, 144, 153, 162, 171, 189, 198, 207, 216, 234, 243, 252, 261, 279, 288, 297, and 306 in the X translation. • Constrain nodse 82, 127, 172, 217, and 307 in the X and Y translation. 258 • Constrain nodes 46, 55, 64, 73, 91, 100, 109, 118, 136, 145, 154, 163, 181, 190, 199, 208, 226, 235, 244, 253, 271, 280, 289, and 298 in the Y translation. Constraints (sslv01c) • Constrain nodes 13, 26, 39, and 52 in the Z translation. • Constrain node 65 in the X and Z translations. Constraints (sslv01d) • Constrain node 1 in the X and Z translation • Constrain nodes 2, 5, 6, and 7 in the Z translation. 259 Loads (all tests) • Set uniformly distributed force -F/A on the free end in the Z direction • Elemental pressure, F/A = 100 MPa Loads, Tests 1 and 2 Loads, Tests 3 and 4: Solution Type Statics Results Node # Displacements Bench Value Test # FEMAP Structural Difference 6 T3 Translation 1.5E-3 1 1.5E-3 0.00% 279 T3 Translation 1.5E-3 2 1.5E-3 0.00% 1 T3 Translation 1.5E-3 3 1.5E-3 0.00% 4 T3 Translation 1.5E-3 4 1.5E-3 0.00% 4 T3 Translation 1.5E-3 1 1.5E-3 0.00% 307 T3 Translation 1.5E-3 2 1.5E-3 0.00% 53 T3 Translation 1.5E-3 3 1.5E-3 0.00% 260 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLV01/89/89. 3 T3 Translation 1.5E-3 4 1.5E-3 0.00% 37 T3 Translation 1E-3 1 1E-3 0.00% 189 T3 Translation 1E-3 2 1E-3 0.00% 5 T3 Translation 1E-3 3 1E-3 0.00% 25 T3 Translation 1E-3 4 1E-3 0.00% 41 T3 Translation 0.5E-3 1 0.5E-3 0.00% 99 T3 Translation 0.5E-3 2 0.5E-3 0.00% 9 T3 Translation 0.5E-3 3 0.5E-3 0.00% 29 T3 Translation 0.5E-3 4 0.5E-3 0.00% 6 T2 Translation -0.15E-3 1 -0.15E-3 0.00% 279 T2 Translation -0.15E-3 2 -0.15E-3 0.00% 1 T1 Translation -0.15E-3 3 -0.15E-3 0.00% 4 T1 Translation -0.15E-3 4 -0.15E-3 0.00% 37 T1 Translation -0.15E-3 1 -0.15E-3 0.00% 189 T1 Translation -0.15E-3 2 -0.15E-3 0.00% 5 T2 Translation -0.15E-3 3 -0.15E-3 0.00% 25 T1 Translation -0.15E-3 4 -0.15E-3 0.00% 41 T1 Translation -0.15E-3 1 -0.15E-3 0.00% 99 T2 Translation -0.15E-3 2 -0.15E-3 0.00% 9 T1 Translation -0.15E-3 3 -0.15E-3 0.00% 29 T1 Translation -0.15E-3 4 -0.15E-3 0.00% Internal Pressure on a Thick-Walled Spherical Container The complete model and results for this test case are in the following files: • sslv03a.neu (Test 1, linear solids) • sslv03b.neu (Test 2, parabolic solids) • sslv03c.neu (Test 3, linear axisymmetric solids) • sslv03d.neu (Test 4, parabolic axisymmetric solids) This test is a linear statics analysis of a thick sphere with internal pressure. It provides the input data and results for benchmark test SSLV03/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (sslv03a) - Mapped meshing • 1600 linear brick elements E 2.0x10 5 Pa = ν 0.30 = 262 • 1898 nodes Test 2 (sslv03b) - Mapped meshing • 250 parabolic brick elements • 1256 nodes Test 3 (sslv03c) - Mapped meshing • 400 linear quadrilateral axisymmetric solid elements 263 • 451 nodes Test 4 (sslv03d) - Mapped meshing • 400 parabolic quadrilateral axisymmetric solid elements • 1301 nodes Boundary Conditions Constraints • The equivalent of the center of the sphere being fixed is modeled via symmetric boundary conditions. Constraints - Tests 1 and 2: 264 Constraints - Tests 3 and 4: Loads • Uniform radial elemental pressure = 100 MPa The boundary conditions are shown in the following figure: Pressure -Tests 1 and 2: Pressure - Tests 3 and 4: 265 Solution Type Statics Results Results for Point R = 1m Point Node # Displacement Stress Bench Value Test Number FEMAP Structural Difference r=1 m 1 Solid Z Normal Stress -100 1 -90.07 9.93% 1 Solid Z Normal -100 2 -104.33 4.33% 41 Axisym C1 Radial Stress -100 3 -95.50 4.50% 41 Axisym C1 Radial Stress -100 4 -94.81 5.19% 1 Solid Y Normal Stress 71.43 1 72.04 0.85% 1 Solid Y Normal Stress 71.43 2 73.70 3.18% 41 Axisym C1 Azi- muth Stress 71.43 3 69.20 3.12% 41 Axisym C1 Azi- muth Stress 71.43 4 69.50 2.70% 1 u (m) T3 Translation 0.4E-3 1 0.40E-3 0.00% σ Π MPa ( ) σ θ MPa ( ) σ θ MPa ( ) σ θ MPa ( ) σ θ MPa ( ) 266 Results for Point R = 2m 1 u (m) T3 Translation 0.4E-3 2 0.40E-3 0.00% 41 u (m) T3 Translation 0.4E-3 3 0.41E-3 2.50% 41 u (m) T3 Translation 0.4E-3 4 0.40E-3 0.00% Point Node # Displacement Stress Bench Value Test Number FEMAP Structural Difference r=2 m 1826 Solid Z Normal Stress 0 1 -.041 N/A 2221 Solid Z Normal Stress 0 2 -.649 N/A 1 Axisym C1 Radial Stress 0 3 -.233 N/A 1 Axisym C1 Radial Stress 0 4 -.430 N/A 1826 Solid Y Normal Stress 21.43 1 21.18 1.16% 2221 Solid Y Normal Stress 21.43 2 21.76 1.53% 1 Axisym C1 Radial Stress 21.43 3 21.39 0.19% 1 Axisym C1 Radial Stress 21.43 4 21.58 0.70% σ Π MPa ( ) σ Π MPa ( ) σ θ MPa ( ) σ θ MPa ( ) 267 All results are averaged. Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLV03/89. 1826 u (m) T3 Translation 1.5E-4 1 1.50E-4 0.00% 2221 u (m) T3 Translation 1.5E-4 2 1.50E-4 0.00% 1 u (m) T3 Translation 1.5E-4 3 1.53E-4 2.00% 1 u (m) T3 Translation 1.5E-4 4 1.50E-4 0.00% Internal Pressure on a Thick-Walled Infinite Cylinder The complete model and results for this test case are in the following files: • sslv04a.neu (solid, linear brick) • sslv04b.neu (solid, parabolic brick) • sslv04c.neu (solid, axisymmetric quadrilateral) • sslv04d.neu (solid, axisymmetric parabolic) This test is a linear statics analysis of a thick cylinder with internal pressure. It provides the input data and results for benchmark test SSLV04/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling All tests are executed with mapped meshing. Test 1 (sslv04a) - Mapped meshing • 400 solid (linear brick) elements • 902 nodes Test 2 (sslv04b) - Mapped meshing • 240 solid (parabolic brick) elements • 1873 nodes E 2.0x10 5 Pa = ν 0.30 = 269 FE Model - Tests 1 and 2: Test 3 (sslv04c) - Mapped meshing • 600 axisymmetric (linear quadrilateral solid) elements • 656 nodes Test 4 (sslv04d) - Mapped meshing • 600 axisymmetric (parabolic quadrilateral solid) elements • 1911 nodes FE Model - Tests 3 and 4: Boundary Conditions Constraints (sslv04a) • Nodes 1-41, 452-492: Constrain in the X translation. • Nodes 411-451, 862-902: Constrain in the Z translation. 270 Constraints (sslv04b) • Nodes 1-61, 1038-1098, 2075-2135: Constrain in the X translation. • Nodes 977-1037, 2014-2074, 3051-3111: Constrain in the Z translation. Constraints (sslv04c) • Nodes 1-41: Constrain in the Z translation. Constraints (sslv04d) • Nodes 1-81: Constrain in the Z translation. Loads (all tests) • Unlimited cylinder • Internal elemental pressure p = 60 MPa Boundary Conditions - Tests 1 and 2: Boundary Conditions - Tests 3 and 4: 271 Solution Type Statics Results All results are averaged. Results for R=0.1m Test Case Point Displacement Stress Bench Value Node # FEMAP Structural Difference sslv04a r=0.1 m Solid X Normal Stress -60 411 -57.07 4.88% sslv04b Solid X Normal Stress -60 977 -60.97 1.62% sslv04c Axisymm C1 Radial Stress -60 616 -58.03 3.28% sslv04d Axisymm C1 Radial Stress -60 1831 -59.98 0.03% sslv04a Solid Z Normal Stress 100 411 99.69 0.31% sslv04b Solid Z Normal Stress 100 977 100.98 0.98% sslv04c Axisymm C1 Azi- muth Stress 100 616 100.77 0.77% sslv04d Axisymm C1 Azi- muth Stress 100 1831 99.98 0.02% sslv04a Solid Max Shear Stress 80 411 79.35 0.81% σ r MPa ( ) σ θ MPa ( ) σ θ MPa ( ) τ max MPa ( ) 272 Results for R=0.2m sslv04b Solid Max Shear Stress 80 977 80.97 1.21% sslv04a u (m) T1 Translation 59E-6 411 59E-6 0.00% sslv04b T1 Translation 59E-6 977 59E-6 0.00% sslv04c T1 Translation 59E-6 616 59E-6 0.00% sslv04d T1 Translation 59E-6 1831 59E-6 0.00% Test Case Point Displacement Stress Bench Value Node # FEMAP Structural Difference sslv04a r=0.2m Solid X Normal Stress 0 451 -.006 NA sslv04b Solid X Normal Stress 0 1037 -.250 NA sslv04c Axisymm C1 Radial Stress 0 656 -.253 NA sslv04d Axisymm C1 Radial Stress 0 1911 .002 NA sslv04a Solid Z Normal Stress 40 451 39.70 0.75% sslv04b Solid Z Normal Stress 40 1037 40.25 0.62% sslv04c Axisymm C1 Axi- muth Stress 40 656 40.61 1.53% sslv04d Axisymm C1 Axi- muth Stress 40 1911 39.90 0.25% sslv04a Solid Max Shear Stress 20 451 20.10 0.50% σ r MPa ( ) σ θ MPa ( ) τ max MPa ( ) 273 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLV04/89. sslv04b Solid Max Shear Stress 20 1037 20.25 1.25% sslv04a u (m) T1 Translation 40E-6 451 40E-6 0.00% sslv04b T1 Translation 40E-6 1037 40E-6 0.00% sslv04c T1 Translation 40E-6 656 39.9E-6 0.25% sslv04d T1 Translation 40E-6 1911 40E-6 0.00% Prismatic Rod in Pure Bending The complete model and results for this test case are in the following files: • sslv08a.neu (Test 1, solid elements, linear tetrahedrons) • sslv08b.neu (Test 2, solid elements, parabolic tetrahedrons) • sslv08c.neu (Test 3, solid elements, linear bricks) • sslv08d.neu (Test 4 solid elements, parabolic bricks) This test is a linear statics analysis of a solid rod with bending. It provides the input data and results for benchmark test SSLV08/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 (sslv08a) - Free meshing • 198 solid (linear tetrahedron) elements • 76 nodes Test 2 (sslv08b) - Free meshing • 198 solid (parabolic tetrahedron) elements • 409 nodes E 2.0x10 5 Pa = ν 0.30 = 275 FE Model - Tests 1 and 2: Test 3 (sslv08c) - Mapped meshing • 48 solid (linear brick) elements • 117 nodes Test 4 (sslv08d) - Mapped meshing • 48 solid (parabolic brick) elements • 381 nodes FE Model - Tests 3 and 4: Boundary Conditions Constraints (sslv08a) • Nodes 29, 33: Constrain in the X and Z translations. • Nodes 30-32, 34, 39, 40: Constrain in the Z translation. • Node 57: Constrain in the X, Y, and Z translations. 276 Constraints (sslv08b) • Nodes 127, 131: Constrain in the X and Z translations. • Nodes 128-130, 132-146, 188-195: Constrain in the Z translation only. • Node 187: Constrain in the X, Y, and Z translations. Constraints (sslv08c) • Nodes 1-4, 6-9: Constrain in the Z translation. • Node 5: Constrain in the X, Y, and Z translations. Constraints (sslv08d) • Nodes 1-8, 10, 12, 14-21: Constrain in the Z translation. • Nodes 9, 13: Constrain in the X translation. • Nodes 11: Constrain in the X, Y, and Z translations. Loads (all tests) • Set moment M x equal to (4/3)E+7 N.m Boundary Conditions - Tests 1 and 2: 277 Boundary Conditions - Tests 3 and 4: Solution Type Statics Results Test # Node # Displacement/ Stress Bench Value FEMAP Structural Difference 1 5 Solid Z Normal Stress (Pa) -10E6 -4.268E6 57.00% 2 5 Solid Z Normal Stress (Pa) -10E6 10.03E6 0.30% 3 75 Solid Z Normal Stress (Pa) -10E6 10.07E6 0.70% 4 245 Solid Z Normal Stress (Pa) -10E6 10.01E6 0.10% 1 26 T2 Translation 4E-4 2.964E-4 26.00% 2 90 T2 Translation 4E-4 4E-4 0.00% 3 77 T2 Translation 4E-4 4E-4 0.00% 4 251 T2 Translation 4E-4 4.044E-4 1.10% 1 19 T3 Translation 2E-4 1.460E-4 27.00% 2 40 T3 Translation 2E-4 2E-4 0.00% 3 76 T3 Translation 2E-4 2E-4 0.00% 4 249 T3 Translation 2E-4 2.010E-4 0.50% 1 5 T1 Translation 0.15E-4 7.449E-6 50.34% 2 5 T1 Translation 0.15E-4 0.1514E-4 0.93% 3 75 T1 Translation 0.15E-4 0.1480E-4 1.33% 4 245 T1 Translation 0.15E-4 0.1511E-4 0.73% 278 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLV08/89. 1 8 T1 Translation -0.15E-4 -6.2620E-6 58.20% 2 8 T1 Translation -0.15E-4 -0.1509E-4 0.60% 3 73 T1 Translation -0.15E-4 -0.1480E-4 1.33% 4 241 T1 Translation -0.15E-4 -0.1511E-4 0.73% Thick Plate Clamped at Edges The complete model and results for this test case are in the following files: • sslv09a10.neu (Test 1, parabolic brick, length/thickness =10) • sslv09a20.neu (Test 1, parabolic brick, length/thickness =20) • sslv09a50.neu (Test 1, parabolic brick, length/thickness =50) • sslv09a75.neu (Test 1, parabolic brick, length/thickness =75) • sslv09a100.neu (Test 1, parabolic brick, length/thickness =100) • sslv09b10.neu (Test 2, linear plate, length/thickness =10) • sslv09b20.neu (Test 2, linear plate, length/thickness =20) • sslv09b50.neu (Test 2, linear plate, length/thickness =50) • sslv09b75.neu (Test 2, linear plate, length/thickness =75) • sslv09b100.neu (Test 2, linear plate, length/thickness =100) This test is a linear statics analysis of a square thick plate with pressure and transverse bending. It provides the input data and results for benchmark test SSLV09/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Test 1 - Mapped meshing • 25 parabolic brick elements • 228 nodes E 2.1x10 11 Pa = ν 0.30 = 280 • length/thickness =10, 20, 50, 75, 100 Test 2 - Mapped meshing • 25 linear quadrilateral plate elements • 36 nodes • length/thickness =10, 20, 50, 75, 100 Test 2 is done using plate elements with the following thickness values: • length/thickness =10, t=0.1 • length/thickness =20, t=0.05 • length/thickness =50, t=0.02 • length/thickness =75, t=0.01333 • length/thickness =100, t=0.01 281 Boundary Conditions Constraints – Test 1 • Fully constrain the nodes on edges AB, A’B’, AD, and A’D’ in all translations and rotations. • Constrain the nodes on edge BC and B’C’ in the X translation and Y and Z rotations. • Constrain the corner nodes at C and C’ in all translations and rotations except for the Z translation. • Constrain the nodes on edge DC and D’C’ in the Y translation and X and Z rotations. Constraints – Test 2 • Fully constrain the nodes on edges AB and AD in all translations and rotations. • Constrain the nodes on edge BC in the X translation and Y and Z rotations. • Constrain the corner nodes at C in all translations and rotations except for the Z translation. • Constrain the nodes on edge DC in the Y translation and X and Z rotations. Loads • Load case 1: Elemental pressure p = 1E6 Pascals in -Z direction • Load case 2: Point C Nodal force F = 2.5E5 N in -Z direction Boundary conditions for Test 1: 282 Boundary conditions for Test 2: Solution Type Statics Results Test Case 1 (T3 Translation at location C) File Name Length/ Thick- ness Load Case Node # Analytical Reference FEM FEMAP Structural Difference sslv09a10 10 Pressure 242 -.6552E-4 -.76231E-4 -.735942E-4 12.32% sslv09a10 10 Force 242 -.29146E-3 -.42995E-3 -.426662E-3 46.38% sslv09a20 20 Pressure 242 -.52416E-3 -.53833E-3 -.523376E-3 0.15% sslv09a20 20 Force 242 -.23317E-2 -.25352E-2 -.242500E-2 4.00% sslv09a50 50 Pressure 242 -.81900E-2 -.80286E-2 -.778247E-2 4.98% sslv09a50 50 Force 242 -.36433E-1 -.35738E-1 -.346276E-1 4.96% sslv09a75 75 Pressure 242 -.27641E-1 -.26861E-1 -.259820E-1 6.00% sslv09a75 75 Force 242 -.12296 -.11837 -.114411 6.95% sslv09a100 100 Pressure 242 -.65520E-1 -.63389E-1 -.612191E-1 6.56% sslv09a100 100 Force 242 -.29146 -.27794 -.268120 8.00% 283 Test Case 2 (T3 Translation at location C) Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLV09/89. Part Name Length/ Thick- ness Load Case Node # Analytical Reference FEM FEMAP Structural Difference sslv09b10 10 Pressure 1 -.6552E-4 -.78661E-4 -.797294E-4 21.69% sslv09b10 10 Force 1 -.29146E-3 -.41087E-3 -.395973E-3 35.86% sslv09b20 20 Pressure 36 -.52416E-3 -.55574E-3 -.564973E-3 8.69% sslv09b20 20 Force 36 -.23317E-2 -.25946E-2 -.260199E-2 11.59% sslv09b50 50 Pressure 36 -.81900E-2 -.83480E-2 -.849953E-2 3.78% sslv09b50 50 Force 36 -.36433E-1 -.37454E-1 -.381471E-1 4.70% sslv09b75 75 Pressure 36 -.27641E-1 -.28053E-1 -.285676E-1 3.35% sslv09b75 75 Force 36 -.12296 -.12525 -.127845 3.97% sslv09b10 0 100 Pressure 1 -.65520E-1 -.66390E-1 -.676175E-1 3.20% sslv09b10 0 100 Force 1 -.29146 -.29579 -.302292 3.72% Mechanical Structures - Normal Modes/Eigenvalue Analysis The normal modes/eigevanlues test cases from the Societe Francaise des Mecaniciens include: • "Lumped Mass-Spring System" • "Short Beam on Simple Supports" • "Axial Loading on a Rod" • "Thin Circular Ring" • "Cantilever Beam with a Variable Rectangular Section" • "Thin Circular Ring Clamped at Two Points" • "Vibration Modes of a Thin Pipe Elbow" • "Cantilever Beam with Eccentric Lumped Mass" • "Thin Square Plate (Clamped or Free)" • "Simply-Supported Rectangular Plate" • "Thin Ring Plate Clamped on a Hub" • "Vane of a Compressor - Clamped-free Thin Shell" • "Bending of a Symmetric Truss" • "Hovgaard’s Problem - Pipes with Flexible Elbows" • "Rectangular Plates" Lumped Mass-Spring System The complete model and results for this test case are in file sdld02.neu. This test is a normal modes/eigenvalue analysis of an elastic link with lumped mass. It provides the input data and results for benchmark test SDLD02/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Spring constant Finite Element Modeling • 8 mass elements • 9 DOF springs • 8 nodes The mesh is shown in the following figure: Boundary Conditions Constraints • Constrain all the nodes (1-8) in all translations and rotations except for the X translation. 286 The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI method Results The mode shapes results are exact. The multiplication coefficient is 0.4642 for mode 1 and - 0.4642 for mode 8. Frequency Results: Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 1 5.5274 5.5274 0.00% 2 10.8868 10.8868 0.00% 3 15.9155 15.9155 0.00% 4 20.4606 20.4606 0.00% 5 24.3840 24.3840 0.00% 6 27.5664 27.5664 0.00% 7 29.9113 29.9113 0.00% 8 31.3474 31.3474 0.00% 287 Mode Shapes Results: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLD02/89, p. 178. Normal Mode Point Bench Value FEMAP Structural 1 P1 0.1612 0.3473 1 P2 0.3030 0.6527 1 P3 0.4082 0.8794 1 P4 0.4642 1.0000 1 P5 0.4642 1.0000 1 P6 0.4082 0.8794 1 P7 0.3030 0.6527 1 P8 0.1612 0.3473 8 P1 0.1612 -0.3473 8 P2 -0.3030 0.6527 8 P3 0.4082 -0.8794 8 P4 -0.4642 1.0000 8 P5 0.4642 -1.0000 8 P6 -0.4082 0.8794 8 P7 0.3030 -0.6527 8 P8 -0.1612 0.3473 Short Beam on Simple Supports The complete model and results for this test case are in the following files: • sdll01a.neu • sdll01b.neu This test is a modal analysis of a straight short beam with simple supports both inline and offset. It provides the input data and results for benchmark test SDLL01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Problem 1 (sdll01a) • 10 bar elements • 11 nodes E 2x10 11 Pa = ν 0.3 = ρ 7800 kg m 3 ------- = 289 Problem 2 (sdll01b) • 10 bar elements • 2 rigid elements (master node 4 to slave node 2; master node 3 to slave node 1) Boundary Conditions Constraints • Node 1: Constrain in all directions and rotations, except the Z rotation. • Node 2: Constrain in all directions and rotations, except for the X translation and Z rotation. • Constrain all other nodes in the Z translation and the X and Y rotations. Loads • no load case The boundary conditions for both problems are shown in the following figure: 290 Solution Type Normal Modes/Eigenvalue – SVI method Results Problem 1: Frequency Results Problem 2: Frequency Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLL01/89. Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference Bending 1 431.555 431.555 0.03% Tension 1 1265.924 1267.226 0.10% Bending 2 1498.295 1503.171 0.33% Bending 3 2870.661 2904.096 1.16% Tension 2 3797.773 3833.003 0.93% Bending 4 4377.837 4493.912 2.65% Mode number Bench Value (Hz) FEMAP Structural (Hz) Difference 1 392.8 394.3 0.38% 2 902.2 922.4 2.24% 3 1591.9 1641.0 3.08% 4 2629.2 2800.0 6.50% 5 3126.2 3291.2 5.28% Axial Loading on a Rod The complete model and results for this test case are in the following file: • sdll05a.neu • sdll05b.neu This test is a modal analysis of a simply–supported beam with stress stiffening. It provides the input data and results for benchmark test SDLL05/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 10 bar elements • 11 nodes The mesh is shown in the following figure: E 2x10 11 Pa = ρ 7800 kg m3 -------- = 292 Boundary Conditions Problem 1 (sdll05a): • Node 1: Leave the Z rotation free and constrain the node in all other translations and rotations. • Node 2 : Leave the X translation and Z rotation free and constrain in all other translations and rotations. Problem 2 (sdll05b): • Node 1: Leave the Z rotation free and constrain the node in all other translations and rotations. • Node 2: Leave the X translation and Z rotation free and constrain the node in all other translations and rotations. • Load Set 1 (node 2): Define a nodal force = to 1E5N in the -X direction. Ensure that Stress Stiffening is turned on in the analysis set. Solution Type Normal Modes/Eigenvalue - SVI method 293 Results Frequency Results: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLL05/89. Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference sdll05a Mode 1 28.702 28.672 0.10% sdll05a Mode 3 114.807 114.351 0.40% sdll05b Mode 1 22.434 22.399 0.16% sdll05b Mode 3 109.080 108.61 0.43% Cantilever Beam with a Variable Rectangular Section The complete model and results for this test case are in the following file: sdll09a.neu This test is a modal analysis of a straight cantilever beam with a variable section. It provides the input data and results for benchmark test SDLL09/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 10 beam elements (tapered) • 11 nodes b0 b1 β b0 b1 ------ = E 2x10 11 Pa = ρ 7800 kg m3 -------- = 295 The mesh is shown in the following figure: Boundary Conditions • Constrain node 1 in all directions. • Constrain all other nodes in the Z translation and X and Y rotations only. • no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI method 296 Results Frequency Results Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLL09/89. Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 4 1 54.18 54.13 0.09% 2 171.94 171.36 0.34% 3 384.40 381.70 0.70% 4 697.24 688.89 1.20% 5 1112.28 1092.92 1.74% β Thin Circular Ring The complete model and results for this test case are in file sdll11.neu. This test is a modal analysis of a thin curved beam. It provides the input data and results for benchmark test SDLL11/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 36 bar elements • 36 nodes The mesh is shown in the following figure: E 7.2x10 10 Pa = ν 0.3 = ρ 2700 kg m 3 ------- = 298 Boundary Conditions Constraints • Unconstrained (free) conditions • Create 1 constraint set (Kinematic DOF set) to fully constrain the 3 nodes shown below (nodes 7, 21, 30). Loads • no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI method Results Frequency Results Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference Modes 1-6 0 0 0.00% Modes 7, 8 318.36 318.99 0.20% Modes 9, 10 511 508 0.59% Modes 11, 12 900.46 900.19 0.03% Modes 13, 14 1590 1569 1.32% 299 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLL11/89. Modes 15, 16 1726.55 1721.56 0.29% Modes 17, 18 2792.21 2774.91 0.62% Modes 19, 20 3184 3116 2.14% Thin Circular Ring Clamped at Two Points The complete model and results for this test case are in file sdll12.neu. This test is a modal analysis of a thin curved beam. It provides the input data and results for benchmark test SDLL12/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 29 bar elements • 29 nodes The mesh is shown in the following figure: E 7.2x10 10 Pa = ν 0.3 = ρ 2700 kg m 3 ------- = 301 Boundary Conditions • Points A and B (nodes 1 and 2): Fully constrained in all directions • All other nodes: Constrained the Z translation and X and Y rotations only. • no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI method Results Frequency Results Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 1 235.3 235.9 0.25% 2 575.3 575.1 0.03% 3 1105.7 1102.7 0.27% 4 1405.6 1398.0 0.54% 5 1751.1 1740.8 0.59% 6 2557.0 2536.6 0.80% 7 2801.5 2723.0 2.80% 302 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLL12/89. Vibration Modes of a Thin Pipe Elbow The complete model and results for this test case are in the following files: • sdll014a.neu • sdll014b.neu • sdll014c.neu This test is a modal analysis of a straight cantilever beam, and a thin curved beam. It provides the input data and results for benchmark test SDLL14/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI A D C B L L 304 Material Properties Finite Element Modeling Problem 1 (sdll14a) where L=0 and Problem 2 (sdll14b) where L=0.6: • 18 bar elements • 19 nodes Problem 3 (sdll14c) where L=2: • 28 bar elements • 29 nodes The FE model is shown below: E 2.1x10 11 Pa = ν 0.3 = ρ 7800 kg m 3 ------- = 305 Boundary Conditions Problem 1 (sdll14a): • Fully constrain points C and D (nodes 1 and 2) in all translations and rotations. Problem 2 (sdll14b) and Problem 3 (sdll14c): • Fully constrain points C and D (nodes 1 and 4) in all translations and rotations. • Constrain point B (node 2) in the X and Z translations. • Constrain point C (node 3) in the Y and Z translations. Solution Type Normal Modes/Eigenvalue - SVI method 306 Results Problem 1 (sdll14a) Frequency Results: Problem 2 (sdll14b) Frequency Results: Problem 3 (sdll14c) Frequency Results: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLL14/89. L Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 0 1 44.23 44.11 0.27% 2 119 119 0.00% 3 125 126 0.80% 4 227 225 0.88% L Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 0.6 1 33.4 33.3 0.30% 2 94 94 0.00% 3 100 99 1.00% 4 180 184 2.22% L Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 2 1 17.9 17.7 1.12% 2 24.8 24.4 1.61% 3 25.3 24.9 1.58% 4 27 26.67 0.01% Cantilever Beam with Eccentric Lumped Mass The complete model and results for this test case are in the following files: • sdll15a.neu • sdll15b.neu This test is a modal analysis of a straight cantilever beam and a mass element. It provides the input data and results for benchmark test SDLL15/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Problem 1 (sdll15a) • 10 bar elements • 1 mass element at point B • 11 nodes E 2.1x10 11 Pa = ρ 7800 kg m 3 ------- = A B 308 Problem 2 (sdll15b) • 10 bar elements • 1 rigid element from point B to point C • 1 mass element at point C • 12 nodes Boundary Conditions Constraints: • Fully constrain point A (node 1) in all translations and rotations. Solution Type Normal Modes/Eigenvalue - SVI A B C 309 Results Frequency Results: Mode Shapes Results: • wc=T3 translation at point C • wb= T3 translation at point B • uc=T1 translation at point C • vb= T2 translation at point B yc Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 0 1,2 1.65 1.65 0.00% 3,4 16.07 15.91 1.00% 5,6 50.02 48.75 2.54% 7 76.47 76.48 0.01% 8 80.47 80.84 0.46% 9,10 103.20 98.53 4.53% 1 1 1.636 1.635 0.06% 2 1.642 1.640 0.12% 3 13.46 13.37 0.67% 4 13.59 13.52 0.52% 5 28.90 28.68 0.76% 6 31.96 31.54 1.31% 7 61.61 59.97 2.66% 8 63.93 61.82 3.30% yc Normal Mode Modal Displacement Bench Value FEMAP Structural Difference 1 1 wc/wb 1.030 1.030 0.00% 2 uc/vb 0.148 0.148 0.00% 3 uc/vb 2.882 2.845 1.28% 4 wc/wb -0.922 -0.956 3.69% 310 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLL15/89. Thin Square Plate (Clamped or Free) The complete model and results for this test case are in the following files: • sdls01a.neu • sdls01b.neu This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a thin plate. It provides the input data and results for benchmark test SDLS01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 100 linear quadrilateral plate elements • 121 nodes The mesh is shown in the following figure: E 2.1x10 11 Pa = ν 0.3 = ρ 7800 kg m 3 ------- = A D B C 312 Boundary Conditions • Problem 1 (sdls01a): Constrain the nodes along side BC in all translations and rotations. • Problem 2 (sdls01b) : Free plate; Create a constraint set (Kinematic DOF set) to constrain the three nodes shown below (nodes 1, 11, and 111) in all translations and rotations. Solution Type Normal Modes/Eigenvalue - SVI method Results Problem 1 (sdls01a) Frequency Results: Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 1 8.7266 8.6719 0.63% 2 21.3042 21.1474 0.74% 3 53.5542 53.9586 0.76% 313 Problem 2 (sdls01b) Frequency Results: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLS01/89. 4 68.2984 68.4467 0.21% 5 77.7448 77.7814 0.05% 6 136.0471 135.783 0.19% Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 7 33.7119 32.9104 2.38% 8 49.4558 47.4165 4.12% 9 61.0513 59.1873 3.05% 10,11 87.5160 83.0785 5.07% Simply-Supported Rectangular Plate The complete model and results for this test case are in file sdls03.neu. This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a thin plate. It provides the input data and results for benchmark test SDLS03/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 150 linear quadrilateral plate elements • 176 nodes The mesh is shown in the following figure: E 2.1x10 11 Pa = ν 0.3 = ρ 7800 kg m 3 ------- = 315 Boundary Conditions • Constrain the Z translation of the nodes on all sides of the plate. • Create a constraint set to define the Master (ASET) DOFs on nodes 47, 55, 119. Con- strain these nodes in all directions except for the Z translation. • no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI method Results Frequency Results: Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 4 35.63 35.21 1.18% 5 68.51 67.21 1.90% 6 109.62 108.96 0.60% 7 123.32 121.13 1.78% 8 142.51 138.30 2.95% 9 197.32 187.94 4.75% 316 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLS03/89. Thin Ring Plate Clamped on a Hub The complete model and results for this test case are in file sdls04.neu. This test is a normal modes/eigenvalue analysis (three–dimensional problem) of an annular thin plate. It provides the input data and results for benchmark test SDLS04/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Mapped meshing • 400 linear quadrilateral plate elements • 440 nodes The mesh is shown in the following figure: E 2.1x10 11 Pa = ν 0.3 = ρ 7800 kg m 3 ------- = 318 Boundary Conditions Constraints • Fully constrain all the nodes on the inner ring as shown below. Loads • no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue – SVI Results Frequency Results: Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 1 79.26 79.41 0.19% 2, 3 81.09 81.05 0.05% 4, 5 89.63 89.64 0.01% 6, 7 112.79 113.45 0.58% 8, 9 not available 158.38 10, 11 not available 226.02 12, 13 not available 317.04 14, 15 not available 433.04 16, 17 not available 527.51 18 518.85 532.19 2.57% 319 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLS04/89. 19, 20 528.61 561.91 6.30% 21, 22 559.09 576.90 3.18% 23 609.70 612.63 0.48% Vane of a Compressor - Clamped- free Thin Shell The complete model and results for this test case are in the following files: • sdls05a.neu (linear quadrilateral, coarse mesh) • slds05b.neu (linear quadrilateral, fine mesh) This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a cylindrical thin shell. It provides the input data and results for benchmark test SDLS05/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling - Coarse Mesh Mapped meshing • 100 linear quadrilateral plate elements • 121 nodes E 2.0685x10 11 Pa = ν 0.3 = ρ 7857.2 kg m 3 ------- = 321 The coarse mesh is shown in the following figure: Finite Element Modeling - Fine Mesh Mapped Meshing • 225 linear quadrilateral plate elements • 256 nodes The fine mesh is shown in the following figure: 322 Boundary Conditions Fully constrain the nodes on one side as shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI method Results Frequency Results: Reference Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLS05/89. Normal Mode Bench Value (Hz) FEMAP Structural coarse mesh (Hz) FEMAP Structural fine mesh (Hz) 1 85.6 85.6 85.7 2 134.5 138.2 138.3 3 259.0 249.8 248.0 4 351.0 345.9 343.7 5 395.0 386.5 386.0 6 531.0 549.8 537.7 Bending of a Symmetric Truss The complete model and results for this test case are in file sdlx01.neu. This test is a normal modes/eigenvalue analysis (plane problem) of a straight cantilever beam structure. It provides the input data and results for benchmark test SDLX01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 24 bar elements • 24 nodes The mesh is shown in the following figure: E 2.1x10 11 Pa = ν 0.3 = ρ 7800 kg m 3 ------- = 324 Boundary Conditions Constraints • Fully constrain nodes 1 and 4 in all translations and rotations. • Constrain nodes 2-3 and 5-24 in the Z translation and X and Y rotations. The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue – SVI Results Frequency Results: Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 1 8.8 8.8 0.00% 2 29.4 29.4 0.00% 3 43.8 43.8 0.00% 4 56.3 56.3 0.00% 5 96.2 96.2 0.00% 6 102.6 102.7 0.10% 7 147.1 147.4 0.20% 8 174.8 175.3 0.29% 9 178.8 179.3 0.28% 325 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLX01/89. 10 206.0 206.9 0.44% 11 266.4 268.1 0.64% 12 320.0 322.4 0.75% 13 335.0 338.7 1.10% Hovgaard’s Problem - Pipes with Flexible Elbows The complete model and results for this test case are in file sdlx02.neu. This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a straight, thin curved cantilever beam. It provides the input data and results for benchmark test SDLX02/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Material Properties Units SI Finite Element Modeling • 25 bar elements • 26 nodes The mesh is shown in the following figure: E 1.658x · 10 11 Pa = ν 0.3 = ρ 13404.106 kg m 3 ------- = 327 Boundary Conditions • Fully constrain nodes 1 and 6 in all translations and rotations. The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI Results Frequency Results: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLX02/89. Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 1 10.18 10.40 2.16% 2 19.54 19.87 1.69% 3 25.47 25.36 0.43% 4 48.09 47.71 0.79% 5 52.86 51.80 2.01% 6 75.94 82.84 9.09% 7 80.11 85.20 6.35% 8 122.34 125.53 2.61% 9 123.15 127.64 3.65% Rectangular Plates The complete model and results for this test case are in file sdlx03.neu. This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a thin plate with rigid body modes. It provides the input data and results for benchmark test SDLX03/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 300 linear quadrilateral plate elements • 320 nodes The mesh is shown in the following figure: E 2.1x · 10 11 Pa = ν 0.3 = ρ 7800 kg m 3 ------- = 329 Boundary Conditions Constraints • Constraint Set 1 (Kinematic DOF Set): Fully constrain nodes 2, 69, and 84 in all translations and rotations. The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue - SVI Results Frequency Results: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SDLX03/89. Normal Mode Bench Value (Hz) FEMAP Structural (Hz) Difference 7 584 586 0.34% 8 826 824 0.24% 9 855 854 0.11% 10 911 904 0.76% 11 1113 1072 3.68% 12 1136 1140 0.35% Stationary Thermal Tests - Steady State Heat Transfer Analysis The stationary thermal test cases for steady-state heat transfer analysis from the Societe Francaise des Mecaniciens include: • "Hollow Cylinder - Fixed Temperatures" • "Hollow Cylinder - Convection" • "Cylindrical Rod - Flux Density" • "Hollow Cylinder with Two Materials - Convection" • "Wall - Fixed Temperatures" • "Wall - Convection" • "Hollow Sphere - Fixed Temperatures, Convection" • "L-Plate" • "Hollow Sphere with Two Materials -Convection" Hollow Cylinder - Fixed Tempera- tures The complete model and results for this test case are in file htpla01.neu. This test is a steady–state heat transfer analysis of a 2D axisymmetric cylinder with fixed temperatures. It provides the input data and results for benchmark test TPLA01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Two tests: • Test 1 - 5 linear quadrilateral axisymmetric solid elements • Test 2 - 5 parabolic quadrilateral axisymmetric solid elements The meshes are shown in the following figure: Boundary Conditions • One temperature set: λ 1 W m -----°C = 332 Internal temperature External temperature Solution Type Steady–State Heat Transfer Ti 100°C = Te 20°C = 333 Results Temperature Results (0 degrees Celsius): Total Heat Flux Results (W/m**2): Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLA01/89. Radius(m) Bench Value FEMAP Structural 5 linear quads. FEMAP Structural 5 parabolic quads. 0.30 100.00 100.00 100.00 0.31 82.98 82.98 82.98 0.32 66.51 66.51 66.51 0.33 50.54 50.54 50.54 0.34 35.04 35.04 35.04 0.35 20.00 20.00 20.00 Radius (m) Bench Value FEMAP Structural 5 linear quads. FEMAP Structural 5 parabolic quads. 0.30 1729.91 1701.69 1701.70 0.31 1674.11 1674.68 1674.69 0.32 1621.79 1622.32 1622.32 0.33 1572.64 1573.13 1573.13 0.34 1526.39 1526.84 1526.83 0.35 1482.78 1504.39 1504.38 Hollow Cylinder - Convection The complete model and results for this test case are in file htpla03.neu. This test is a steady–state heat transfer analysis of a 2D axisymmetric cylinder with convection. It provides the input data and results for benchmark test TPLA03/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Three tests: • Test 1 - 10 linear axisymmetric quadrilateral solid elements • Test 2 - 2 linear axisymmetric quadrilateral solid elements • Test 3 - 2 parabolic axisymmetric quadrilateral solid elements The meshes are shown in the following figure: λ 40 W m -----°C = 335 Boundary Conditions Elemental Convection • Convection on internal surface (nodes 3, 14, 16): • Convection on external surface (nodes 12, 15, 17): Solution Type Steady–State Heat Transfer Results Temperature and Element Total Heat Flux Bench Value FEMAP Structural 10 linear quads. FEMAP Structural 2 linear quads. FEMAP Structural 2 parabolic quads. Ti (°C) 272.27 272.35 272.17 272.35 hi 150.0 W m 2 -------°C = Ti 500°C = he 142.0 W m 2 -------°C = Ti 20°C = 336 So: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLA03/89. Te (°C) 205.05 204.51 204.66 204.51 34160.00 33637.10 31746.69 31792.7 26276.90 26508.40 27824.15 27853.8 ϕi W m 2 -------     ϕe W m 2 -------     ϕ L --- ϕ2πR = ϕ L --- 34173.82 2 π 0.300 ⋅ ⋅ ⋅ 64416.13 W m ----- = = Cylindrical Rod - Flux Density The complete model and results for this test case are in file htpla05.neu. This test is a steady–state heat transfer analysis of a 2D axisymmetric rod with fixed temperatures and flux density. It provides the input data and results for benchmark test TPLA05/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 20 linear quadrilateral axisymmetric solid elements • 42 nodes The mesh is shown in the following figure: λ 33.33 W m -----°C = 338 Boundary Conditions Nodal Temperatures • z = 0 (nodes 1 and 3): • z = 1 (nodes 2 and 4): Elemental Heat Flux • Cylindrical surface (elements 1-20): The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer Set temperature to 0°C Set temperature to 500°C Set flux ϕ to 200 W m2 -------- – 339 Results Temperature Results (degrees C): Results are post–processed on the internal surface. Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLA05/89. Node # z (m) Bench Value FEMAP Structural Difference Node 3 0.0 0.00 0.00 0.00% Node 41 0.1 -4.00 -4.02 0.50% Node 39 0.2 4.00 3.98 0.50% Node 37 0.3 24.00 23.97 0.13% Node 35 0.4 56.00 55.97 0.05% Node 33 0.5 100.00 99.97 0.03% Node 31 0.6 156.00 155.97 0.02% Node 29 0.7 224.00 223.97 ~0.00% Node 27 0.8 304.00 303.98 ~0.00% Node 25 0.9 396.00 395.98 0.01% Node 4 1.0 500.00 500.00 0.00% Hollow Cylinder with Two Materials - Convection The complete model and results for this test case are in file htpla08.neu. This test is a steady–state heat transfer analysis of a 2D axisymmetric cylinder with two materials and convection. It provides the input data and results for benchmark test TPLA08/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties • Material 1: • Material 2: Finite Element Modeling • 7 linear quadrilateral axisymmetric solid elements • 16 nodes λ 1 40.0 W m -----°C = λ 2 20.0 W m -----°C = 341 The mesh is shown in the following figure. Boundary Conditions Elemental Convection • Convection on internal surface: • Convection on external surface: hi 150.0 W m 2 -------°C = Ti 70°C = hi 200.0 W m 2 -------°C = Ti 15° – ( )C = 342 Solution Type Steady–State Heat Transfer Results Node # Temperature/ Element X Heat Flux Bench Value FEMAP Structural Difference Node 9 Ti (°C) 25.42 25.42 0.00% Node 14 Tm (°C) 17.69 17.69 0.00% Node 16 Te (°C) 12.11 12.11 0.00% Node 9 6687.44 6577.88 1.64% Node 14 5732.09 5733.33 0.02% Node 16 5422.25 5496.59 1.37% ϕi W m 2 -------     ϕm W m 2 -------     ϕe W m 2 -------     ϕ L --- ϕ2πR = 343 So: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLA08/89. ϕ L --- 5733.33 2 π 0.35 ⋅ ⋅ ⋅ 12608.25 W m ----- = = Wall - Convection The complete model and results for this test case are in file htpl03.neu. This test is a steady–state heat transfer analysis of a 1D wall with fixed convection. It provides the input data and results for benchmark test TPLL03/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 1 linear quadrilateral plate element • 4 nodes The plate element thickness is set to 1m. The mesh is shown in the following figure: λ 1.0 W m -----°C = 345 Boundary Conditions Elemental Convection • Convection on internal surface: • Convection on external surface: • Convection coefficient is defined as energy / (length*time*temperature) in the current system of units. The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer hA 20.0 W m 2 -------°C = TA 20.0°C – = hB 10.0 W m 2 -------°C = TB 500°C = A B 346 Results Temperature Results (Degrees Celsius): Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLL03/89. Node # Temperature Flux Bench Value FEMAP Structural Difference Node 1 (Temp) TA (°C) 21.71 21.71 0.00% Node 4 (Temp) TB (°C) 416.58 416.57 ∼0.00% Node 1 (Flux) ϕ (W/m**2) 834.2 834.3 0.01% Wall - Fixed Temperatures The complete model and results for this test case are in file htpl01.neu. This test is a steady–state heat transfer analysis of a 1D wall with fixed temperatures. It provides the input data and results for benchmark test TPLL01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information The mesh is shown in the following figure: Units SI Material Properties Finite Element Modeling • 5 beam (line 2) elements • 6 nodes λ 0.75 W m -----°C = 348 Boundary Conditions Nodal Temperatures • Internal temperature • External temperature The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer Results Temperature Results (Degrees Celsius): Node # Length: x (m) Bench Value FEMAP Structural Difference Node 1 0.00 100.0 100.0 0.00% Node 2 0.01 84.0 84.0 0.00% Node 3 0.02 68.0 68.0 0.00% Node 4 0.03 52.0 52.0 0.00% Node 5 0.04 36.0 36.0 0.00% Node 6 0.05 20.0 20.0 0.00% Ti 100°C node 1 ( ) = Te 20°C node 6 ( ) = 349 The flux calculated with the software is exact: Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLL01/89. ϕ 1200 Ω µ 2 ------ = L-Plate The complete model and results for this test case are in the following files: • htpp01a.neu (linear quadrilateral) • htpp01b.neu (parabolic quadrilateral) This test is a steady–state heat transfer analysis of a 2D L–plate with fixed temperatures. It provides the input data and results for benchmark test TPLP01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling Two tests: • 21 nodes, 12 linear quadrilateral plate elements • 53 nodes, 12 parabolic quadrilateral plate elements The mesh is shown in the following figure: λ 1.0 W m -----°C = 351 Boundary Conditions Nodal Temperatures • AF side: • DE side: The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer Results Temperature Results (Degrees Celsius): Node Bench Values FEMAP Structural linear quads. % Difference FEMAP Structural parabolic quads. % Difference 8 7.869 7.861 1.10 7.883 0.18 9 5.495 5.502 0.13 5.519 0.43 10 2.816 2.845 1.03 2.834 0.64 Set temperature to 10°C Set temperature to 0°C A B C D E F 352 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLP01/89. 19 8.018 8.026 0.10 8.015 0.04 18 5.680 5.669 0.19 5.666 0.25 20 2.881 2.959 2.71 2.877 0.14 17 8.514 8.505 0.11 8.519 0.06 6 6.667 6.667 0.00 6.667 0.00 16 2.972 2.990 0.61 2.963 0.30 21 9.001 9.015 0.16 9.108 1.20 15 8.640 8.661 0.24 8.669 0.34 14 9.316 9.294 0.24 9.283 0.35 5 9.009 8.996 0.14 8.961 0.53 Hollow Sphere - Fixed Tempera- tures, Convection The complete model and results for this test case are in file htpv02.neu. This test is a steady–state heat transfer analysis of a 3D sphere with fixed temperatures and convection. It provides the input data and results for benchmark test TPLV02/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 500 solid (brick and wedge) elements • 666 nodes The test is executed on 1/8 of a mapped meshed sphere. The mesh is shown in the following figure: λ 1.0 W m -----°C = 354 Boundary Conditions Elemental Convection • Convection on internal surface: Nodal Temperature • Set external surface temperature The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer hi 30 W m 2 -------°C = Ti 100°C(elements 401-500) = Te to 20°C(nodes 1-111) 355 Results Temperature results (Degrees C): Element X Heat Flux results (W/m**2): Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLV02/89. Radius r (m) Node # Bench Value FEMAP Structural Difference 0.3 566 65.00 64.87 0.20% 0.31 455 54.84 54.74 0.18% 0.32 344 45.31 45.24 0.15% 0.33 233 36.36 36.32 0.11% 0.34 122 27.94 27.92 0.07% 0.35 11 20.00 20.00 0.00% Radius r (m) Node # Bench Value FEMAP Structural Difference 0.3 566 1050.00 1019.34 2.92% 0.31 455 983.35 987.57 0.43% 0.32 344 922.85 926.90 0.43% 0.33 233 867.47 871.65 0.48% 0.34 122 817.47 821.21 0.45% 0.35 11 771.43 797.11 3.32% Hollow Sphere with Two Materials - Convection The complete model and results for this test case are in the following files: • htpv04a.neu (linear brick) • htpv04b.neu (parabolic tetrahedron) • htpv04c.neu (axisymmetric solid) This test is a steady–state heat transfer analysis of a 3D sphere with two materials and convection. It provides the input data and results for benchmark test TPLV04/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties • Material 1: • Material 2: Finite Element Modeling Three tests: λ 1 40.0 W m -----°C = λ 2 20.0 W m -----°C = 357 • Test 1 - 888 nodes, 700 solid (brick and wedge) elements • Test 2 - 3818 nodes, 2192 solid parabolic tetrahedron elements • Test 3 - 23 nodes, 4 axisymmetric solid parabolic quadrilateral elements The test is executed on 1/8 of a mapped meshed sphere. 358 Boundary Conditions Elemental Convection • Convection on internal surface: • Convection on external surface: The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer hi 150.0 W m 2 -------°C = Ti 70°C = he 200.0 W m 2 -------°C = Te 9° – ( )C = 359 Results Temperature Results (Degrees Celsius): Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLV04/89. Temperature Bench Value FEMAP Structural linear brick (htpv04a) FEMAP Structural parabolic tetrahedron (htpv04b) FEMAP Structural axisymmetric solid (htpv04c) Ti (C°) 25.06 N1 25.03 N19 25.06 N2 25.01 Tm (C°) 17.84 N556 17.84 N9 17.84 N6 17.75 Te (C°) 13.16 N778 13.18 N5 13.15 N5 13.17 Thermo-mechanical Test - Linear Statics Analysis The stationary thermal-mechanical test cases for linear statics analysis from the Societe Francaise des Mecaniciens include: • "Thermal Gradient on a Thin Pipe" Thermal Gradient on a Thin Pipe The complete model and results for this test case are in file hsla01.neu. This test is a thermo–mechanical linear statics analysis of a thin pipe with thermal gradient and plane strain. It provides the input data and results for benchmark test HSLA01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties Finite Element Modeling • 500 axisymmetric (linear quadrilateral solid) elements • 561 nodes The mesh is shown in the following figure: E 1x · 10 11 Pa = ν 0.3 = Coefficient of expansion: α 1x 10 5 – C° ----------- = 362 Boundary Conditions Constraints • Constrain nodes 1-11 in the X and Z translations. Nodal Temperature • Radial temperature The boundary conditions are shown in the following figure: Solution Type Statics T Ti 1 r Ri – ( ) – ( ) Re Ri – ( ) -------------------------------- with Ti=100°C ⋅ = 363 Results Post Processing Point Stress Bench Value FEMAP Structural Difference r = Ri 0 -0.85E6 -74.07E6 -74.20E6 0.18% r=(Re+Ri)/2 -3.95E6 -3.89E6 1.52% 1.306E6 1.40E6 1.22% r=Re 0 -0.65E6 68.78E6 68.53E6 0.36% Value Definition = the axisymmetric C1 radial stress at node 265 = the axisymmetric C4 Azimuth stress at node 265 =the axisymmetric C1 radial stress at node 270 =the axisymmetric C1 Azimuth stress at node 270 = the axisymmetric C1 radial stress at node 275 σ r Pa ( ) σ θ Pa ( ) σ r Pa ( ) σ θ Pa ( ) σ r Pa ( ) σ θ Pa ( ) σ r σ θ σ r σ θ σ r 364 Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. HSLA01/89. = the axisymmetric C2 Azimuth stress at node 275 Value Definition σ θ 365 Index A Annular membrane 152 Annular plate 117, 140, 171, 182 Anti-symmetric modes 108 Articulated plane truss 203 Articulated rod truss 201 Articulated supports 192 Axial distributed load 6 Axial loading 291 Axisymmetric solid elements 165, 168, 255, 268, 331, 334, 337, 340 Axisymmetric vibration 165, 171 B Bar elements 76, 78, 83, 92, 95, 98, 101, 192, 194, 196, 199, 203, 206, 288, 291, 297, 300, 303, 307, 323, 326 Beam 4, 6, 9, 12, 15, 18, 95, 101, 174, 186, 192, 194, 206, 288, 294, 307 Beam elements 294, 347 Bending 27, 196, 199, 274, 323 Bending load 210 C Cantilever 92 Cantilever beam 4, 9, 12, 76, 101, 294, 307 Cantilever mass 78 Cantilevered plate 105 Cantilevered solid beam 186 Cantilevered square membrane 144 Cantilevered tapered membrane 148 Cantilevered thin square plate 124, 156, 161 Circular hole 212 Circular plate 215 Circular ring 98 Clamped beams 194 Clamped thick rhombic plate 136 Clamped thin rhombic plate 121 Clamped-free thin shell 320 Compressor 320 Convection 334, 340, 344, 353, 356 Curved beam elements 196 Curved pipe 196 Cylindrical rod 337 Cylindrical shell 39, 42, 221 D Deep simply-supported beam 95 Deep simply-supported solid beam 174 Displacement 15 Distorted mesh 124 Distributed loads 9, 18 E Elastic foundation 206 Elliptic membrane 34 F Fixed temperatures 331, 347, 353 Flux density 337 Free annular membrane 152 Free cylinder 165 G Gravity loading 232 H Heated beam 15 Hemisphere point loads 44 Hollow cylinder 331, 334, 340 Hollow sphere 353, 356 Hovgaard’s Problem 326 hsla01.neu 361 htpl01.neu 347 htpl03.neu 344 htpla01.neu 331 htpla03.neu 334 htpla05.neu 337 htpla08.neu 340 htpp01a.neu 350 366 htpp01b.neu 350 htpv02.neu 353 htpv04a.neu 356 htpv04b.neu 356 htpv04c.neu 356 Hydrostatic pressure 229 I Infinite plate 212 In-plane vibrations 83, 98 Internal pressure 221, 261, 268 K Kirchhoff formulation 251 L le1001.neu 53 le1002.neu 53 le1003.neu 53 le101.neu 34 le102.neu 34 le103.neu 34 le1101a.neu 58 le1101b.neu 58 le1102a.neu 58 le1102b.neu 58 le1103a.neu 58 le1103b.neu 58 le1104a.neu 58 le1104b.neu 58 le1105a.neu 58 le1105b.neu 58 le1106a.neu 58 le1106b.neu 58 le201a.neu 39, 42 le201b.neu 39, 42 le202a.neu 39, 42 le202b.neu 39, 42 le301.neu 44 le302.neu 44 le303.neu 44 le304.neu 44 le501.neu 47 le502.neu 47 le601.neu 49 le602.neu 49 Linear beam 6, 18 Linear Statics 4, 6, 9, 12, 15, 18, 21, 24, 27, 30, 34, 39, 42, 44, 49, 53, 58, 192, 194, 196, 199, 201, 203, 210, 212, 215, 218, 221, 225, 229, 232, 236, 239, 242, 247, 251, 261, 268, 274, 361 L-Plate 350 Lumped mass 285, 307 M Mass elements 65, 68, 71, 78, 285, 307 Membrane 21 Membrane loads 21 Mindlin formulation 251 Moment load 12 mstv1001.neu 4 mstv1002.neu 6 mstv1003.neu 9 mstv1004.neu 12 mstv1007.neu 15 mstv1008.neu 18 mstv1009.neu 21 mstv1014.neu 24 mstv1015.neu 27 mstv1016.neu 30 mstvn002.neu 65 mstvn003.neu 68 mstvn004.neu 71 mstvn005.neu 73 mstvn006.neu 76 mstvn007.neu 78 N Natural frequency 78 ne014ll.neu 117 nf001ac.neu 83 nf002ac.neu 86 367 nf003ac.neu 89 nf004a.neu 92 nf005ac.neu 95 nf006ac.neu 98 nf011alc.neu 105 nf011all.neu 105 nf011apc.neu 105 nf011apl.neu 105 nf011blc.neu 108 nf011bll.neu 108 nf011bpc.neu 108 nf011bpl.neu 108 nf0121c.neu 111 nf012ll.neu 111 nf012pc.neu 111 nf012pl.neu 111 nf013lc.neu 114 nf013ll.neu 114 nf013pc.neu 114 nf013pl.neu 114 nf014lc.neu 117 nf014pc.neu 117 nf014pl.neu 117 nf015lc.neu 121 nf015ll.neu 121 nf015pc.neu 121 nf015pl.neu 121 nf021alc.neu 129 nf021all.neu 129 nf021apc.neu 129 nf021apl.neu 129 nf021blc.neu 133 nf021bll.neu 133 nf021bpc.neu 133 nf021bpl.neu 133 nf0221c.neu 136 nf022ll.neu 136 nf022pc.neu 136 nf022pl.neu 136 nf023lc.neu 140 nf023ll.neu 140 nf023pc.neu 140 nf023pl.neu 140 nf031ll.neu 144 nf031llc.neu 144 nf031pc.neu 144 nf031pl.neu 144 nf032lc.neu 148 nf032ll.neu 148 nf032pc.neu 148 nf032pl.neu 148 nf033lc.neu 152 nf033ll.neu 152 nf033pc.neu 152 nf033pl.neu 152 nf041lc.neu 165 nf041ll.neu 165 nf041pc.neu 165 nf041pl.neu 165 nf042lc.neu 168 nf042ll.neu 168 nf042pc.neu 168 nf042pl.neu 168 nf043lc.neu 171 nf043ll.neu 171 nf043pc.neu 171 nf043pl.neu 171 nf051lc.neu 174 nf051ll.neu 174 nf051pc.neu 174 nf051pl.neu 174 nf052lc.neu 178 nf052ll.neu 178 nf052pc.neu 178 nf052pl.neu 178 nf053lc.neu 182 nf053ll.neu 182 nf053pc.neu 182 368 nf053pl.neu 182 nf071a.neu 101 nf071b.neu 101 nf071c.neu 101 nf072ac.neu 186 nf072al.neu 186 nf072bc.neu 186 nf072bl.neu 186 nf073ac.neu 156 nf073al.neu 156 nf073bc.neu 156 nf073bl.neu 156 nf073cc.neu 156 nf073cl.neu 156 nf073dc.neu 156 nf073dl.neu 156 nf074c.neu 161 nf074l.neu 161 Nodal loads 4, 201 Normal Modes/Eigenvalue 65, 68, 71, 76, 78, 83, 92, 95, 98, 101, 105, 108, 114, 117, 121, 124, 129, 133, 136, 140, 144, 148, 152, 156, 161, 165, 168, 171, 174, 178, 182, 186, 285, 291, 294, 297, 300, 303, 307, 311, 314, 317, 320, 323, 326, 328 O Off-center point masses 92 Out-of-plane vibration 98 P Patch test 39, 42 Pinched cylindrical shell 236 Pin-ended cross 83 Pipes 326 Plane bending 199, 210 Plane strain elements 34 Plane truss 203 Plate elements 34, 39, 42, 44, 49, 105, 108, 114, 117, 121, 124, 129, 133, 136, 140, 148, 152, 156, 161, 210, 212, 215, 218, 221, 225, 229, 232, 236, 239, 242, 247, 251, 279, 311, 314, 317, 320, 328, 344, 350 plate elements 144 Pressure 53, 221, 229, 268 Prismatic rod 274 Pure bending 27, 274 Pure tension 24, 255 R Rectangular plates 328 Rhombic plate 121, 136 Rhomboid plate 247 Rigid elements 65, 194 Rod elements 201 S sdld02.neu 285 sdll014a.neu 303 sdll014b.neu 303 sdll014c.neu 303 sdll01a.neu 288 sdll01b.neu 288 sdll05a.neu 291 sdll05b.neu 291 sdll09a.neu 294 sdll11.neu 297 sdll12.neu 300 sdll15a.neu 307 sdll15b.neu 307 sdls01a.neu 311 sdls01b.neu 311 sdls03.neu 314 sdls04.neu 317 sdls05a.neu 320 sdls05b.neu 320 sdlx01.neu 323 sdlx02.neu 326 sdlx03.neu 328 Shear loading 251 369 Short beam 192, 288 Simply-supported annular plate 117, 171 Simply-supported rectangular plate 242, 314 Simply-supported rhomboid plate 247 Simply-supported solid annular plate 182 Simply-supported solid square plate 178 Simply-supported thick annular plate 140 Simply-supported thick square plate 133 Simply-supported thin square plate 114 Single DOF 65 Skew plate normal pressure 49 Solid cylinder 58, 255 Solid elements 53, 58, 174, 178, 182, 186, 255, 268, 274, 279, 353, 356, 361 Solid sphere 58 Solid square plate 178 Solid taper 58 Spherical shell 239 Spring elements 65, 68, 71, 206, 285 Square tube 218 ssll02.neu 192 ssll05.neu 194 ssll07a.neu 196 ssll07b.neu 196 ssll08.neu 199 ssll11.neu 201 ssll14a.neu 203 ssll14b.neu 203 ssll16.neu 206 sslp01.neu 210 sslp02.neu 212 ssls03a.neu 215 ssls03b.neu 215 ssls05.neu 218 ssls06a.neu 221 ssls06b.neu 221 ssls07a.neu 225 ssls07b.neu 225 ssls08.neu 229 ssls09.neu 232 ssls20a.neu 236 ssls20b.neu 236 ssls21a.neu 239 ssls21b.neu 239 ssls21c.neu 239 ssls24a.neu 242 ssls24b.neu 242 ssls24c.neu 242 ssls25a.neu 247 ssls25b.neu 247 ssls27a.neu 251 ssls27b.neu 251 ssls27c.neu 251 sslv01a.neu 255 sslv01b.neu 255 sslv01c.neu 255 sslv01d.neu 255 sslv03a.neu 261 sslv03b.neu 261 sslv03c.neu 261 sslv03d.neu 261 sslv04a.neu 268 sslv04b.neu 268 sslv04c.neu 268 sslv04d.neu 268 sslv08a.neu 274 sslv08b.neu 274 sslv08c.neu 274 sslv08d.neu 274 sslv09a10.neu 279 sslv09a100.neu 279 sslv09a20.neu 279 sslv09a50.neu 279 sslv09a75.neu 279 sslv09b10.neu 279 370 sslv09b100.neu 279 sslv09b20.neu 279 sslv09b50.neu 279 sslv09b75.neu 279 Steady-State Heat Transfer 331, 334, 337, 340, 344, 347, 350, 353, 356 Strain energy 30 Stress 15 Symmetric modes 105 Symmetric truss 323 T Tapered beam elements 294 Tapered membrane 148 Temperatures 58, 331, 347, 353 Tension 24 Thermal gradient 361 Thermal strain 15 Thick annular plate 140 Thick hollow sphere 168 Thick plate 279 Thick plate pressure 53 Thick square plate 129, 133 Thick-walled infinite cylinder 268 Thick-walled spherical container 261 Thin arc 199 Thin circular ring 297, 300 Thin pipe 361 Thin pipe elbow 303 Thin ring plate 317 Thin shell 320 Thin shell beam wall 27 Thin square cantilevered plate 105, 108 Thin square plate 124, 156, 161, 311 Thin wall cylinder 24, 225, 229, 232 Three DOF 71 Torque loading 218 Torsional system 71 Transverse bending 196 Truss 30 Two DOF 68 U Undamped free vibration 65, 68 Undamped free vibrations 76 Uniform axial load 225 Uniform radial vibration 168 Uniformly distributed load 215, 242, 247 V Vibrations 65, 68, 76, 83, 98, 165, 168, 171, 303 W Wall 344, 347 Proprietary and Restricted Rights Notice This information product is licensed to the user for the period set forth in the applicable license agreement, subject to termination of the license by Unigraphics Solutions Inc. at any time and at all times remains the property of Unigraphics Solutions Inc. or third parties from whom Unigraphics Solutions Inc. has obtained a licensing right. The information contained within including, but not limited to, the ideas, concepts and know-how, is proprietary, confidential and trade secret to Unigraphics Solutions Inc. or such third parties and the information contained therein shall be maintained as proprietary, confidential and trade secret to Unigraphics Solutions Inc. or to such third parties. The information contained within shall not be copied or reproduced in any form whatsoever, nor is any information to be disclosed to anyone other than an authorized representative of the user’s employer who is contractually obligated not to disclose same, without express prior written consent of Unigraphics Solutions Inc. The user of this information and the computer program(s) referred to herein retains full control over and is solely responsible for the mechanical design of the user’s equipment, machinery, systems, and products. Unigraphics Solutions Inc. makes no warranties of any kind, including the warranty of merchantability or fitness for a particular purpose in respect to the equipment, machinery, systems, and products derived or resulting hereunder, and the user assumes all risks and liability for results obtained by the manufacturing, use or implementation of the computer program(s) described herein, whether used singly or in combination with other designs or products. Unigraphics Solutions Inc. shall not be liable for any special or consequential damages. Unigraphics Solutions Inc. makes no warranty that the equipment, machinery, systems, and products derived or resulting hereunder will not infringe the claims of domestic or foreign patents and further does not warrant against infringement by reason of the user thereof in combination with other designs, products, or materials or in the operation of any process. User shall protect, indemnify and hold harmless Unigraphics Solutions Inc. of and from any loss, cost, damage or expense arising from any claim that is in any way associated with the computer program(s) described within. Data presented in examples do not necessarily reflect actual test results and should not be used as design criteria. By acceptance of this product, the user agrees to the above conditions and further agrees that the product will not be exported (or re-exported from a country of installation), directly or indirectly, separately or as part of a system, without user or user’s employer, at its own cost, first obtaining all licenses from the United States Department of Commerce and any other appropriate agency of the United States Government as may be required by law. Copyright © 1986, 1987, 1988, 1989, 1990, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002 Unigraphics Solutions Inc. All rights reserved. Restricted Rights Legend: This commercial computer software, documentation, and related materials are provided with restricted rights. Use, duplication, or disclosure by the U.S. Government is subject to the protections and restrictions as set forth in the Unigraphics Solutions Inc. commercial license agreement for the software, documentation, and related material as prescribed in DOD FAR 227-7202-3(a), or for Civilian agencies, in FAR 27.404(b)(2)(i), and any successor or similar regulation, as applicable. Unigraphics Solutions Inc., 10824 Hope Street, Cypress, CA 90630. EDS, SDRC, I-DEAS, FEMAP, Dual Engine Geometry Modeling, FEMAP Professional, FEMAP Enterprise and FEMAP Structural and the EDS logo are trademarks, registered trademarks, or service marks of Electronic Data Systems Corporation or its subsidiaries. All other trademarks, registered trademarks, or service marks belong to their respective holders. The information contained within is subject to change without notice and should not be construed as a commitment by Unigraphics Solutions Inc. Unigraphics Solutions Inc. assumes no responsibility for any errors or omissions that may appear within.. EDS PLM Solutions P.O. Box 1172, Exton, PA 19341 Phone: FAX: Web: (610) 458-3660 (610) 458-3665 http://www.femap.com Conventions This manual uses different fonts to highlight command names or input that you must type. a:setup OK, Cancel Shows text that you should type. Shows a command name or text that you will see in a dialog box. Throughout this manual, you will see references to Windows. Windows refers to Microsoft® Windows NT, Windows 2000, Windows 95, Windows 98, Windows Me, or Windows XP. You will need one of these operating environments to run FEMAP for the PC. This manual assumes that you are familiar with the general use of the operating environment. If you are not, you can refer to the Windows User’s Guide for additional assistance. Similarly, throughout the manual all references to FEMAP, refer to the latest version of our software. Table of Contents Proprietary and Restricted Rights Notice Overview Linear Statics Verification Using Theoretical Solutions Nodal Loads on a Cantilever Beam ....................................................................................4 Axial Distributed Load on a Linear Beam ..........................................................................6 Distributed Loads on a Cantilever Beam ............................................................................9 Moment Load on a Cantilever Beam ................................................................................12 Thermal Strain, Displacement, and Stress on Heated Beam ............................................15 Uniformly Distributed Load on Linear Beam ..................................................................18 Membrane Loads on a Plate .............................................................................................21 Thin Wall Cylinder in Pure Tension .................................................................................24 Thin Shell Beam Wall in Pure Bending ...........................................................................27 Strain Energy of a Truss ...................................................................................................30 Linear Statics Verification Using Standard NAFEMS Benchmarks Elliptic Membrane ............................................................................................................34 Cylindrical Shell Patch Test .............................................................................................39 Laminate Strip ..................................................................................................................42 Hemisphere-Point Loads ..................................................................................................44 Z–Section Cantilever ........................................................................................................47 Skew Plate Normal Pressure .............................................................................................49 Thick Plate Pressure .........................................................................................................53 Solid Cylinder/Taper/Sphere–Temperature ......................................................................58 Normal Modes/Eigenvalue Verification Using Theoretical Solutions Undamped Free Vibration - Single Degree of Freedom ...................................................65 Two Degrees of Freedom Undamped Free Vibration - Principle Modes .........................68 Three Degrees of Freedom Torsional System ..................................................................71 Two Degrees of Freedom Vehicle Suspension System ....................................................73 Cantilever Beam Undamped Free Vibrations ...................................................................76 Natural Frequency of a Cantilevered Mass ......................................................................78 Normal Modes/Eigenvalue Verification Using Standard NAFEMS Benchmarks Bar Element Test Cases ....................................................................................................82 Pin-ended Cross - In-plane Vibration ........................................................................83 Pin-ended Double Cross - In-plane Vibration ...........................................................86 Free Square Frame - In-plane Vibration ....................................................................89 72& Cantilever with Off-Center Point Masses ................................................................. 92 Deep Simply-Supported Beam .................................................................................. 95 Circular Ring - In-plane and Out-of-plane Vibration ................................................ 98 Cantilevered Beam .................................................................................................. 101 Plate Element Test Cases ................................................................................................ 104 Thin Square Cantilevered Plate -Symmetric Modes ............................................... 105 Thin Square Cantilevered Plate - Anti-symmetric Modes ...................................... 108 Free Thin Square Plate ............................................................................................ 111 Simply-Supported Thin Square Plate ...................................................................... 114 Simply-Supported Thin Annular Plate .................................................................... 117 Clamped Thin Rhombic Plate ................................................................................. 121 Cantilevered Thin Square Plate with Distorted Mesh ............................................. 124 Simply-Supported Thick Square Plate, Test A ....................................................... 129 Simply-Supported Thick Square Plate, Test B ........................................................ 133 Clamped Thick Rhombic Plate ............................................................................... 136 Simply-Supported Thick Annular Plate .................................................................. 140 Cantilevered Square Membrane .............................................................................. 144 Cantilevered Tapered Membrane ............................................................................ 148 Free Annular Membrane ......................................................................................... 152 Cantilevered Thin Square Plate ............................................................................... 156 Cantilevered Thin Square Plate #2 .......................................................................... 161 Axisymmetric Solid and Solid Element Test Cases ....................................................... 164 Free Cylinder - Axisymmetric Vibration ................................................................ 165 Thick Hollow Sphere - Uniform Radial Vibration .................................................. 168 Simply-Supported Annular Plate -Axisymmetric Vibration ................................... 171 Deep Simply-Supported Solid Beam ...................................................................... 174 Simply-Supported Solid Square Plate ..................................................................... 178 Simply-Supported Solid Annular Plate ................................................................... 182 Cantilevered Solid Beam ......................................................................................... 186 Verification Test Cases from the Societe Francaise des Mechaniciens Mechanical Structures - Linear Statics Analysis with Bar or Rod Elements ................. 191 Short Beam on Two Articulated Supports .............................................................. 192 Clamped Beams Linked by a Rigid Element .......................................................... 194 Transverse Bending of a Curved Pipe ..................................................................... 196 Plane Bending Load on a Thin Arc ......................................................................... 199 Nodal Load on an Articulated Rod Truss ................................................................ 201 Articulated Plane Truss ........................................................................................... 203 Beam on an Elastic Foundation ............................................................................... 206 Mechanical Structures - Linear Statics Analysis with Plate Elements ........................... 209 Plane Shear and Bending Load on a Plate ............................................................... 210 Infinite Plate with a Circular Hole .......................................................................... 212 Uniformly Distributed Load on a Circular Plate ..................................................... 215 Torque Loading on a Square Tube .......................................................................... 218 Cylindrical Shell with Internal Pressure .................................................................. 221 72& Uniform Axial Load on a Thin Wall Cylinder ........................................................225 Hydrostatic Pressure on a Thin Wall Cylinder ........................................................229 Gravity Loading on a Thin Wall Cylinder ..............................................................232 Pinched Cylindrical Shell ........................................................................................236 Spherical Shell with a Hole .....................................................................................239 Uniformly Distributed Load on a Simply-Supported Rectangular Plate .................242 Uniformly Distributed Load on a Simply-Supported Rhomboid Plate ...................247 Shear Loading on a Plate .........................................................................................251 Mechanical Structures - Linear Statics Analysis with Solid Elements ...........................254 Solid Cylinder in Pure Tension ...............................................................................255 Internal Pressure on a Thick-Walled Spherical Container ......................................261 Internal Pressure on a Thick-Walled Infinite Cylinder ...........................................268 Prismatic Rod in Pure Bending ...............................................................................274 Thick Plate Clamped at Edges .................................................................................279 Mechanical Structures - Normal Modes/Eigenvalue Analysis .......................................284 Lumped Mass-Spring System ..................................................................................285 Short Beam on Simple Supports ..............................................................................288 Axial Loading on a Rod ..........................................................................................291 Cantilever Beam with a Variable Rectangular Section ...........................................294 Thin Circular Ring ...................................................................................................297 Thin Circular Ring Clamped at Two Points ............................................................300 Vibration Modes of a Thin Pipe Elbow ...................................................................303 Cantilever Beam with Eccentric Lumped Mass ......................................................307 Thin Square Plate (Clamped or Free) ......................................................................311 Simply-Supported Rectangular Plate ......................................................................314 Thin Ring Plate Clamped on a Hub .........................................................................317 Vane of a Compressor - Clamped-free Thin Shell ..................................................320 Bending of a Symmetric Truss ................................................................................323 Hovgaard’s Problem - Pipes with Flexible Elbows .................................................326 Rectangular Plates ...................................................................................................328 Stationary Thermal Tests - Steady State Heat Transfer Analysis ...................................330 Hollow Cylinder - Fixed Temperatures ...................................................................331 Hollow Cylinder - Convection ................................................................................334 Cylindrical Rod - Flux Density ...............................................................................337 Hollow Cylinder with Two Materials - Convection ................................................340 Wall - Convection ....................................................................................................344 Wall - Fixed Temperatures ......................................................................................347 L-Plate .....................................................................................................................350 Hollow Sphere - Fixed Temperatures, Convection .................................................353 Hollow Sphere with Two Materials -Convection ....................................................356 Thermo-mechanical Test - Linear Statics Analysis ........................................................360 Thermal Gradient on a Thin Pipe ............................................................................361 Index ...............................................................................................................................365 Overview This guide contains verification test cases for the FEMAP Structural solver. These test cases verify the function of the different FEMAP Structural analysis types using theoretical and benchmark solutions from well–known engineering test cases. Each test case contains test case data and information, such as element type and material properties, results, and references. The guide contains test cases for: • • • • • Linear Statics verification using theoretical solutions Linear Statics verification using standard NAFEMS benchmarks Normal Modes/Eigenvalue verification using theoretical solutions Normal Modes/Eigenvalue verification using standard NAFEMS benchmarks Verification Test Cases from the Societe Francaise des Mechaniciens Linear Statics Verification Using Theoretical Solutions The purpose of these linear statics test cases is to verify the function of the FEMAP Structural Statics Analysis software using theoretical solutions. The test cases are relatively simple in form and most of them have closed–form theoretical solutions. If you remesh a model. your node numbering may differ. All theoretical reference texts are listed at the end of this topic.finite element modeling (modeling procedure or hints) .boundary conditions (loads.element type .units .neu) files associated with this guide.physical and material properties . . The verification tests provided are not exhaustive in exploring all possible problems. The node numbers listed in each case refer to the node numbers in the neutral (. The theoretical solutions shown in these examples are from well–known engineering texts.solution type . The finite element method is very flexible in the types of physical problems represented. but represent common types of applications. This overview provides information on the following: • • • understanding the test case format understanding comparisons with theoretical solutions references Understanding the Test Case Format Each test case is structured with the following information: • test case data and information . or rebuild that model from scratch. For each test case. constraints) • • results references (text from which a closed–form or theoretical solution was taken) Note: . a specific reference is cited. Strength of Materials. 4th Edition. S.) 2.K. and Mitchel L. Elementary Theory and Problems. (New York: McGraw–Hill. Other results available from the analyses are not reported here.) have been executed. Mechanical Engineering Design. 1975. In addition. References The following references have been used in the Linear Statics Analysis verification problems presented: 1. Roark. Elements are chosen to achieve reasonable engineering accuracy with reasonable computing times. Glasgow. Inc. and Young. O. W. (New York: McGraw–Hill Book Company. but are used for comparison purposes. Part I. Verification to real world problems is more difficult but should be done when possible.) . R. Shigley. some tests would require an infinite number of elements to achieve the exact solution.. Results reported here are results which you can compare to the referenced theoretical solution.) 3. (New York: McGraw–Hill Book Company. J. Formulas for Stress and Strain. U. 1955. 5th Edition. test cases from NAFEMS (National Agency for Finite Element Methods and Standards. (1959.. Introduction to Stress Analysis.. 1992. Results for both theoretical and finite element solutions are carried out with the same significant digits of accuracy. The actual results from the FEMAP Structural software may vary insignificantly from the results presented in this document. Harris. negligible. The closed–form theoretical solution may have restrictions.) 4. Understanding Comparisons with Theoretical Solutions While differences in finite element and theoretical results are. These limiting restrictions are not necessary for the finite element model.. Beer and Johnston. This variation is due to different methods of performing real numerical arithmetic on different systems. Timoshenko. that do not exist in the real world. In addition to these example problems.. 1983. in most cases. Results for these test cases can be found in the next section. (New YorK: Van Norstrand Reinhold Company. C. it is due to changes in element formulations which SDRC has made to improve results under certain circumstances. such as rigid connections.) 5. National Engineering Laboratory. Linear Statics Analysis Verification Using NAFEMS Standard Benchmarks. Mechanics of Materials. Determine the stress at the end of the beam. Determine the deflection of a beam at the free end. Test Case Data and Information Element Types bar Units Inch Model Geometry Length=480 in Cross Sectional Properties • • Area = 30 x 30 in Iy =Iz = 67500 in4 Material Properties • E = 30 E+06 psi Finite Element Modeling • • 5 nodes 4 successive bar elements along the X axis .neu.Nodal Loads on a Cantilever Beam The complete model and results for this test case are in file mstvl001. 3 5333.91022 0.30% Reference • Beer and Johnston. Boundary Conditions Constraints Constrain the left end (node 1) of the beam in all six degrees. Inc. Solution Type Statics Results Beam End A1 Z Shear Force Stress (Node 1) Bench Value FEMAP Structural Difference 5333.913 0. .. Mechanics of Materials.) p. in the negative Y direction. (New York: McGraw–Hill. 716.000 lb.3 0% T2 Translation (Node 5) 0. Loads Set nodal force to 50. 1992. neu. elongation.Axial Distributed Load on a Linear Beam The complete model and results for this test case are in file mstvl002.75 in4 Material Properties E = 30E+6 psi Finite Element Modeling • 31 nodes . Determine the stress. Test Case Data and Information Element Type bar Units Inch Model Geometry Length = 300 in Cross Sectional Properties • • • Area = 9 in2 square cross section (3 in x 3 in) I = 6. and constraint force due to an axial loading along a linear beam. Solution Type Statics . Boundary Conditions Constraints Constrain one end of the beam (node 1) in all translations and rotations. each 10 inches long. • 30 bar elements along the X axis. Loads Set the axial distributed load (force per unit length) to 1000lb/in for the 10–inch long element (element 30) furthest from the constrained end. 000 0 Reference • Beer and Johnston.1 1111.0109258 1. (New York: McGraw–Hill. 1992. Inc.1 0 T1 Translation (Node 2) 0. Results Beam End A1 Axial Stress (Node 1) Bench value FEMAP Structural Difference 1111.0111111 0.000 -10. 76.6% T1 Constraint Force (Node 1) -10..) p. . Mechanics of Materials. Distributed Loads on a Cantilever Beam The complete model and results for this test case are in file mstvl003. Determine the stress at the midpoint of the beam and the reaction force at the restrained end. Determine the deflection of a beam at the free end. Test Case Data and Information Element Type bar Units Inch Model Geometry • Length = 480 in Cross Sectional Properties • • • Area = 900 in2 square cross section (30 in x 30 in) Iy = Iz = 67500 in4 Material Properties E = 30 E+06 psi Finite Element Modeling • 9 nodes .neu. 0% Total Translation (node 5) 0. • 8 successive bar elements along the X axis Boundary Conditions Constraints Constrain the left end of the beam (node 1) in all translations and rotations.400.8225* 0. Loads Define a distributed load on the elements of 250 lb/in in the negative Y direction.8190 0.43% Total Constraint Force (lb) 120.400.000 120. Solution Type Statics Results Beam End A1Z Bend Stress (node 1) Bench Value FEMAP Structural Difference 6.0 0.000 0 .0 6. ) p.. Inc. Mechanics of Materials. (New York: McGraw–Hill. Reference • Beer and Johnston. 716. * Includes shear deformation which is neglected in theoretical value. 1992. . neu.Moment Load on a Cantilever Beam The complete model and results for this test case are in file mstvl004. Determine the bending stress of the beam and the reaction force at the restrained end. Determine the deflection of a beam at the free end. Test Case Data and Information Element Type bar Units Inch Model Geometry Length = 480 in Cross Sectional Properties • • • Area = 900 in2 square cross section (30 in x 30 in) Iy = Iz = 67500 in4 Material Properties E = 30 E+06 psi Finite Element Modeling • 9 nodes . 5e+6 in–lb. Loads Set the Z–moment of the end node (node 5) to 2. Boundary Conditions Constraints Constrain the left end of the beam (node 1) in all translations and rotations. Solution Type Statics . • 8 successive bar elements along the X axis. Results Beam End A1 Z Bend Total Translation (in) Stress (psi) (node 5) (node 1) Bench Value FEMAP Structural Difference 555.5E+06 2. 716.) (node 1) 2.6 555.6 0 0. 1992.) p.5E+06 0 Reference • Beer and Johnston.1422 0 Total Constraint Moment (lb.. (New York: McGraw–Hill Inc. .1422 0. Mechanics of Materials. In case 1. fix the beam at both ends.2E-05 m/(m-C) v = 0. In both cases.Thermal Strain. fix the beam at the free end. and stresses along the beam.meter Model Geometry Length = 1 m Cross Sectional Properties Area = 0. Test Case Data and Information Element Type bar Units SI . In case 2. of thermal expansion = 1. and Stress on Heated Beam The complete model and results for this test case are in file mstvl007. Displacement. determine the displacement. Determine the displacement and thermal strain on a cantilever beam. A beam originally 1 meter long and at -50° C is heated to 25° C.01 m2 Material Properties • • • E = 2.3 Finite Element Modeling • 11 nodes .068E+11 PA Coeff. constraint forces.neu. • 10 bar elements on the X axis. Loads Set the temperature on all nodes to 25°C. Boundary Conditions Constraints • • Case 1: Constrain the node on one end (node 1) of the beam in all translations and rotations. Solution Type Statics . Case 2: Constrain the nodes on both ends (nodes 1 and 11) of the beam in all translations and rotations. Set the reference temperature to -50°C. Inc.. Results Case: One Fixed End Total Translation (Node 11) (m) Bench Value FEMAP Structural Difference 9E-04 9E-04 0 Beam End A1 Axial Strain 9E-04 9E-04 0 Case: Both Ends Fixed Total Constraint Force(N) (node 1) 1.86+06 0 Beam End A1 Axial Stress (Pa) –1. 1992. (New York: McGraw–Hill.86E+08 –1. 65.86+06 1.86E+08 0 Total Translation (m) Bench Value FEMAP Structural Difference 0 0 0 Reference • Beer and Johnston. Mechanics of Materials.) p. . Determine the beam end torque stress and the deflection at the middle of the beam. Test Case Data and Information Element Type bar Units Inch Model Geometry Length = 480 in Cross Sectional Properties • • Rectangular cross section (1.Uniformly Distributed Load on Linear Beam The complete model and results for this test case are in file mstvl008.neu. A beam 40 feet long is restrained and loaded with a distributed load of –833 lb.17 in x 43.24 in) Iz = 7892 in4 Material Properties • E = 30E6 psi Finite Element Modeling • 5 nodes . (global negative Y direction) on the elements 1 and 4. Loads Define a distributed load (force per unit length) of -833 lb. Solution Type Statics . Do not constrain rotation about Z. • 4 successive bar elements that are each 10 feet long Boundary Conditions Constraints Constrain nodes 2 and 4 in five degrees of freedom. 439 16.439 0 Reference • Timoshenko. (New York: Van Norstrand Reinhold Company. Strength of Materials. S.182 0 Beam End A1 Z Bend Stress (psi) (node 3) 16.. 98. 1955. Part I. Elementary Theory and Problems.182 0. Results Total Translation (in) (node 3) Bench Value FEMAP Structural Difference 0. .) p. 000 lb. A circle is scribed on an unstressed aluminum plate./in F(z)/l = 15. Test Case Data and Information Element Types plate Units Inch Model Geometry • • • Length = 15 in Diameter = 9 in Thickness = 3/4 in Material Properties • • • • E = 10 E+06 psi Poisson’s ratio = 1/3 F(x)/l = 9.Membrane Loads on a Plate The complete model and results for this test case are in file mstvl009.000 lb. Forces acting in the plane of the plate cause normal stresses.neu./in . Determine the change in the length of diameter AB and of diameter CD. Finite Element Modeling Create 1/4 of the model and apply symmetry boundary conditions. • • • Node 1: Fully constrain in all translations and rotation. Nodes 12. Boundary Conditions Constraints Constrain nodes along adjacent sides of the plate to allow only translation along the corresponding axis.000 lb/in in the Z direction. . Remember to account for the ratio of the circle diameter to plate length.000 lb. 31: Constrain in the X and Y translations and the X and Z rotations./in in the X direction and 15. 25. 13. Loads Set the elemental edge load to 9. 19. Then multiply the answer by 2 for correct results. Nodes 2-6: Constrain in the Y and Z translations and the X and Z rotations. 4E-03 14. Solution Type Statics Results T1 Translation (in) Bench Value FEMAP Structural Difference 4.8E-03 4.012-.T1 translation at node 10) x2 = (.) p. .4E-03 0 Post Processing • • (T1 translation at node 7 .0016) x2 = . 85.0048) x2 = .8E-03 0 T3 Translation (in) 14. Inc. 1992.004-. Mechanics of Materials.0048 (T3 translation at node 7 .T3 translation at node 24) x2 = (.. (New York: McGraw–Hill.0144 Reference • Beer and Johnston. Determine the stress and deflection of a thin wall cylinder with a uniform axial load.5 in Thickness = 0.Thin Wall Cylinder in Pure Tension The complete model and results for this test care are in file mstvl014.neu.0 in Material Properties • • E = 10000 psi v = 0.3 Finite Element Modeling • • 25 nodes Create 1/4 model of the cylinder with 16 linear quadrilateral plate elements and symmetry boundary conditions. . Test Case Data and Information Element Type linear quadrilateral plate Units Inch Model Geometry • • • R = 0.01 in y = 1. 9509 pounds Solution Type Statics Results Top Y Normal Stress T3 Translation (in) (psi) Bench Value 1000.0 0. and 21 in the X translation and Z rotation. Constrain node 5 in the Y and Z translation and Z rotation. Apply the following nodal forces: Nodes 21. 20. Loads • • • Nodal forces of p/(pi)D = 3. 11. 24: 1. 25: .015 -0.0 Difference 0 T1 Translation (in) -0.1 0 FEMAP Structural 1000. Constrain nodes 6.9757 pounds Nodes 22.1 0. 15.1831 where p = 10 psi. Constrain nodes 2-4 in the Z translation. 23. and 25 in the Y translation and Z rotation.015 0 . Boundary Conditions Constraints • • • • • Constrain node 1 in the X and Z translation and the Z rotation. 16. Constrain nodes 10. 6th Edition.. and Young. 518. 1989. Reference • Roark. W. Case 1a. R. (New York: McGraw–Hill Book Company. Formulas for Stress and Strain.) p. . Thin Shell Beam Wall in Pure Bending The complete model and results for this test case are in file mstvl015.neu. Determine the maximum stress.1 in Material Properties • • E = 30E6 psi v = 0. Test Case Data and Information Element Type linear quadrilateral plate Units Inch Model Geometry • • • Length = 30 in Width = 5 in Thickness = 0.03 Finite Element Modeling • 14 nodes . maximum deflection. and strain energy of a thin shell beam wall with a uniform bending load. Out–of–plane Loads Apply nodal forces (nodes 1 and 8) of p/w = 1.2 lbs/in. where p = 6.0 lb Solution Type Statics . • 6 linear quadrilateral plate elements Boundary Conditions Constraints Constrain the nodes at one end (nodes 7 and 14) in all translations and rotations. (New York: McGraw–Hill.17% Reference • Shigley.16% FEMAP Structural 4.242 Difference 2.) pp. Results T3 Translation (in) Node 1 Bench Value 4. and Mitchel L. 804. .320 Plate Bottom Major Stress (psi) Node 7 21600 20983 1.. 1983. Mechanical Engineering Design.73 2.96 12. 134. Inc. J. 4th Edition.39% Total Strain Energy (lb in) 12.. Determine the strain energy of a truss. Test Case Data and Information Element Type rod Units Inch Model Geometry • Length = 10 in Cross Sectional Properties Cross sectional area (A) = 0.neu.01 in2 Material Properties E = 30E6 psi Finite Element Modeling • • 4 nodes 5 rod elements .Strain Energy of a Truss The complete model and results for this test case are in file mstvl016. The cross–sectional area of the diagonal members is twice the cross–sectional area of the horizontal and vertical members. 588. Loads • Apply nodal force in Y direction on node 2.846 0 Reference • Beer and Johnston. Y.846 5. (New York: McGraw–Hill. and Z translations and the X and Y rotations. Constrain node 3 in the Y and Z translations and the X and Y rotations. Boundary Conditions Constraints • • Constrain node 1 in the X. p = 300 lb Solution Type Statics Results Total Strain Energy (lb in) Bench Value FEMAP Structural Difference 5. . Mechanics of Materials.) p.. Inc. 1992. The results for all of these test cases illustrate the need for adequate mesh refinement for obtaining accurate stresses. especially when using linear elements. cited below. your node numbering may differ. If you remesh a model.K.boundary conditions (loads and constraints) . The linear triangular and linear tetrahedral elements are particularly poor performers for stress analysis and are not generally recommended. Glasgow. These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elements in commercial software. Results of these test cases using other commercial finite element analysis software programs are available from NAFEMS. National Engineering Laboratory.solution type • • results reference Note: The node numbers listed in each case refer to the node numbers in the neutral (. A detailed discussion of the linear statics NAFEMS benchmarks can be found in the NAFEMS publication Background to Benchmarks. References The following references have been used in these test cases: . All results obtained using the FEMAP Structural Statics Analysis software compare favorably with other commercial finite element analysis software.physical and material properties .units . Understanding the Test Case Format Each test case is structured with the following information: • test case data and information .).neu) files associated with this guide.Linear Statics Verification Using Standard NAFEMS Benchmarks The purpose of these linear statics test cases is to verify the function of the FEMAP Structural Statics Analysis software using standard benchmarks published by NAFEMS (National Agency for Finite Element Methods and Standards. or rebuild that model from scratch.finite element modeling information .finite element modeling (modeling procedure or hints) . U. T. Fenner. Rev. • • NAFEMS Finite Element Methods & Standards. . R. R. Background to Benchmarks. (Glasgow: NAFEMS. and Lewis. (Glasgow: NAFEMS..) Davies. W. 3. A.. The Standard NAFEMS Benchmarks. G. 1993). 1990.. O. neu (quadrilateral plane strain) le102. = 1  2.Elliptic Membrane The complete model and results for this test case are in the following files: • • • le101. +  --------.25 Test Case Data and Information Physical and Material Properties • • • Thickness = 0. The plane strain elements use a plane stress element formulation.75  3.neu (triangular plane strain) le103. B Y A X C D Ellipses: 2 x 2 Ellipse AC:  -- + y = 1  2 y 2 x 2 Ellipse BD:  --------.1 m Isotropic material E = 210 x 103 MPa . It provides the input data and results for NAFEMS Standard Benchmark Test LE1.neu (quadrilateral plate) This test is a linear elastic analysis of an elliptic membrane (shown below) using coarse and fine meshes of plane strain elements and plate elements. linear and parabolic quadrilaterals .coarse and fine mesh .linear and parabolic triangles coarse and fine mesh plate . • v = 0.linear and parabolic quadrilaterals coarse and fine mesh plane strain (with plane stress element formulation) .3 Units SI Finite Element Modeling • • • plane strain (with plane stress element formulation) . Linear Triangle B Fine Mesh A C B Coarse Mesh A C D D B Parabolic Triangle A C D B A C D Linear Quadrilateral B Fine Mesh A C D A B Parabolic Quadrilateral C D B Coarse Mesh A C D B A C D Boundary Conditions Constraints • • Constrain the nodes along edge AB in the X translation. Constrain the nodes along edge CD in the Y translation. . The fine mesh is created by approximately halving the coarse mesh. Plate Mid Y Normal Stress at point D Node # Element Type & Mesh NAFEMS Bench Value (MPa) FEMAP Structural Result (MPa) Plane Strain Elements with a Plane Strain Formulation (le101): Node 4 Node 204 Node 104 Node 304 linear quad .2 72.7 92.7 92.7 54.0 .fine mesh Plane Strain Elements with a Plane Strain Formulation (le102): linear triangle .8 80.7 92.0 93.7 Node 4 Node 204 Node 104 Node 304 92.7 92.coarse mesh parabolic triangle – fine mesh 92.coarse mesh linear quad .7 92. Loads • • Uniform outward pressure on the elements on outer edge BD = 10MPa Inner curved edge AC is unloaded Solution Type Statics Results Output .fine mesh parabolic triangle .fine mesh parabolic quad .coarse mesh parabolic quad .7 92.0 94.3 90.coarse mesh linear triangle .7 62.3 88. Background to Benchmarks. R.fine mesh parabolic quad . A. (Glasgow: NAFEMS.7 66. Node 4 Node 204 Node 104 Node 304 Plate Elements (le 103): linear quad . Rev.coarse mesh linear quad . and Lewis.6 91. O. • Davies.3 88. (Glasgow: NAFEMS.7 92.fine mesh 92.4 82...) Test No. 1990.7 92.coarse mesh parabolic quad . The Standard NAFEMS Benchmarks. R.7 92. LE1.. W. 1993). G. 3.7 References • NAFEMS Finite Element Methods & Standards. . Fenner. T. 3 Units SI Finite Element Modeling • • le201a and le202a: 9 nodes. 4 parabolic quadrilateral plates Linear Quadrilaterals A B Parabolic Quadrilaterals A B E E C D C D . It provides the input data and results for NAFEMS Standard Benchmark Test LE2. case 1) le201b.01 m Isotropic material E = 210 x 103 MPa v = 0.neu (parabolic plate.neu (parabolic plate. case 1) le202a. case 2) This test is a linear elastic analysis of a cylindrical shell (shown below) using plate elements and two different loadings.Cylindrical Shell Patch Test The complete model and results for this test case are in the following files: • • • • le201a. 4 linear quadrilateral plates le201b and le202b: 21 nodes.neu (linear plate. Test Case Data and Information Physical and Material Properties • • • • Thickness = 0.neu (linear plate. case 2) le202b. Boundary Conditions Constraints Fully constrain the nodes on edge AB in all translations and rotations.000N Node 4 = 150. Constrain the nodes on edge AD and edge BC in the Z translation and X and Y rotations.0 kNm/m: Node 3 = -125 Node 4 = -250 Node 9 = -125 Case 2 Loading: • Nodal forces: Nodes 3. Case 1 Loading: • Nodal moments along DC = 1. and 9 = 75.000N . Fenner.case 1 (le201a) linear plate . LE2.case 2 (le202b) NAFEMS Bench Value (MPa) 60. References • NAFEMS Finite Element Methods & Standards. an edge load will not be in the correct direction.0 60. 3.000Pa Solution Type Statics Results Output .0 FEMAP Structural Result (MPa) 57. T. (Glasgow: NAFEMS.0 60. O. 1993)...case 1 (le201b) parabolic plate . Rev..0 * 54.0 60. the edge load must be input as nodal loads in the tangential direction. and Lewis. W.case 2 (le202a) parabolic plate . R. The Standard NAFEMS Benchmarks. G. Background to Benchmarks. . A.7 * *Since the shapes of the plates are an approximation to a cylindrical surface. (Glasgow: NAFEMS. • Apply an elemental pressure on elements 1-4 = 600. 1990.) Test No. R.Plate Top Major Stress at point E (node 2) Plate Element & Loading linear plate .8 55.9 66. To get this result. • Davies. 4 0° 90° 0° 90° Material Properties Laminate material: E = 1.0E3 MPa ν12 ν 21 ------.1 0.0E3 MPa .0E5 MPa ν 12 = 0.1 0° 90° 0° D F E 0.1 0.1 0.= ------E1 E2 G 12 = 3.Laminate Strip The complete model and results for this test case are in the following file: • r0031.3 E2 = 5. Test Case Data and Information Geometry 0° fiber direction Y X 10 15 15 10 C 10N/mm 1 Z X A E B 0.neu This test is a linear statics analysis of plate using plate elements with a laminate material.0E3 MPa G 33 = 2.1 0.1 0. It provides the input data and results for NAFEMS Report R0031.4 ν 23 = 0. (Glasgow: NAFEMS. R0031. 3. **Recovered from post-processing.1 FEMAP Structural Result (MPa) -1. Solution Type Statics Results NAFEMS Bench Value (MPa) -1. The Standard NAFEMS Benchmarks. (FEMAP Structural calculates stress at the center of the ply (F)). 1990. Rev.) Test No.1 -2.9 -4. Reference • NAFEMS Finite Element Methods & Standards. Units SI Finite Element Modeling 8 x 40 4-noded shells (quarter model) Boundary Conditions Constraints The one quarter model is: • • simply supported at A (Z=0) reflective symmetry about X=25 and Y=5 Loads Line load of 10N/mm at C (X=25.2 Results Z deflection at E Bending stress at E Bending stress at F Interlaminar shear stress at D Shear stress at F *Value extrapolated from FEMAP Structural results at F.06 683.06 *668 601 **-4. . Z=1). It provides the input data and results for NAFEMS Standard Benchmark Test LE3.25 x 103 MPa v = 0. coarse mesh) le304. EA   10 Point G at X = Y = Z =  ----- Node 7  1  -.linear & parabolic quadrilaterals . fine mesh) This test is a linear elastic analysis of hemisphere point loads (shown below) using coarse and fine meshes of plate elements.04 m Isotropic material E = 68.neu (linear quadrilateral plate. CE.neu (parabolic quadrilateral plate.neu (parabolic quadrilateral plate.3 Units SI Finite Element Modeling plate .coarse & fine mesh equally spaced nodes on AC. Test Case Data and Information Physical and Material Properties • • • • Thickness = 0.Hemisphere-Point Loads The complete model and results for this test care are in the following files: • • • • le301.neu (linear quadrilateral plate. coarse mesh) le302. fine mesh) le303. 2 3 . Constrain the nodes along edge AE (symmetry about X–Z plane) in the Y translation. and X and Z rotations. and Y and Z rotations. Constrain the nodes along edge CE (symmetry about Y–Z plane) in the X translation. Coarse Mesh E F G D F Fine Mesh E D G A B A C B C Boundary Conditions Constraints • • • Fully constrain point E in all translations and rotations. Loads • Concentrated radial load outward at A = 2KN . 185 0. Rev. The Standard NAFEMS Benchmarks..171 Test Case Number le301 le302 le303 le304 Plate Element & Mesh linear quadrilateral plate .185 FEMAP Structural Result at node 1 (point A) T1 Translation (m) 0.coarse mesh linear quadrilateral plate .. Fenner. G. . R. Background to Benchmarks.185 0..coarse mesh parabolic quadrilateral plate . A. W.185 0. LE3. (Glasgow: NAFEMS. 3. R.0861 0. 1990.fine mesh parabolic quadrilateral plate . O. • Concentrated radial load inward at C = 2KN Solution Type Statics Results NAFEMS Bench Value(m) 0.113 0. T. 1993). and Lewis.) Test No.185 0.fine mesh References • NAFEMS Finite Element Methods & Standards. (Glasgow: NAFEMS. • Davies. . 24 parabolic quadrilateral plate elements Boundary Conditions Constraints • Fully constrain the nodes on edges B1. B3 in all translations and rotations. B2. Test Case Data and Information Physical and Material Properties • • • • Thickness = 0. It provides the input data and results for NAFEMS Standard Benchmark Test LE5. 24 linear quadrilateral plate elements Test 2: 95 nodes.3 Units SI Finite Element Modeling • • Test 1: 36 nodes.Z–Section Cantilever The complete model and results for this test case are in the following files: • • le501.1 m Isotropic material E = 210 x 103 MPa v = 0.neu (parabolic quadrilateral plate) This test is a linear elastic analysis of a Z–section cantilever (shown below) using plate elements.neu (linear quadrilateral plate) le502. ) Test No. The Standard NAFEMS Benchmarks.point A/node 30 NAFEMS Bench Value (MPa) -108 -108 FEMAP Structural Result (MPa) -117.point A/node 30 parabolic quad . 3. point A. W. LE5. Rev. O.2MN applied at end C by two nodal forces (at nodes 9 and 27) of 0. (Glasgow: NAFEMS..6MN Solution Type Statics Results Output . .. Background to Benchmarks. and Lewis. (Glasgow: NAFEMS. G. 1993). 1990. node 30 (compression) Plate Element & Loading linear quad . Loads • B1 B2 B3 C Torque of 1. R.Plate Top Von Mises Stress (σxx). A. T. • Davies.3 -109. R. Fenner..2 References • NAFEMS Finite Element Methods & Standards. It provides the input data and results for NAFEMS Standard Benchmark Test LE6. 10m o 150 o 30 E A B D C Test Case Data and Information Physical and Material Properties • • • • Thickness = 0.neu (linear and parabolic quadrilateral) le602.Skew Plate Normal Pressure The complete model and results for this test case are in the following files: • • le601.01m Isotropic material E = 210 x 103 MPa v = 0.3 Units SI .neu (linear and parabolic triangle) This test is a linear elastic analysis of a plate (shown below) using plate elements. linear and parabolic triangles . Y. and 44 in the X. Constrain nodes 4. . 10.coarse and fine mesh • plate .linear and parabolic quadrilaterals . 38. Finite Element Modeling • plate . and Z translations. 47 in the X and Z translations.coarse and fine mesh Boundary Conditions Constraints (le601) • • Constrain nodes 1. 35. 13. • Constrain all other nodes in the Z translation. Constraints (le602) • • Fully constrain nodes 1, 10, 35, 44 in all directions and rotations. Constrain all other nodes in the Z translation. Loads • Elemental pressure = -0.7KPa in the Z–direction Solution Type Statics Results Output - Plate Bottom Major Stress on the bottom surface at the plate center. Test Case Name le601 le601 le601 le601 le602 le602 le602 le602 Node # Node 9 Node 18 Node 43 Node 52 Node 9 Node 18 Node 43 Node 52 Plate Element & Mesh linear quad - coarse mesh linear quad - fine mesh parabolic quad - coarse mesh parabolic quad - fine mesh linear triangle - coarse mesh linear triangle - fine mesh parabolic triangle - coarse mesh parabolic triangle - fine mesh NAFEMS Bench Value (MPa) 0.802 0.802 0.802 0.802 0.802 0.802 0.802 0.802 FEMAP Structural Result (MPa) 0.365 0.714 1.055 0.791 0.390 0.709 0.847 0.822 References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE6. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glasgow: NAFEMS, 1993). Thick Plate Pressure The complete model and results for this test case are in the following files: • • • le1001.neu (linear and parabolic brick) le1002.neu (linear and parabolic wedge) le1003.neu (linear and parabolic tetrahedron) This article provides the input data and results for NAFEMS Standard Benchmark Test LE10. This test is a linear elastic analysis of a thick (shown below) using coarse and fine meshes of solid elements. B’ B B A’ A A D’ C’ D C D C Ellipses: 2 x 2 Ellipse AD:  -- + y = 1  2 y 2 x 2 Ellipse BC:  ---------  +  ---------  = 1  2.75  3.25 Test Case Data and Information Physical and Material Properties • • • Isotropic material E=210x103 MPa v = 0.3 Units SI Finite Element Modeling • • • Solid brick Solid wedge Solid tetrahedron Solid Brick Linear and parabolic, coarse and fine mesh. Solid Wedge Linear and parabolic, coarse and fine mesh. Solid Tetrahdron Linear and parabolic, fine mesh. Boundary Conditions Constraints • • • Constrain the nodes on faces DCD’C’ and ABA’B’ in the X and Y translations. Constrain the nodes on face BCB’C’ in the X and Y translation. Constrain the nodes along the mid–plane in the Z translation. Loads • • Uniform normal elemental pressure on the elements on the upper surface of the plate = 1MPa Inner curved edge AD unloaded Solution Type Statics Results Output - Solid Y normal stress at point D3σyy Test Case Name le1001 le1001 le1001 le1001 le1002 le1002 le1002 le1002 le1003 le1003 Node # N4 N204 N104 N304 N4 N204 N104 N304 N40 N171 Element Type & Mesh linear brick - coarse mesh linear brick - fine mesh parabolic brick - coarse mesh parabolic brick - fine mesh linear wedge - coarse mesh linear wedge - fine mesh parab wedge - coarse mesh parab wedge - fine mesh linear tetra - fine mesh parabolic tetra - fine mesh NAFEMS Bench Value (MPa) -5.38 -5.38 -5.38 -5.38 -5.38 -5.38 -5.38 -5.38 -5.38 -5.38 FEMAP Structural Result (MPa) -6.31 -6.01 -5.73 -5.84 -3.52 -4.97 -5.53 -6.10 -2.41 -5.29 References • NAFEMS Finite Element Methods & Standards, The Standard NAFEMS Benchmarks, (Glasgow: NAFEMS, Rev. 3, 1990.) Test No. LE10. • Davies, G. A. O., Fenner, R. T., and Lewis, R. W., Background to Benchmarks, (Glasgow: NAFEMS, 1993) 3 x 10-4/oC Units SI . Test Case Data and Information Physical and Material Properties • • • • Isotropic material E = 210 x 103 MPa v = 0. fine mesh) This test is a linear elastic analysis of a solid cylinder with a temperature gradient (shown below) using coarse and fine meshes of solid elements. fine mesh) le1104a.neu (linear tetrahedron.neu (linear wedge.neu (linear brick.Solid Cylinder/Taper/Sphere–Temperature The complete model and results for this test case are in the following files: • • • • • • • • • • • • le1101a.neu (parabolic brick. It provides the input data and results for NAFEMS Standard Benchmark Test LE11.neu (parabolic wedge. coarse mesh) le1103b.neu (parabolic tetrahedron. coarse mesh) le1106b.neu (parabolic brick.neu (linear tetrahedron. coarse mesh) le1104b. fine mesh) le1106a.neu (parabolic wedge. fine mesh) le1102a. coarse mesh) le1101b.neu (linear brick. fine mesh) le1105a.3 a = 2.neu (parabolic tetrahedron.neu (linear wedge. coarse mesh) le1102b. coarse mesh) le1105b. fine mesh) le1103a. Finite Element Modeling • • • Solid brick .coarse and fine mesh Solid wedge . Constrain the nodes on the XY plane in the X translation.coarse and fine mesh Solid Brick Coarse and fine mesh: Coarse and fine mesh: Boundary Conditions Constraints • • • Constrain the nodes on the XZ plane and on the opposite face in the Y translation. Constrain the nodes on the YZ plane in the Z translation. .linear (6–nodes) and parabolic (15–noded) .linear (4–noded) and parabolic (10–noded) .coarse and fine mesh Solid tetrahedron .linear (8–noded) and parabolic (20–noded) . Loads • Nodal temperatures: linear temperature gradient in the radial and axial direction 1 -2 2 T°C = ( X + Y ) + Z 2 . Solid Y Normal Stress at point A.fine mesh linear wedge .2 References • NAFEMS Finite Element Methods & Standards.2 -89. T.fine mesh parabolic tetra . . (Glasgow: NAFEMS. Background to Benchmarks. 3. LE11. 1993).fine mesh parabolic brick .coarse mesh parabolic wedge . • Davies.5 -96.4 -65. Case le1101a le1101b le1102a le1102b le1103a le1103b le1104a le1104b le1105a le1105b le1106a le1106b Node # at Point A 30 71 67 159 33 74 71 187 8 8 8 8 Element Type & Mesh linear brick .coarse mesh linear brick .coarse mesh parabolic tetra .49 -46..9 -88.fine mesh NAFEMS Bench Value (MPa) -105 -105 -105 -105 -105 -105 -105 -105 -105 -105 -105 -105 FEMAP Structural Result (MPa) -95.5 -93.coarse mesh linear tetra .7 -99. Rev.fine mesh parabolic wedge .coarse mesh linear wedge .coarse mesh parabolic brick . 1990.) Test No. A.fine mesh linear tetra ..9 -9. O. The Standard NAFEMS Benchmarks. W..6 -97. G. Note that the Y direction in the models corresponds to the Z direction in NAFEMS. R.9 -105. (Glasgow: NAFEMS. and Lewis. R.8 -31. Fenner. Solution Type Statics Results Output . . finite element modeling (modeling procedure or hints) . If you remesh a model. or rebuild that model from scratch. The finite element method is very flexible in the types of physical problems represented. your node numbering may differ.physical and material properties . The test cases are relatively simple in form and most of them have closed–form theoretical solutions. a specific reference is cited. The theoretical solutions shown in these examples are from well known engineering texts.element type .Normal Modes/Eigenvalue Verification Using Theoretical Solutions The purpose of these normal mode dynamics test cases is to verify the function of the FEMAP Structural Normal Modes/Eigenvalue Analysis software using theoretical solutions. The verification tests provided are not exhaustive in exploring all possible problems.neu) files associated with this guide. This overview provides information on the following: • • • understanding the test case format understanding comparisons with theoretical solutions references Understanding the Test Case Format Each test case is structured with the following information: • test case data and information . For each test case.solution type . All theoretical reference texts are listed at the end of this topic. . but represent common types of applications.units .boundary conditions (loads and constraints) • • results references (text from which a closed–form or theoretical solution was taken) Note: The node numbers listed in each case refer to the node numbers in the neutral (. 1st Edition.. Vibration Problems in Engineering. Other results available from the analyses are not reported here.. it is due to changes in element formulations which SDRC has made to improve results under certain circumstances. but are used for comparison purposes. such as rigid connections. and Hinkle. (Boston: Allyn and Bacon. I. Morse. Understanding Comparisons with Theoretical Solutions While differences in finite element and theoretical results are. 1979. The actual results from the FEMAP Structural software may vary insignificantly from the results presented in this document.. In addition. These limiting restrictions are not necessary for the finite element model. References The following references have been used in the Normal Mode Dynamics Analysis verification problems presented: • • • • Blevins. R. I. some tests would require an infinite number of elements to achieve the exact solution. negligible. (Boston: Allyn and Bacon. Morse. (New York: Van Norstrand Reinhold Company. Inc. 2nd Edition. 1978. Results for both theoretical and finite element solutions are carried out with the same significant digits of accuracy.) Tse. Elements are chosen to achieve reasonable engineering accuracy with reasonable computing times..) Timoshenko and Young. R. Results reported here are results which you can compare to the referenced theoretical solution.. This variation is due to different methods of performing real numerical arithmetic on different systems.. 1978..) Tse.. Inc. (New York: Van Norstrand Reinhold Company. Mechanical Vibrations. Theory and Applications. that do not exist in the real world.) . Mechanical Vibrations. The closed–form theoretical solution may have restrictions. Verification to real world problems is more difficult but should be done when possible. F. in most cases. 1955. F. R. Formulas For Natural Frequency and Mode Shape.. and Hinkle. 3 m Physical Properties • • mass = 20 Kg k = 8 KN/m Finite Element Modeling • • Create 5 rigid elements along the X axis. Create a mass element on the end node.1m long.5 m a = 0.Single Degree of Freedom The complete model and results for this test case are in file mstvn002.Undamped Free Vibration . . Test Case Data and Information Element Types • • • rigid mass DOF springs Units SI . Determine the natural frequency of the system.neu.meter Model Geometry • • Length = 0. Each rigid should be 0. 90986 0.0% . Boundary Conditions Constraints Constrain node 6 in all directions except the Z rotation. Solution Type Normal Modes/Eigenvalue – Guyan method Results Frequency (Hz) Bench Value FEMAP Structural Difference 1. Constrain all other nodes in the X and Y translations and in the Z rotation.90985 1. • Create 3 DOF spring elements 0.2m from the mass element. .) p. and Hinkle... . Reference • Tse. Theory and Applications. 75. 1978. Inc. (Boston: Allyn and Bacon. I. R.. F. Mechanical Vibrations. Morse. Determine the natural frequencies of a dynamic system with two degrees of freedom. Test Case Data and Information Element Types • • DOF springs mass Units SI.meter Physical Properties • • mass = 1 kg k = 1 N/m Finite Element Modeling • • Create four nodes on the Y axis. Create DOF three springs with stiffness of 1 N/m and with a stiffness reference coordinate system being uniaxial.Principle Modes The complete model and results for this test case are in file mstvn003.neu. .Two Degrees of Freedom Undamped Free Vibration . Boundary Conditions Constraints • • Constraint Set 1: Constrain nodes 1 and 4 in all DOF. Use this set as the Master (ASET) DOF set. Constraint Set 2: On the inner nodes. On the other nodes. • Create mass elements with a mass of 1 kg. constrain the Y translation. Solution Type Normal Modes/Eigenvalue – Guyan method . constrain all DOF except the Y translation. Mechanical Vibrations.159155 0. R. Results Frequency of Mode 1 (Hz) Bench Value FEMAP Structural Difference 0. 1978..2756644 0. I. Inc.00% Frequency of Mode 2 (Hz) 0.00% Reference • Tse..159155 0.. . and Hinkle. 2nd Edition.. Morse. F. (Boston: Allyn and Bacon.2756644 0. 145-149.) pp. 1 (mass) k = k1 = k2 = k3 = 1 N*m (stiffness) Finite Element Modeling • • • Create four nodes on the X axis. Create three DOF springs with stiffness of 1 N*m and with a stiffness reference coordinate system being uniaxial. 0. 0.0. 0.0. . Create three mass elements with a mass coordinate system = 1 and with mass inertia system of: 0.Three Degrees of Freedom Torsional System The complete model and results for this test case are in file mstvn004.0.0. 0. Test Case Data and Information Element Types • • DOF springs mass Units SI . 0.meter Physical Properties • • J = J1 = J2 = J3 = 0.0. Determine the natural frequencies of a dynamic system with three degrees of freedom.1.neu. 00% Frequency of Mode 3 (Hz) 0.906901 0.223986 Difference 0. and Hinkle.. R. Use this set as the Master (ASET) DOF set. constrain all DOF. F. 1978. constrain the DOF in RX. Inc. Solution Type Normal Modes/Eigenvalue – Guyan method Results Frequency of Mode 1 (Hz) Bench Value 0.. Mechanical Vibrations. 153–155 . Constraint Set 2: On the other nodes (nodes 2-4). Boundary Conditions Constraints • • Constraint Set 1: On one end node (node 1).00% Frequency of Mode 2 (Hz) 0.627595 0. constrain all DOF except RX.. On the other nodes.627595 0.. Morse. I. 2nd Edition. (Boston: Allyn and Bacon.00% Reference • Tse.223986 FEMAP Structural 0.) pp.906901 0. 0) . 0) N3 = (-L1.6 m Length2 = 2. Test Case Data and Information Element Types 5 nodes. Determine the natural frequencies of dynamic system with two degrees of freedom.neu.4 m (radius of gyration.0 m r = 1.meter Model Geometry • • • Length1 = 1. Degrees of freedom are one translational and one rotational. J=m*r*r) Physical Properties • • • mass = 1800 kg K1 = 42000 N/m K2 = 48000 N/m Finite Element Modeling • Create five nodes in the X–Y plane with coordinates: N1 = (0. 4 elements: • • • 2 DOF springs 1 mass element 1 rigid element Units SI . 0) N2 = (L2.Two Degrees of Freedom Vehicle Suspension System The complete model and results for this test case are in file mstvn005. 0. and Z translations. • Constraint Set 2 (Master (ASET) DOF Set): Constrain nodes 1-3 in the Y translation and Z rotation. 0. . Create a DOF spring with stiffness of k2 between nodes 2 and 4. 0.0. Create a mass element with a mass coordinate system = 1 and with mass inertia system of: 0. N4 = (L2. -1) • • • • Create a DOF spring with stiffness of k1 between nodes 3 and 5. Boundary Conditions Constraints • Constraint Set 1: Constrain nodes 1-3 in the X and Z translation and X and Y rotations.0. Create a three–noded rigid element using node 1 as the master node and nodes 2 and 3 as the slave nodes. 0. Constrain nodes 4-5 in the X. Y. -1) N5 = (-L1. 3528. 0.0.0. 150-153. (Boston: Allyn and Bacon. Inc.00% Frequency of Mode 2 (Hz) 1.495612 1.495612 0. I. R. F.. Morse.00% Reference • Tse. Mechanical Vibrations. 1978.086347 1.086347 0. and Hinkle. .. Solution Type Normal Modes/Eigenvalue – Guyan method Results Frequency of Mode 1 (Hz) Bench Value FEMAP Structural Difference 1. 2nd Edition.) pp... Test Case Data and Information Element Type bar Units Inch Model Geometry • • Length = 100 in Height = 2 in Physical and Material Properties • • • w = 1 lb/in J = .neu.54 m = w/g = 2.Cantilever Beam Undamped Free Vibrations The complete model and results for this test case are in file mstvn006.3 Calculated Data • • • • • A = h2 = 4 in2 I = h4/12 = 1. . Determine the natural frequencies of a cantilever beam.66666 Finite Element Modeling • Create 11 nodes on X axis.33333 G = E/2 x 1/1+nu = 11538461.59067375E-3 Ip = Ixx + Iyy = 2.10 Poisson’s ratio = . 684410 122. Solution Type Normal Modes/Eigenvalue – SVI method Results Mode 1&2 3&4 5 6&7 8 9 & 10 Bench Values (Hz) 6.8567 195. Formulas For Natural Frequency and Mode Shape.9533571 43. . 108.128% 0..85388 238.6024 238.193.54267 64. 1979) pp.6964 Difference -0.901% -0. • Create 10 bars between the nodes. R.254% -0.75784 FEMAP Structural (Hz) 6.033% -0. Boundary Conditions Constraints • Fully constrain one end node (node 1) in all directions and rotations.01391 193.951037 43.026% Reference • Blevins.575945 64. 1st Edition. (New York: Van Norstrand Reinhold Company.66795 121.076% -0. 0) and (30.0E-06 I = 1.0.5 lbm E = 30E6 psi Density = 1.0.5 in 4 Finite Element Modeling • • Create 2 nodes on the X axis with coordinates (0. . Test Case Data and Information Element Types • • bar mass Units Inch Model Geometry • Length = 30 in Physical and Material Properties • • • • Mass = 0.neu. Create a bar between nodes with shear area ratio=0.Natural Frequency of a Cantilevered Mass The complete model and results for this test case are in file mstvn007.0). Determine the natural frequencies of a dynamic system consisting of a massless bar element and a mass element at the end. Constraint Set 2: On the mass end node. Solution Type Normal Modes/Eigenvalue – Guyan method Results Natural Frequency (Hz) Bench Value FEMAP Structural Difference 15. and RZ.00% . Use this set as the Master (ASET) DOF set. Boundary Conditions Constraints • • −Constraint Set 1: On the wall end (at node 1).9155 15.5 lbm. constrain the DOF in Z. Y. • Create a mass on one node with mass of 0. and RY. RX. On the mass end. constrain the DOF in Z. constrain all DOF.9154 0. Reference • Tse. R. 1978. Morse. I. and Hinkle. 2nd Edition.. (Boston: Allyn and Bacon.. 72 . Mechanical Vibrations.. F. Inc.) p.. .) .Normal Modes/Eigenvalue Verification Using Standard NAFEMS Benchmarks The purpose of these normal mode dynamics test cases is to verify the function of the FEMAP Structural Normal Modes/Eigenvalue solver using standard benchmarks published by NAFEMS (National Agency for Finite Element Methods and Standards.material properties .). Abbassian. F. D.finite element modeling information . Reference The following reference has been used in these test cases: • NAFEMS Finite Element Methods & Standards. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.. Glasgow. C. Dawswell.boundary conditions (loads and constraints) . Nov. National Engineering Laboratory.. Understanding the Test Case Format Each test case is structured with the following information: • test case data and information . All results obtained using the FEMAP Structural software compare favorably with other commercial finite element analysis software. your node numbering may differ. U..solution type • • results reference Note: The node numbers listed in each case refer to the node numbers in the neutral (. If you remesh a model. and Knowles.K. Results of these test cases using other commercial finite element analysis software programs are available from NAFEMS. J.units . N.neu) files associated with this guide. 1987. These standard benchmark tests were created by NAFEMS to stretch the limits of the finite elements in commercial software. or rebuild that model from scratch. In-plane Vibration" "Free Square Frame .In-plane Vibration" "Cantilever with Off-Center Point Masses" "Deep Simply-Supported Beam" "Circular Ring .Bar Element Test Cases The normal mode dynamics test cases using the standard NAFEMS benchmarks include these bar element test cases: • • • • • • • "Pin-ended Cross .In-plane Vibration" "Pin-ended Double Cross .In-plane and Out-of-plane Vibration" "Cantilevered Beam" . 0 m Attributes of this test are: • • coupling between flexural and extensional behavior repeated and close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Key–in section: • Area = .In-plane Vibration The complete model and results for this test case are in file nf001ac. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. This test is a normal modes/eigenvalue analysis of a pin–ended cross (shown below) using bar elements.125 m D . Test 1.neu.Pin-ended Cross .015625 m2 Shear ratio: . B A C .125 m 5. 5) in all directions except for the Z rotation. • • Y=0 Z=0 Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m η = 0.29 ( Poissons ratio ) G = 8. four elements per arm Boundary Conditions Constraints • • Constrain points A. 4. . 3. Constrain node point Z (node 1) in the Z translation and X rotation. B.01x10 10 Finite Element Modeling • • 17 nodes 16 bar elements. D (nodes 2. C. C.390 57. Nov. 1987. 3 4 5 6.364 57.715 45.336 17.477 57.364 57.. D.336 17.683 FEMAP Structural (Hz) 11. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. J. ..687 17.683 Note: Reference value (Ref. and Knowles.709 45. Value (Hz) 11.336 17. F. Dawswell. Abbassian..345 57. N.709 17. Solution Type Normal Modes/Eigenvalue – SVI method Results Mode # 1 2. 7 8 Ref.. • Constrain all other nodes (6-17) in the Z translation and X and Y rotations. Value) refers to the accepted solution to the problem.687 17.) Test No. Reference • NAFEMS Finite Element Methods & Standards.715 45. 1.477 57.390 Mesh linear linear linear linear linear linear NAFEMS Target Value (Hz) 11. 0m 5. C B D .015625 m2 Shear ratio: .0 m Attributes of this test are: • • coupling between flexural and extensional behavior repeated and close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Key–in section: • Area = .125 m A E . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.125 m H G F 5.Pin-ended Double Cross .In-plane Vibration The complete model and results for this test case are in file nf002ac.neu. Test 2. This test is a normal modes/eigenvalue analysis of a pin–ended double cross (shown below) using bar elements. . B. F. G. D. C. Constrain all other nodes 1. E. H (nodes 2-9) in all directions except for the Z rotation. four elements per arm Boundary Conditions Constraints • • Constrain points A. • • Y=0 Z=0 Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m Finite Element Modeling • • 33 nodes 32 bar elements. (10-33) in the Z translation and X and Y rotations. . and Knowles. Value) refers to the accepted solution to the problem.336 17. C. Solution Type Normal Modes/Eigenvalue – SVI method Results Mode # 1 2. Dawswell. Reference • NAFEMS Finite Element Methods & Standards..) Test No.683 Note: Reference value (Ref.477 57. 1987.8 9 10.715 45.7. Value (Hz) 11.336 17.687 17.5.345 57. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. Abbassian.687 17.709 17.364 57.709 45.. D. 6.364 57. N. The following figure shows the boundary conditions. 11 12.390 Mesh linear linear linear linear linear linear NAFEMS Target Value (Hz) 11.715 45.15. . 2. Nov. 3 4.683 FEMAP Structural Result (Hz) 11.477 57.336 17. J. F.390 57..13. 16 Ref. 14. In-plane Vibration The complete model and results for this test are in file nf003ac.0 Z = 1.125 m 10. This test is a normal modes/eigenvalue analysis of a free square frame (shown below) using bar elements.neu.0m 10.0 m Attributes of this test are: • • • coupling between flexural and extensional behavior rigid body modes (3 modes) repeated and close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear ratio: • • Y = 1. .Free Square Frame .125 m . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. Test 3.0 . four elements per arm Boundary Conditions Constraints • Constraint Set 1: Constrain all nodes in the Z translation and X and Y rotations. . Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m Finite Element Modeling • • 16 nodes 16 bar elements. 261 5.127 12.833 24.. .. 1987.664 28.262 5.570 28. D. 11 Ref. N. Value) refers to the accepted solution to the problem. Value (Hz) 3. Abbassian.665 11.136 12.. 3. 7 8 9 10.611 28.) Test No. Nov. Solution Type Normal Modes/Eigenvalue – SVI method Results Mode # 4 5 6. C.259 5.700 Note: Reference value (Ref. F.145 12. • Constraint Set 2 (Kinematic DOF): Constrain nodes 1 and 3 in the X and Y translation and the Z rotation. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. J. and Knowles.662 11.849 24. Dawswell. Reference • NAFEMS Finite Element Methods & Standards.668 11.695 Mesh linear linear linear linear linear linear NAFEMS FEMAP Structural Target Value (Hz) (Hz) 3.793 24.813 3.. Cantilever with Off-Center Point Masses The complete model and results for this test is in file nf004a.neu. Attributes of this test are: • • • • coupling between torsional and flexural behavior inertial axis non–coincident with flexibility axis discrete mass.128 Material Properties 9 N E = 200x10 -----2 m gρ = 8000k -----3 m ν = 0. Test 4. This test is a normal modes/eigenvalue analysis of a cantilever with off–center point masses (shown below) using bar elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.3 Finite Element Modeling • • 8 nodes 9 elements . rigid links close eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear ratio: • • Y = 1.128 Z = 1. five bar elements along cantilever two mass elements two rigid elements Boundary Conditions Constraints • Fully constrain point A (node 1) in all directions. Solution Type Normal Modes/Eigenvalue – SVI method . . C..160 26.947 18.723 1. Value) refers to the accepted solution to the problem. Value (Hz) Value (Hz) (Hz) 1.155 26.. Dawswell.723 1. Results FEMAP NAFEMS Target Structural Result Ref. and Knowles.410 9.957 1.726 7.712 Mode # 1 2 3 4 5 6 Note: Reference value (Ref.722 1.413 9.972 1. Reference • NAFEMS Finite Element Methods & Standards.972 18. J. Nov. Abbassian. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. F.972 18.051 26. N.413 9.727 7.) Test No.727 7.. 1987. 4 . D. Attributes of this test are: • • • shear deformation and rotary inertial (Timoshenko beam) possibility of missing extensional modes when using iteration solution methods repeated eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear Ratio • • Y = 1. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.3 Finite Element Modeling • 6 nodes .176923 Z = 1.176923 Material Properties 9 N E = 200x10 -----2 m g ρ = 8000k -----3 m ν = 0. This test is a normal mode dynamic analysis of a deep simply–supported beam.Deep Simply-Supported Beam The complete model and results for this test are in file nf005ac. Test 5.neu. 51 145. Solution Type Normal Modes/Eigenvalues – SVI method Results Mode # 1.649 77.46 241.31 233.568 77.01 FEMAP Structural Result (Hz) 42.52 150. 2 3 4 5. Z translation an X rotation at point A (node 1) Constrain the Y and Z translation at point B (node 10) The boundary conditions are shown in the following diagram.710 77.00 148.10 284.841 125. • 5 bar elements Boundary Conditions Constraints • • Constrain the X.542 125. 9 Ref.55 NAFEMS Target Value (Hz) 42.24 267.841 125.24 301.76 241. 6 7 8. Y.08 . Value (Hz) 42. 1987. Dawswell. N. .. D. Note: Reference value (Ref. 5... Reference • NAFEMS Finite Element Methods & Standards. J. F. C. Value) refers to the accepted solution to the problem.. and Knowles. Abbassian. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. Nov.) Test No. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. Test 6. This test is a normal modes/eigenvalue analysis of a circular ring using bar elements.128205 Z = 1.3 Finite Element Modeling • 20 nodes .Circular Ring .128205 Material Properties 9 N E = 200x10 -----2 m gρ = 8000k -----3 m ν = 0. Attributes of this test are: • • rigid body modes (six modes) repeated eigenvalues Test Case Data and Information Units SI Cross Sectional Properties Shear ratio: • • Y = 1.In-plane and Out-ofplane Vibration The complete model and results for this test are in file nf006ac.neu. Solution Type Normal Modes/Eigenvalue – SVI method . • 20 bar elements Boundary Conditions Constraints • Constraint Set 1 (Kinematic DOF): Constrain nodes 10 and 11 in all directions and rotations. Value (Hz) 51.44 288.849 53... 14 (in plane) 15 (out of plane) 16 (in plane) Ref. N. Dawswell. Abbassian. 10 (in plane) 11. .. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.92 151.775 148. J.25 FEMAP Structural Result (Hz) 52.971 149. 1987.98 289.70 152.77 150. 6. Nov.) Test No. C. and Knowles. F. Reference • NAFEMS Finite Element Methods & Standards. Results Mode # 7.51 NAFEMS Target Value (Hz) 52.25 288.33 Note: Reference value (Ref. Value) refers to the accepted solution to the problem.33 285.290 53.99 286.. 12 (out of plane) 13. D.382 148. 8 (out of plane) 9.211 53.25 285. Cantilevered Beam The complete model and results for this test case are in the following files: • • • nf071a. Attributes of this test are: • ill–conditioned stiffness matrix Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m gρ = 8000k -----3 m Finite Element Modeling Three tests . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.neu (Test 3) This test is a normal modes/eigenvalue analysis of a cantilevered beam.neu (Test 1) nf071b. Test 71.neu (Test 2) nf071c.all use 8 bar elements and 9 nodes • • Test 1: a=b Test 2: a = 10b . . Solution Type Normal Modes/Eigenvalue – SVI method Bar elements always use a consistent mass formulation. Constrain all other nodes in the Z translation and X and Y rotations. • Test3: a = 100b Boundary Conditions Constraints • • Fully constrain point A (node 1) in all directions and rotations. D. Results FEMAP Structural Result (Hz) 1.010 Mesh 1 2 6.390 6 85.3260 6.730 a=b a = 10b a = 100b a=b a = 10b a = 100b a=b a = 10b a = 100b a=b a = 10b a = 100b a=b a = 10b a = 100b a=b a = 10b a = 100b Note: Reference value (Ref.717 5 57.) Test No. J.422 60. Value) refers to the accepted solution to the problem.675 34. Abbassian.751 86.. 1987.061 57. .0095 1. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.0095 1.595 64..819 34.654 Mode # Ref.791 17.135 101.3289 17.3223 6. F. Nov. and Knowles.327 3 17.693 17. N. Reference • NAFEMS Finite Element Methods & Standards. Dawswell. Value (Hz) 1.854 35..716 4 34. 71.673 104. C.0095 6.. Test A" "Clamped Thick Rhombic Plate" "Simply-Supported Thick Square Plate.Plate Element Test Cases The normal mode dynamics test cases using the standard NAFEMS benchmarks include these plate element test cases: • • • • • • • • • • • • • • • • "Thin Square Cantilevered Plate -Symmetric Modes" "Thin Square Cantilevered Plate .Anti-symmetric Modes" "Free Thin Square Plate" "Simply-Supported Thin Square Plate" "Simply-Supported Thin Annular Plate" "Clamped Thin Rhombic Plate" "Cantilevered Thin Square Plate with Distorted Mesh" "Simply-Supported Thick Square Plate. Test B" "Simply-Supported Thick Annular Plate" "Cantilevered Square Membrane" "Cantilevered Tapered Membrane" "Free Annular Membrane" "Cantilevered Thin Square Plate" "Cantilevered Thin Square Plate #2" . consistent mass) nf011all. lumped mass) nf011apc.neu (linear quadrilateral plate. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. Attributes of this test are: • symmetric modes. consistent mass) nf011apl. symmetric boundary conditions along the cutting plane Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.neu (parabolic quadrilateral plate. lumped mass) This test is a normal modes/eigenvalue analysis of a thin. square.thickness = 0. Test 11a.Thin Square Cantilevered Plate Symmetric Modes The complete model and results for this test case are in the following files: • • • • nf011alc.neu (parabolic quadrilateral plate.05m Test 2 and Test 3 (nf011apc and nf011apl) • 37 nodes .3 Finite Element Modeling Test 1 and Test 2 (nf011alc and nf011all) • • 45 nodes 32 linear quadrilateral plate elements . cantilevered plate meshed with plate elements.neu (linear quadrilateral plate. 16. Constrain nodes 6. Constrain all other nodes in the X and Y translations and Z rotation. 21. 11. 36.05m Mesh only half the plate (10m x 5m). 41 in the X and Y translations and X and Z rotations. Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . • 8 parabolic quadrilateral plate elements . 31.thickness = 0. Linear Quadrilateral Plates Parabolic Quadrilateral Plates Boundary Conditions • • • • Constraints (all tests) Fully constrain nodes 1-5 in all translations and rotations. 26. 241 6. D.306 6. Reference • NAFEMS Finite Element Methods & Standards. Dawswell.555 7. N.493 FEMAP Structural Result (consistent mass) (Hz) 0.112 11.418 2. 1987.117 3.525 12. C. Value (Hz) 0.315 3. Abbassian.415 0.381 11.. Nov.979 7..281 6. 11a.950 Mode # 1 2 3 4 5 6 Mesh linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref. .414 2.418 0. F.984 6.954 10.387 10.) Test No. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.081 5..018 7. Results Ref.582 3.444 3.421 2.402 FEMAP Structural Result (lumped mass) (Hz) 0. and Knowles..569 3. J.551 7.507 2.623 2.573 6. Value) refers to the accepted solution to the problem. neu (parabolic quadrilateral plate.neu (linear quadrilateral plate. consistent mass) nf011bll. 32 linear quadrilateral plate elements . square.neu (linear quadrilateral plate.neu) • 37 nodes. lumped mass) nf011bpc. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.neu) • 45 nodes.neu and nf011bll. consistent mass) nf011bpl. Attributes of this test are: • anti–symmetric modes Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.Thin Square Cantilevered Plate Anti-symmetric Modes The complete model and results for this test case are the in following files: • • • • nf011blc.05m .neu (parabolic quadrilateral plate.thickness = 0. lumped mass) This test is a normal modes/eigenvalue analysis of a thin. 8 parabolic quadrilateral plate elements . Test 11b.3 Finite Element Modeling Tests 1 and 2 (nf011blc. cantilevered plate meshed with plate elements.neu and nf011bpl.thickness = 0.05m Tests 3 and 4 (nf011bpc. Constrain nodes 6. Boundary Conditions Constraints (all tests) • • • Fully constrain nodes 1-5 in all directions. 26. Y. 16. Z translations and Z rotation. Mesh only half the plate (10m x 5m). 11. 36. 21. Constrain all other nodes in the X and Y translations and Z rotation. 31. Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . 41 in the X. Value) refers to the accepted solution to the problem.192 16.541 7. Reference • NAFEMS Finite Element Methods & Standards.693 11.012 1. Value (Hz) 1..162 7. Dawswell.087 13.818 15.483 11.082 7.024 3.730 8.019 1. C.755 0. Abbassian.018 3. .130 6.999 3. N.728 8.710 8.561 not available not available FEMAP FEMAP NAFEMS Structural Result Structural Result Target Value (lumped mass) (consistent mass) (Hz) (Hz) (Hz) 1.553 3.954 13. J. 11b.750 3. and Knowles.451 17...993 0.846 9.424 8. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.918 Mode # 1 2 3 4 5 6 Mesh linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref.526 11.079 8.728 11. Nov.185 17.847 8..768 9.839 3.753 7.805 9. 1987. Results Ref.894 9.724 1. F.) Test No.313 7. D.029 3. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. lumped mass) nf012pc. lumped mass) This test is a normal modes/eigenvalue analysis of a free thin square plate meshed with plate elements.05m .neu (parabolic quadrilateral plate. consistent mass) nf012pl.neu (parabolic quadrilateral plate.neu (linear quadrilateral plate.neu and nf012pl.05m Tests 3 and 4 (nf012pc. consistent mass) nf012ll.thickness = 0. 16 parabolic quadrilateral plate elements . 64 linear quadrilateral plate elements .neu and nf012ll.3 Finite Element Modeling Tests 1 and 2 (nf012lc.neu) • 65 nodes. Attributes of this test are: • • • rigid body modes (three modes) repeated eigenvalues use of kinematic DOF for the rigid body mode calculation with the SVI eigensolver Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.Free Thin Square Plate The complete model and results for this test case are in the following files: • • • • nf012lc.neu (linear quadrilateral plate. Test 12.neu) • 81 nodes.thickness = 0. Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . • Constraint Set 2 (Kinematic DOF): Constrain nodes 1 and 3 in all directions and rotations. Boundary Conditions Constraints • Constraint Set 1: Constrain all the nodes in the X and Y translations and Z rotation. 922 4. Value (Hz) 1.990 2.218 4.615 1.) Test No.622 2.006 2.586 6. Reference NAFEMS Finite Element Methods & Standards.861 4.532 2.903 6.494 Note: Reference value (Ref.750 3.570 1.246 2..494 7.122 7. Value) refers to the accepted solution to the problem. 8 9 10 Ref..751 7.879 6.360 2.632 1. J.902 6. Abbassian.027 7. 12. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS..363 8. Results Mode # 4 5 6 7.186 7. N.251 4.859 7.402 2. Dawswell. D.815 2. C. Nov.567 2.586 1.619 2.394 2.930 4.912 3.392 FEMAP Structural FEMAP Structural Result (lumped Result (consistent mass) (Hz) mass) (Hz) 1. F.356 3. . 1987.884 7.364 2.416 not available Mesh linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic NAFEMS Target Value (Hz) 1.183 2.233 7. and Knowles.. neu (linear quadrilateral plate.thickness = 0.neu (linear quadrilateral plate. consistent mass) nf013ll. consistent mass) nf013pl. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. 64 linear quadrilateral plate elements .3 Finite Element Modeling Tests 1 and 2 (nf013lc. lumped mass) nf013pc.Simply-Supported Thin Square Plate The complete model and results for this test case are in the following files: • • • • nf013lc. Test 13.neu and nf013ll.neu (parabolic quadrilateral plate.05m Tests 3 and 4 (nf013pc. lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thin square plate meshed with plate elements.neu) • 81 nodes.neu) .neu (parabolic quadrilateral plate.neu and nf013pl. Attributes of this test are: • • well established repeated eigenvalues Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. • 65 nodes.05m Boundary Conditions Constraints • • • • Constrain all nodes in the X and Y translations and Z rotation.thickness = 0. Constrain the nodes along edges X = 0 and X = 10m in the Z translation and X rotation. 13. 16 parabolic quadrilateral plate elements . 41. Fully constrain the DOF on the four corner nodes (9. 68). Constrain the nodes along edges Y = 0 and Y = 10m in the Z translation and Y rotation. Solution Type Normal Modes/Eigenvalue – SVI method Results were obtained two different ways: . 820 5.375 12.383 6. • • using lumped mass using consistent mass Results Mode # 1 2.942 9.034 9. 1987. 3 4 5. and Knowles.932 8.. J.215 15.590 16. C.. Reference • NAFEMS Finite Element Methods & Standards.) Test No.392 11..449 Mesh 4–noded 8–noded 4–noded 8–noded 4–noded 8–noded 4–noded 8–noded 4–noded 8–noded FEMAP Structural Result (lumped mass) (Hz) 2. Value) refers to the accepted solution to the problem. 6 7.884 15. 8 Ref. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. Abbassian.033 FEMAP Structural Result (consistent mass) (Hz) 2.831 13. D. Value (Hz) 2.399 2.909 9. F. Dawswell.879 14. ..507 11.338 2.375 5.206 6.770 11.873 9. Nov. N.377 5.734 Note: Reference value (Ref.786 16. 13. neu (linear quadrilateral plate.06m Tests 3 and 4 (nf014pc and nf014pl) .Simply-Supported Thin Annular Plate The complete model and results for this test case are in the following files: • • • • nf014lc. 160 linear quadrilateral plate elements . consistent mass) nf014pl.neu (parabolic quadrilateral plate.thickness = 0. lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thin annular plate meshed with shell elements.neu (parabolic quadrilateral plate. lumped mass) nf014pc. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. Test 14.3 Finite Element Modeling Tests 1 and 2 (nf014lc and nf014ll): • 192 nodes.neu (linear quadrilateral plate. consistent mass) nf014ll. Attributes of this test are: • • curved boundary (skewed coordinate system) repeated eigenvalues Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. • 176 nodes.thickness = 0.06m Boundary Conditions • Constraint Set 1 (All Tests): Constrain all nodes in in the X and Y translation and Z rotation. • Constraint Set 2 (Kinematic DOF): Tests 1 and 2: Constrain nodes 258 and 290 in the X and Y translations. Additionally constrain all nodes around the model’s circumference in the Z translation and X rotation. . 48 parabolic quadrilateral plate elements . 547 17.686 9. Tests 3 and 4: Constrain nodes 21 and 133 in the X and Y translations.672 14. Value) refers to the accepted solution to the problem.850 15. 5 6 7.176 15.713 15. Solution Type Normal Mode Dynamics .188 13.859 1.870 5.111 9.708 19. 3 4.175 5.412 14.249 5.088 18. .151 9.380 1.983 9.946 15.137 9.924 16.840 5.673 14.382 Mesh linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic FEMAP Structural FEMAP Structural Result (lumped Result (consistent mass) (Hz) mass) (Hz) 1.877 1.594 17. 8 9 Ref.326 15.873 5.521 Note: Reference value (Ref.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results Mode # 1 2.573 18. Value (Hz) 1. . D. 1987. and Knowles. C. Reference • NAFEMS Finite Element Methods & Standards.) Test No.. . Abbassian. J.. N. Dawswell. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. 14. Nov. F.. lumped mass) nf015pl. 144 linear quadrilateral plate elements . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.thickness = 0.neu (parabolic quadrilateral plate.neu (parabolic quadrilateral plate.neu (linear quadrilateral plate.Clamped Thin Rhombic Plate The complete model and results for this test case are in the following files: • • • • nf015lc. lumped mass) nf015pc.neu (linear quadrilateral plate. Attributes of this test are: • distorted elements Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.neu and nf015ll.05m .neu): • 169 nodes. consistent mass) This test is a normal modes/eigenvalue analysis of a clamped thin rhombic plate meshed with plate elements.3 Finite Element Modeling Tests 1 and 2 (nf015lc. consistent mass) nf015ll. Test 15. 05m Boundary Conditions Constraints • • Completely constrain the nodes along all four edges of the part in all directions and rotations.neu): • 133 nodes. Constrain all other nodes in the X and Y translation and Z rotation. Solution Type Normal Modes/Eigenvalue .thickness = 0. Tests 3 and 4 (nf015pc.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass .neu and nf015pl. 36 parabolic quadrilateral plate elements . 009 27. .480 20. J.810 Note: Reference value (Ref.831 12.891 12.955 7. N.929 13. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.964 23. F.883 7.704 27.938 12.816 28.950 32.036 17.818 7.472 19.554 18. Reference • NAFEMS Finite Element Methods & Standards.226 29. Nov.698 27. C.165 18.902 12.185 25. Value) refers to the accepted solution to the problem.142 7. Results Mode # 1 2 3 4 5 6 Ref.) Test No. and Knowles.388 13.168 26.835 17.133 24.665 23.851 17.312 20...922 Mesh linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic NAFEMS FEMAP Structural FEMAP Structural Target Value Result (lumped Result (consistent mass) (Hz) mass) (Hz) (Hz) 8.952 18.008 19.239 19.738 27..910 7. 1987. 15. D.941 19.873 13. Abbassian. Value (Hz) 7..046 25.879 27.072 18. Dawswell.807 17. Attributes of this test are: • distorted meshes Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. consistent mass) nf016d1.neu (16 parabolic quadrilateral plate.neu (4 parabolic quadrilateral plate.neu (16 parabolic quadrilateral plate.3 Finite Element Modeling All tests . consistent mass) nf016b1.neu (16 parabolic quadrilateral plate. lumped mass) nf016b2.neu (4 parabolic quadrilateral plate. Test 16. consistent mass) This test is a normal modes/eigenvalue analysis of a cantilevered thin square plate meshed with distorted plate elements. lumped mass) nf016d2.thickness = 0. lumped mass) nf016c2.neu (4 parabolic quadrilateral plate.neu (16 parabolic quadrilateral plate.neu (4 parabolic quadrilateral plate. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.parabolic quadrilateral plate elements . lumped mass) nf016a2.05m . consistent mass) nf016c1.Cantilevered Thin Square Plate with Distorted Mesh The complete model and results for this test case are in the following files: • • • • • • • • nf016a1. 25 2.0 2.75 7.75 7. 16 elements with specified nodes at the following XY coordinates: X Coordinate 4.5 7.25 7.5 Y Coordinate 4.75 4.25 4.25 4.25 7.65 nodes.25 2.5 2. nf016a2) .25 7. 16 elements • Test 2 (nf016b1.0 2. Four tests: • Test 1 (nf016a1. nf016b2) .75 5.65 nodes.75 .25 2. • Test 3 (nf016c1, nf016c2) - 21 nodes, 4 elements • Test 4 (nf016d1, nf016d2) - 21 nodes, 4 elements with a specified node at X=4.0, Y=4.0. Boundary Conditions Constraints (nf016a1 and nf016a2) • • Constrain the nodes along the model’s Y axis in the X, Y, and Z translations and in the Y and Z rotations. Constrain all other nodes in the Z rotation only. Constraints (nf016b1 and nf016b2) • • Fully constrain the nodes along the model’s Y axis in all directions. Constrain all other nodes in the Z rotation only. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results Ref. Value (Hz) 0.421 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 NAFEMS Target Value (Hz) 0.4174 0.4174 0.4144 0.4145 1.020 1.020 0.999 1.002 2.564 2.571 2.554 2.565 3.302 3.317 3.401 3.424 3.769 3.780 3.697 3.714 6.805 6.883 5.455 5.133 FEMAP FEMAP Structural Structural Result (consistent Result (lumped mass) (Hz) mass) (Hz) 0.4139 0.4135 0.4021 0.3999 0.9985 0.9967 0.9347 0.9202 2.444 2.445 2.132 2.112 3.082 3.072 2.707 2.697 3.540 3.535 3.136 3.077 6.018 5.994 5.458 5.459 0.4181 0.4182 0.4189 0.4192 1.024 1.024 1.021 1.025 2.569 2.566 2.708 2.698 3.281 3.280 3.449 3.430 3.728 3.731 3.913 3.881 6.551 6.552 7.108 6.858 Mode # 1 Test 2 1.029 3 2.582 4 3.306 5 3.753 6 6.555 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 16. Simply-Supported Thick Square Plate, Test A The complete model and results for this test case are in the following files: • • • • nf021alc.neu (linear quadrilateral plate, consistent mass) nf021all.neu (linear quadrilateral plate, lumped mass) nf021apc.neu (parabolic quadrilateral plate, consistent mass) nf021apl.neu (parabolic quadrilateral plate, lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thick square plate meshed with shell elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis, Test 21a. Attributes of this test are: • • • well–established repeated eigenvalues effect of secondary restraints Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.3 Finite Element Modeling Tests 1 and 2 (nf021alc.neu and nf021all.neu) • 81 nodes, 64 linear quadrilateral plate elements - thickness = 1.0m Tests 3 and 4 (nf021apc.neu and nf021apl.neu) • 65 nodes, 16 parabolic quadrilateral plate elements - thickness = 1.0m Boundary Conditions Constraints • • • Fully constrain the corner nodes in all directions and rotations. Constrain the nodes along edges X=0 and X=10m in all directions, except the Y rotation. Constrain the nodes along edges Y=0 and Y=10m in all directions, except the X rotation. • Constrain all other nodes in the X and Y translation and Z rotation. Solution Type Normal Modes/Eigenvalue - SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results Ref. Value (Hz) 45.897 109.44 167.89 204.51 FEMAP FEMAP NAFEMSTar Structural Structural Result get Value Result (lumped (consistent mass) (Hz) mass) (Hz) (Hz) 46.659 45.936 115.84 110.41 177.53 170.38 233.40 212.81 45.50 46.165 108.70 110.32 160.63 167.30 204.75 204.59 46.35 45.830 114.12 109.38 174.29 169.75 227.05 208.20 Mode # 1 2, 3 4 5, 6 Mesh linear parabolic linear parabolic linear parabolic linear parabolic 7, 8 9 10 256.50 336.62 336.62 linear parabolic linear parabolic linear parabolic 283.60 269.96 371.11 344.77 371.11 344.77 240.84 249.26 298.18 311.32 320.41 347.63 276.88 268.40 364.30 319.40 385.84 319.40 Note: Reference value (Ref. Value) refers to the accepted solution to the problem. Reference • NAFEMS Finite Element Methods & Standards, Abbassian, F., Dawswell, D. J., and Knowles, N. C., Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS, Nov., 1987.) Test No. 21a. neu (parabolic quadrilateral plate elements. 64 linear quadrilateral plate elements . Test B The complete model and results for this test case are in the following files: • • • • nf021blc. consistent mass) nf021bpl.neu (linear quadrilateral plate elements. Attributes of this test are: • • • well–established repeated eigenvalues effect of secondary restraints Test Case Data and Information Units SI Material Properties 9 N E = 200X10 -----2 m kg ρ = 8000 -----3 m ν = 0.neu) • 81 nodes.thickness = 1. Test 21b.3 Finite Element Modeling Tests 1 and 2 (nf021blc. lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thick square plate meshed with plate elements.neu (parabolic quadrilateral plate elements.0m .neu and nf021bll.Simply-Supported Thick Square Plate. consistent mass) nf021bll. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. lumped mass) nf021bpc.neu (linear quadrilateral plate elements. thickness = 1. Constrain all other nodes in the X and Y translation and Z rotation.SVI method Results were obtained two different ways: • using lumped mass . 16 parabolic quadrilateral plate elements .0m Boundary Conditions Constraints • • Constrain the nodes along all edges in the X.Y. Solution Type Normal Modes/Eigenvalue .neu) • 65 nodes. Tests 3 and 4 (nf021plc.neu and nf021pll. and Z translations and Z rotation. 745 44.71 293.80 44.07 274.493 112.96 163. • using consistent mass Results Ref.815 106.19 230.50 336. C. 6 7. D.897 109.98 342.28 164.70 225.57 170. Abbassian. .96 108.64 346. Nov.) Test No.78 318.96 44. 3 4 5. Value) refers to the accepted solution to the problem.40 203.57 203.16 319.94 107..80 355.12 237. J. 1987.46 272. and Knowles.62 FEMAP FEMAP NAFEMS Structural Result Structural Result Target Value (lumped mass) (consistent mass) (Hz) (Hz) (Hz) 44.89 204.51 206.43 318.62 336.19 260. 8 9 10 Mesh linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref.17 165.85 44.61 358.58 Mode # 1 2.32 355. Value (Hz) 45. 21b.23 20.56 384.14 44.44 167. N.95 307.85 170. Reference • NAFEMS Finite Element Methods & Standards.134 112.. F..31 245.47 263.51 256.52 156.. Dawswell.98 342.25 107. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. neu (parabolic quadrilateral plate. lumped mass) This test is a normal modes/eigenvalue analysis of a thick clamped thick rhombic plate meshed with plate elements. consistent mass) nf022ll. Attributes of this test are: • distorted elements Test Case Data and Information Units SI Material Properties 9 N E = 200X10 -----2 m kg ρ = 8000 -----3 m ν = 0.neu (linear quadrilateral plate.neu (parabolic quadrilateral plate.neu and nf022ll.Clamped Thick Rhombic Plate The complete model and results for this test case are in the following files: • • • • nf022lc. Test 22. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. lumped mass) nf022pc.3 Finite Element Modeling Tests 1 and 2 (nf022lc. consistent mass) nf022pl.neu) .neu (linear quadrilateral plate. .neu and nf022pl.thickness = 1. • 121 nodes.0m Boundary Conditions Constraints • Fully constrain the nodes along all four edges in all directions and rotations.0m Tests 3 and 4 (nf022pc. 36 parabolic quadrilateral plate elements .neu) • 133 nodes. 100 linear quadrilateral plate elements .thickness = 1. 48 203.56 346.90 381.80 133. • Constrain all other nodes in the X and Y translations and Z rotation.41 426.30 269.81 282.48 213.79 Mode # 1 2 3 4 5 6 Mesh linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic .51 204.08 266.86 218.06 289.62 133.34 295.SVI Results were obtained two different ways: • • using lumped mass using consistent mass Results Ref.45 not available FEMAP FEMAP Structural NAFEMS Structural Result Target Value Result (lumped (consistent mass) (Hz) mass) (Hz) (Hz) 137.42 204.05 273.17 132.38 296. Value (Hz) 133.33 134.65 377.87 381.05 338.23 270.83 283.28 369.88 411.95 201. Solution Type Normal Mode Dynamics .17 279.59 386.06 200.75 283.74 334.90 135.41 265.68 383.92 338.95 337.28 288.42 271. D. and Knowles. Dawswell.. Value) refers to the accepted solution to the problem. Note: Reference value (Ref. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. 22 . F..) Test No. N. Abbassian. Nov. Reference • NAFEMS Finite Element Methods & Standards.. 1987.. J. C. neu and nf023ll. consistent mass) nf023ll.neu) .neu (linear quadrilateral plate.neu (parabolic quadrilateral plate.Simply-Supported Thick Annular Plate The complete model and results for this test case are in the following files: • • • • nf023lc. Test 23.neu (linear quadrilateral plate. lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported thick annular plate meshed with plate elements. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.3 Finite Element Modeling Tests 1 and 2 (nf023lc. Attributes of this test are: • • curved boundary (skewed coordinate system) repeated eigenvalues Test Case Data and Information Units SI Material Properties 9 N E = 200X10 -----2 m kg ρ = 8000 -----3 m ν = 0. consistent mass) nf023pl. lumped mass) nf023pc.neu (parabolic quadrilateral plate. 6m Tests 3 and 4 (nf023pc.neu) • 176 nodes.thickness = 0. and Z translations and X and Z rotations. .neu and nf023pl.6m Boundary Conditions Constraints • Constrain the nodes around the circumference in the X. 160 linear quadrilateral plate elements .thickness = 0. Y. 48 parabolic quadrilateral plate elements . • 192 nodes. 59 50.61 18.59 49.06 92.19 18. 3 4.90 18.43 93.92 92. • Constrain all other nodes in the X and Y translation and Z rotation.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results FEMAP FEMAP Structural NAFEMS Structural Result Result Target Value (consistent mass) (lumped mass) (Hz) (Hz) (Hz) 18.32 49.44 92.59 Mesh 1 2.82 18.35 49. 5 linear parabolic linear parabolic linear parabolic . Value (Hz) 18.42 Mode # Ref.02 96.99 93.89 48. Solution Type Normal Modes/Eigenvalue .82 49.13 95.49 18.58 48. 68 146.37 174. 23.39 139. 1987.63 174. Value) refers to the accepted solution to the problem.74 160. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. Dawswell..43 145. 6 7..31 136. Nov. 8 9 140.10 166. C.86 153. Abbassian. . D..71 134. and Knowles.34 140. Reference • NAFEMS Finite Element Methods & Standards..15 not available 166.) Test No.28 145.36 linear parabolic linear parabolic linear parabolic 148.27 145.52 167. N.41 151.87 163. J. F.21 146.11 Note: Reference value (Ref. Attributes of this test are well established.neu (parabolic quadrilateral plate.neu and nf031ll.Cantilevered Square Membrane The complete model and results for this test case are in the following files: • • • • nf031lc.neu) .neu (linear quadrilateral plate. consistent mass) nf031pl.neu (parabolic quadrilateral plate.3 Finite Element Modeling Tests 1 and 2 (nf031lc. consistent mass) nf031ll. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.neu (linear quadrilateral plate. Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. lumped mass) nf031pc. lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered square membrane meshed with plate elements. Test 31. neu and nf031pl.neu) • 65 nodes.thickness = 0.thickness = 0. 16 parabolic quadrilateral plate elements .05m Boundary Conditions Constraints • Fully constrain the nodes along the Y axis in all directions and rotations. . 64 linear quadrilateral plate elements . • 81 nodes.05m Tests 3 and 4 (nf031pc. 404 125.04 214. Solution Type Normal Modes/Eigenvalue .83 138.16 125.635 126.20 141.39 126.85 224.41 255.73 Mode # Ref.26 260.905 52.06 251. • Constrain all other nodes in the Z translation and X.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results NAFEMS Target Value (Hz) 52.25 227.47 52.78 222.90 243.46 236.76 FEMAP FEMAP Structural Structural Result Result (consistent mass) (lumped mass) (Hz) (Hz) 52.28 214.48 259.59 125.95 247.01 239.16 252.47 228.11 125.59 247.54 138.77 52.61 209.61 256.18 139.84 239.74 Mesh 1 2 3 4 5 6 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic .48 142. Value (Hz) 52.06 122.31 52.87 143.02 227. Y. and Z rotations.69 140.54 241. C.) Test No. N. 1987. Abbassian.. Nov. 31. F. Value) refers to the accepted solution to the problem. and Knowles. D. Reference • NAFEMS Finite Element Methods & Standards.. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS... Note: Reference value (Ref. Dawswell. . J. neu (parabolic quadrilateral plate.neu (linear quadrilateral plate.Cantilevered Tapered Membrane The complete model and results for this test case are in the following files: • • • • nf032lc. lumped mass) nf032pc. consistent mass) nf032ll. Test 32.neu and nf032ll. Attributes of this test are: • • • shear behavior irregular mesh symmetry Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered tapered membrane meshed with plate elements.3 Finite Element Modeling Tests 1 and 2 (nf032lc. consistent mass) nf032pl.neu (parabolic quadrilateral plate.neu (linear quadrilateral plate.neu) . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. 1m Tests 3 and 4 (nf032pc.thickness = 0.neu) • 153 nodes.1m Boundary Conditions Constraints • Fully constrain the nodes along the Y axis in all directions and rotations. 32 parabolic quadrilateral plate elements .neu and nf032pl. • 153 nodes. .thickness = 0. 128 linear quadrilateral plate elements . 78 393.11 44.11 375. Y.79 374.63 393.80 375.55 44.61 162.83 162.00 391.05 162.28 130.99 246.636 132.50 162.26 391. Solution Type Normal Modes/Eigenvalue .44 Mesh 1 2 3 4 5 6 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic .09 369.905 44.37 244.90 391.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results FEMAP FEMAP Structural NAFEMS Structural Result Result Target Value (consistent mass) (lumped mass) (Hz) (Hz) (Hz) 44.31 382.70 246.80 161.12 130.56 245.02 396.14 131. • Constrain all other nodes in the Z translation and the X.77 Mode # Ref.81 388.14 162.03 162.05 379.84 129.73 44.37 250.92 129.62 241.82 45. Value (Hz) 44.61 389.623 130. and Z rotations.72 252. D. Value) refers to the accepted solution to the problem. 32 . F. N. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.) Test No. C.. Abbassian... 1987. J. and Knowles. Nov. Dawswell.. Reference • NAFEMS Finite Element Methods & Standards. Note: Reference value (Ref. neu and nf033ll. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.neu) .neu (linear quadrilateral plate. Attributes of this test are: • • • repeated eigenvalues rigid body modes (three modes) kinematically incomplete suppressions Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. consistent mass) nf033pl.3 Finite Element Modeling Tests 1 and 2 (nf033lc. lumped mass) nf033pc.neu (linear quadrilateral plate. lumped mass) This test is a normal modes/eigenvalue analysis of a free annular membrane meshed with plate elements.Free Annular Membrane The complete model and results for this test case are in the following files: • • • • nf033lc. Test 33.neu (parabolic quadrilateral plate. consistent mass) nf033ll.neu (parabolic quadrilateral plate. 48 parabolic quadrilateral plate elements .neu and nf033pl. 160 linear quadrilateral plate elements .neu) • 176 nodes.thickness = 0.06m Tests 3 and 4 (nf033pc. . • 192 nodes.06m Boundary Conditions Constraints • Constraint Set 1 (DOF set): Tests 1 and 2: Constrain nodes 254 and 286 in the X and Y translations.thickness = 0. Tests 3 and 4: Constrain nodes 7 and 19 in the X and Y translations.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . and Z rotations. Solution Type Normal Modes/Eigenvalue . Y. • Constraint Set 2: Constrain all other nodes in the Z translation and X. 82 229.24 226.45 328. 10 11.98 378. Nov. 1987.09 368.81 340. Results FEMAP FEMAP Structural NAFEMS Structural Result Result Target Value (consistent mass) (lumped mass) (Hz) (Hz) (Hz) 129.66 224. Dawswell.67 230.52 222.22 218.83 257.52 Mode # Ref.14 270. N..51 126.17 234.12 263.. .86 262.48 128.15 368.95 272..) Test No. 8 9.48 225.34 335.46 224. Value) refers to the accepted solution to the problem. 14 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref..17 234. 33. C.13 264.38 361. and Knowles. Value (Hz) 129.38 389.94 225. 5 6 7.15 225.79 Mesh 4.70 126.27 234. Abbassian. Reference • NAFEMS Finite Element Methods & Standards.61 376. J.93 311.60 127.92 232.74 264. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.70 391.71 126. F.66 336.44 329. D.67 339. 12 13. parabolic quadrilateral plate.parabolic quadrilateral plate.neu (Test 4 .neu (Test 3 . consistent mass) nf073dl.parabolic quadrilateral plate.neu (Test 8 . consistent mass) nf073al. lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered thin square plate. lumped mass) nf073cc. consistent mass) nf073bl.Cantilevered Thin Square Plate The complete model and results for this test case are in the following files: • • • • • • • • nf073ac.neu (Test 1 .parabolic quadrilateral plate. Attributes of this test are: • effect of master DOF selection on frequencies Test Case Data and Information Units SI .neu (Test 6 . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.neu (Test 2 . lumped mass) nf073dc. lumped mass) nf073bc.parabolic quadrilateral plate.neu (Test 7 . Test 73.parabolic quadrilateral plate.parabolic quadrilateral plate. consistent mass) nf073cl.parabolic quadrilateral plate.neu (Test 5 . thickness = 0.05m Boundary Conditions Constraints • Constraint Set 1: Constrain the nodes along the Y axis in the X. 16 parabolic quadrilateral plate elements . • Constraint Set (DOF set) 2: Create a constraint set to define a Master (ASET) DOF set (in Z direction) .four different placements: . Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. Y.3 Finite Element Modeling 65 nodes. and Z translations and Y rotation. Tests 1 and 2: Tests 3 and 4: Tests 5 and 6: . 580 2.4175 0.026 1. Tests 7 and 8: Solution Type Normal Modes/Eigenvalue .524 2.675 2.597 2.020 1.4182 0.564 2.4182 0.000 1.4147 0.025 1.476 2.021 1.4184 1.4139 0.677 2.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results FEMAP FEMAP Structural NAFEMS Structural Result Result Target Value (consistent mass) (lumped mass) (Hz) (Hz) (Hz) 0.4191 1.4183 0.582 test 1 test 2 test 3 test 4 test 1 test 2 test 3 test 4 test 1 test 2 test 3 test 4 .4174 0.4174 0.610 2.027 1.4139 0.850 0.029 3 2.670 0.032 2.4140 0. Value (Hz) 0.001 1.036 2.009 2.421 DOF Set 1 2 1.449 2.020 1.844 Mode # Ref.999 1. 126 3.555 3. Dawswell..753 6 6.781 3.362 3.816 6.805 7.571 3.023 5. J.. 1987.414 6.352 3.. 73.140 3. 4 3.555 Note: Reference value (Ref. Value) refers to the accepted solution to the problem.302 3.663 3..306 test 1 test 2 test 3 test 4 test 1 test 2 test 3 test 4 test 1 test 2 test 3 test 4 3.891 4.) Test No.095 3.517 7. . D.769 3.765 4.035 5.888 4. N.694 6. and Knowles.675 -----3. F. C. Nov. Reference • NAFEMS Finite Element Methods & Standards.563 3. Abbassian.325 3.345 3.365 3.495 ----3.498 7.466 6.798 7.314 3. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.126 6.479 ------ 5 3. 05m . consistent mass) nf074l.thickness = 0.Cantilevered Thin Square Plate #2 The complete model and results for this test case are in the following files: • • nf074c. Test 74.3 Finite Element Modeling 65 nodes.neu (parabolic quadrilateral plate.neu (parabolic quadrilateral plate. lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered thin square plate. 16 parabolic quadrilateral plate elements . Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. 024 2.082 3. Value) refers to the accepted solution to the problem.4139 0. .582 3. Value (Hz) 0.SVI Results were obtained two different ways: • • using lumped mass using consistent mass Results FEMAP Structural Result (lumped mass) (Hz) 0.306 3.569 3.029 2.471 1. Solution Type Normal Modes/Eigenvalues .999 2. Boundary Conditions Constraints Constrain the nodes along the Y axis in the X. and Z translations and the Y rotation. Y.728 Mode # 1 2 3 4 5 Ref.540 FEMAP Structural Result (consistent mass) (Hz) 0.753 Note: Reference value (Ref.281 3.4181 1.444 3. . Abbassian. Reference • NAFEMS Finite Element Methods & Standards. J. C. . 74. Dawswell. 1987. Nov. N. F..) Test No. D.. and Knowles. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.. Axisymmetric Vibration" "Simply-Supported Annular Plate -Axisymmetric Vibration" "Thick Hollow Sphere .Axisymmetric Solid and Solid Element Test Cases The normal mode dynamics test cases using the standard NAFEMS benchmarks include these axisymmetric solid and solid element test cases: • • • • • • • "Free Cylinder .Uniform Radial Vibration" "Simply-Supported Solid Square Plate" "Simply-Supported Solid Annular Plate" "Deep Simply-Supported Solid Beam" "Cantilevered Solid Beam" . lumped mass) nf041pc.neu): . and circumferential behavior close eigenvalues Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.Axisymmetric Vibration The complete model and results for this test case are in the following files: • • • • nf041lc.neu (linear axisymmetric solid quadrilateral.neu (parabolic axisymmetric solid quadrilateral.3 Finite Element Modeling Tests 1 and 2 (nf041lc. Attributes of this test are: • • • rigid body modes (one mode) coupling between axial. radial. consistent mass) nf041ll. consistent mass) nf041pl.neu (parabolic axisymmetric solid quadrilateral. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.neu (linear axisymmetric solid quadrilateral. lumped mass) This test is a normal modes/eigenvalue analysis of a free cylinder meshed with axisymmetric elements.Free Cylinder . Test 41.neu and nf041ll. Solution Type Normal Modes/Eigenvalue . 48 linear axisymmetric quadrilateral solid elements Tests 3 and 4 (nf041pc.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . Tests 3 and 4: Create a constraint set (Kinematic DOF set) to constrain nodes 1 and 51 in the X and Z translations.neu): • 43 nodes. 8 parabolic axisymmetric quadrilateral solid elements Boundary Conditions Constraints • • Tests 1 and 2: Create a constraint set (Kinematic DOF set) to constrain nodes 1 and 68 in the X and Z translations. • 68 nodes.neu and nf041pl. . 41.15 377. Abbassian.18 243.31 356.92 375.00 397. F.94 421.97 406. C.50 379.86 356. Results FEMAP Structural NAFEMS Result Target Value (lumped mass) (Hz) (Hz) 244.56 393..28 401. .49 379.30 398.41 377.50 378.11 397. Value (Hz) 243.01 243.72 405.28 Mesh 2 3 4 5 6 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref.65 FEMAP Structural Result (consistent mass) (Hz) 243. Nov. and Knowles.96 243.46 395. Dawswell. Reference • NAFEMS Finite Element Methods & Standards.44 Mode # Ref.41 394.35 397.85 389.41 243.87 406.46 394.41 394. Value) refers to the accepted solution to the problem.) Test No. D.53 377.88 385..42 394. 1987.85 406. J.. N.24 370. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. consistent mass) nf042ll.α = 5° Tests 3 and 4 (nf042pc.neu (linear axisymmetric solid quadrilateral.neu (parabolic axisymmetric solid quadrilateral.Uniform Radial Vibration The complete model and results for this test case are in the following files: • • • • nf042lc. lumped mass) This test is a normal modes/eigenvalue analysis of a thick. hollow sphere using axisymmetric solid elements. Test 42. Attributes of this test are: • • curved boundary (skewed coordinate system) constraint equations Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.neu) . lumped mass) nf042pc.neu and nf042ll.neu (linear axisymmetric solid quadrilateral.neu (parabolic axisymmetric solid quadrilateral.neu and nf042pl. consistent mass) nf042pl.3 Finite Element Modeling Tests 1 and 2 (nf042lc.neu) • 22 nodes.Thick Hollow Sphere . 10 linear axisymmetric solid quadrilateral elements . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. Constraint Equations: Constrain all nodes at the same R’ are constrained to have same r’ displacement Solution Type Normal Modes/Eigenvalue .SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . 10 parabolic axisymmetric solid quadrilateral elements Boundary Conditions Constraints • • Constraint Set 1: Constrain all nodes in the Z translation. • 53 nodes. 49 831.9 2799.8 369.20 838. D.83 839.7 2852.8 Mesh 1 2 3 4 5 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref. Abbassian.0 2795. N..5 Mode # Ref.49 837.7 2030.0 2192.01 841. .5 1450. F.5 2072.. C..3 2970.) Test No. Dawswell.2 2131. Value (Hz) 369. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.77 1470.7 2975.91 838.2 2706.80 832.08 1473. 1987. J.85 2188.9 2604.03 1451. 42.2 2117. Reference • NAFEMS Finite Element Methods & Standards.72 1421.3 370. and Knowles..3 1433. Nov.6 2117.1 1453.91 369. Results FEMAP FEMAP Structural NAFEMS Structural Result Result Target Value (consistent mass) (lumped mass) (Hz) (Hz) (Hz) 370.08 369.64 370. Value) refers to the accepted solution to the problem. neu (parabolic axisymmetric solid quadrilateral. lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported annular plate meshed with axisymmetric elements.neu): .neu (parabolic axisymmetric solid quadrilateral.Simply-Supported Annular Plate Axisymmetric Vibration The complete model and results for this test case are in the following files: • • • • nf043lc. consistent mass) nf043pl.neu and nf043ll.3 Finite Element Modeling Tests 1 and 2 (nf043lc. consistent mass) nf043ll. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. lumped mass) nf043pc. Test 43.neu (linear axisymmetric solid quadrilateral.neu (linear axisymmetric solid quadrilateral. Attributes of this test are: • well established Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. neu) • 28 nodes.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass .neu and nf043pl. 60 linear axisymmetric solid quadrilateral elements Tests 3 and 4 (nf043pc. 5 parabolic axisymmetric solid quadrilateral elements Boundary Conditions Constraints Constrain point A (node 1) in the Z translation Solution Type Normal Modes/Eigenvalue . • 80 nodes. C.00 361.19 Mesh 1 2 3 4 5 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref.429 138. 1987.20 224.05 Mode # Ref. Dawswell.79 686. Value) refers to the accepted solution to the problem.04 18.543 150.59 374. J.66 135.34 633.97 224.20 224.62 643. Nov. Results FEMAP Structural NAFEMS Result Target Value (lumped mass) (Hz) (Hz) 18.. and Knowles.56 224.16 358.22 224. Abbassian.05 689.570 18.50 353. . N.05 673.582 140.542 18. 43.18 371.29 629.) Test No.15 224. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.. Reference NAFEMS Finite Element Methods & Standards.18 385.46 145.. F. D..16 FEMAP Structural Result (consistent mass) (Hz) 18.711 18.34 686.24 140.582 145. Value (Hz) 18.48 374.56 224. nf051ll.neu (linear solid brick.Deep Simply-Supported Solid Beam The complete model and results for this test case are in the following files: • • • • nf051lc. consistent mass) nf051pl. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. lumped mass) nf051pc.neu. Test 51. lumped mass) This test is a normal mode dynamic analysis of a deep.neu (parabolic solid brick. Attributes of this test are: • • skewed coordinate system skewed restraints Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. solid beam meshed with bricks.3 Finite Element Modeling Tests 1 and 2 (nf051lc.neu (linear solid brick.neu) .neu (parabolic solid brick. consistent mass) nf051ll. 5 parabolic solid brick elements Boundary Conditions Constraints. 30 linear solid brick elements Tests 3 and 4 (nf051pc. • 88 nodes.neu) • 68 nodes. Y. Constrain node 88 in the Z translation. Constrain node 87 in the Y and Z translations. Tests 1 and 2: • • • • Constrain node 7 in the X.neu. and Z translations. Constrain node 8 in the X and Z translations. . nf051pl. Constrain node 30 in the Y and Z translations.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . • Constrain all other nodes along the plane Y’ in the Y translation. Constraints. Constrain node 71 in the Z translation. and Z translations Constrain nodes 12 and 35 in the X and Z translations. Solution Type Normal Modes/Eigenvalue . Constrain all other nodes along the plane Y’ in the Y translation. Tests 3 and 4: • • • • • Constrain node 10 in the X. Y. ) Test No. Reference • NAFEMS Finite Element Methods & Standards.659 157.451 170.. J.86 307.407 87.43 306. D.63 157. F.34 286. Abbassian..977 87.269 83.964 37. Results NAFEMS Target Value (Hz) 42.67 159.. .27 FEMAP Structural Result (consistent mass) (Hz) 38.92 FEMAP Structural Result (lumped mass) (Hz) 37. and Knowles. Nov.53 297.12 259.02 Mode # Ref.20 318. N. C. Value) refers to the accepted solution to the problem.84 150. Value (Hz) Mesh 1 2 3 4 5 38.817 88.76 243.027 152.210 152.53 251. 1987. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.00 298.20 281.23 245..282 38.02 259. 51.10 288.881 38.05 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref.821 93. Dawswell.200 85.788 83.49 265. lumped mass) This test is a normal modes/eigenvalue analysis of a simply–supported solid square plate meshed with bricks. This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis.neu.neu (linear solid brick.Simply-Supported Solid Square Plate The complete model and results for this test case are in the following files: • • • • nf052lc. consistent mass) nf052pl. consistent mass) nf052ll.3 Finite Element Modeling Tests 1 and 2 (nf052lc.neu) .neu (linear solid brick.neu (parabolic solid brick. lumped mass) nf052pc. Attributes of this test are: • • • well established rigid body modes (three modes) kinematically incomplete suppressions Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0. Test 52.neu (parabolic solid brick. nf052ll. 5m in the Z translation.neu. 16 parabolic solid brick elements Boundary Conditions Constraints • Constraint Set 1: Constrain all the nodes along the four edges on the plane ZS = -0. 192 linear solid brick elements Tests 3 and 4 (nf052pc. nf052pl. .neu) • 155 nodes. • 324 nodes. Y.92 209. 10 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic . 6 7 8 9.93 210.73 110.60 45. and Z translations.52 194.11 196.08 197.318 44.44 193.54 173.77 193.16 200.59 206. Value (Hz) 45.654 44.96 110.30 169.14 185.115 44.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass Results FEMAP FEMAP Structural NAFEMS Structural Result Result Target Value (consistent mass) (lumped mass) (Hz) (Hz) (Hz) 51.94 156.64 44.18 193.897 109.65 Mode # Ref.89 193.502 106.37 169. Solution Type Normal Modes/Eigenvalue . • Constraint Set 2 (Kinematic DOF): Tests 1 and 2: Constrain nodes 36 and 264 in the X.73 107.58 193.762 132.796 113.56 206.55 206.44 167.48 161. Tests 3 and 4: Constrain nodes 27 and 219 in the X and Y translation.19 Mesh 4 5. and Knowles. F. Abbassian. Dawswell.) Test No. . 52. C. Value) refers to the accepted solution to the problem. Nov. J. 1987. D... Note: Reference value (Ref. N. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. Reference • NAFEMS Finite Element Methods & Standards... This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. consistent mass) nf053pl. 60 linear solid bricks: α = 5° . Test 53.neu (linear solid brick.neu (linear solid brick. lumped mass) nf053pc. lumped mass) This test is a normal modes/eigenvalue analysis of a solid annular plate using solid elements. consistent mass) nf053ll.neu (parabolic solid brick.Simply-Supported Solid Annular Plate The complete model and results for this test case are in the following files: • • • • nf053lc. Attributes of this test are: • • curved boundary (skewed coordinate system) constraint equations Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.3 Finite Element Modeling • 160 nodes.neu (parabolic solid brick. 5 solid parabolic bricks α = 10° Boundary Conditions Constraints. . • 68 nodes. Constrain all other nodes in the Y translation. Tests 1 and 2: • • Constrain nodes 76-80 and 156-160 in the Y and Z translations. and Z rotations. 33. Constrain all other nodes in the Y translation and X. 44. 77. Constraint equations: Constrain nodes at same R and Z are constrained to have same z displacement Solution Type Normal Modes/Eigenvalues . 66. • Constraint equations: Constrain nodes at same R and Z are constrained to have same z displacement. Constraints.SVI method Results were obtained two different ways: • • using lumped mass using consistent mass . 22. and Z rotations. and 99 in the Y and Z translations and X. Tests 3 and 4: • • • Constrain nodes 11. 88. Y. Y. 62 369. Value (Hz) 18.42 140.582 146.47 686.583 140.03 690. Nov. F. N.48 224.98 668. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS.01 18. Dawswell.74 380. 53. . 1987. Abbassian.44 224.659 18....21 224. C.25 224.19 Mesh 1 2 3 4 5 linear parabolic linear parabolic linear parabolic linear parabolic linear parabolic Note: Reference value (Ref.15 224.641 18. Reference • NAFEMS Finite Element Methods & Standards.09 688.78 141.612 18.34 223.59 Mode # Ref.16 358.73 616.) Test No.04 689.29 629.33 380.70 374.409 140.42 224.629 141.74 345.02 18. Value) refers to the accepted solution to the problem. Results FEMAP FEMAP Structural NAFEMS Structural Result Result Target Value (consistent mass) (lumped mass) (Hz) (Hz) (Hz) 19.. D. and Knowles.13 134. J.18 386. lumped mass) nf072bc. Attributes of this test are: • highly populated stiffness matrix Test Case Data and Information Units SI Material Properties 9 N E = 200x10 -----2 m kg ρ = 8000 -----3 m ν = 0.neu (unconventional numbering. lumped mass) This test is a normal modes/eigenvalue analysis of a cantilevered solid beam. Test 72.neu (conventional numbering.3 Finite Element Modeling Two tests .both use solid parabolic brick elements . This document provides the input data and results for NAFEMS Selected Benchmarks for Natural Frequency Analysis. consistent mass) nf072bl.Cantilevered Solid Beam The complete model and results for this test case are in the following files: • • • • nf072ac. consistent mass) nf072al.neu (conventional numbering.neu (unconventional numbering. and Z translations. Y. • Test 1: conventional node numbering • Test 2: unconventional node numbering Boundary Conditions Constraints • Constrain all nodes on the X=0 plane in the X. . 30 299.82 375.235 82. Selected Benchmarks for Natural Frequency Analysis (Glasgow: NAFEMS. .56 209.81 Mode # 1 2 3 4 5 6 Mesh Test 1 Test 2 Test 1 Test 2 Test 1 Test 2 Test 1 Test 2 Test 1 Test 2 Test 1 Test 2 Note: Reference value (Ref.81 15.96 125.. N. Nov.32 352.33 299.235 125. Value) refers to the accepted solution to the problem. Abbassian.56 209. Dawswell.81 375.40 16.007 16.56 351.) Test No.33 189.96 125.03 125.96 209.11 375. Solution Type Normal Modes/Eigenvalue – SVI Method Results FEMAP FEMAP NAFEMS Structural Structural Target Value (lumped mass) (consistent mass) (Hz) (Hz) (Hz) 16.800 82..11 351. • Constrain all nodes on the Y=1m plane in the Y translation.007 87.56 351.007 16.226 125. J. C.96 209. Reference • NAFEMS Finite Element Methods & Standards...11 351. 1987.03 189.11 375.007 87. 72.226 125.39 352. D. F.800 15. and Knowles.226 87.226 87. finite element modeling information . Understanding the Test Case Format Each test case is structured with the following information: • test case data and information .material properties . or rebuild that model from scratch.units .boundary conditions (loads and constraints) .neu) files associated with this guide. your node numbering may differ. France) in “Guide de validation des progiciels de calcul de structures.Verification Test Cases from the Societe Francaise des Mechaniciens The purpose of these test cases is to verify the function of the FEMAP Structural software using standard benchmarks published by SFM (Societe Francaise des Mecaniciens.” Included here are: • • • test cases on mechanical structures using linear statics analysis and normal modes/eigenvalue analysis stationary thermal test cases using heat transfer analysis a thermo–mechanical test case using linear statics analysis Results published in “Guide de validation des progiciels de calcul de structures” are compared with those computed using the FEMAP Structural software. Paris. Reference The following reference has been used in these test cases: . If you remesh a model.solution type • • results reference Note: The node numbers listed in each case refer to the node numbers in the neutral (. Afnor Technique. • Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures.1990. (Paris.) . Mechanical Structures .Linear Statics Analysis with Bar or Rod Elements The linear statics analysis test cases from the Societe Francaise des Mecaniciens include these bar and rod element test cases: • • • • • • • "Short Beam on Two Articulated Supports" "Clamped Beams Linked by a Rigid Element" "Transverse Bending of a Curved Pipe" "Plane Bending Load on a Thin Arc" "Nodal Load on an Articulated Rod Truss" "Articulated Plane Truss" "Beam on an Elastic Foundation" . Short Beam on Two Articulated Supports The complete model and results for this test case are in file ssll02.” • • • area = 31E-4m2 inertia = 2810E-8m4 Shear area ratio = 2.neu. This test is a linear statics analysis of a short. straight beam with plane bending and shear loading.42 Test Case Data and Information Units SI Material Properties E = 2E11 Pa ν = 0.3 Finite Element Modeling • • 10 bar elements 11 nodes The mesh is shown in the following figure: . It provides the input data and results for benchmark test SSLL02/89 from “Guide de validation des progiciels de calcul de structures. Guide de validation des progiciels de calcul de structures.25926E-3 -1. apply a load = 1E5 N/m in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Total Translation at point B (Node 7) Bench Value FEMAP Structural Value Difference -1.) Test No. Boundary Conditions Constraints • Constrain the nodes at both free ends of the beam (nodes 1 and 2) in all directions except for the Z rotation. (Paris. Afnor Technique. Loads • On nodes 1-10.00% Reference • Societe Francaise des Mecaniciens. SSLL02/89.1990. .25926E-3 0. Clamped Beams Linked by a Rigid Element The complete model and results for this test case are in file ssll05.” Test Case Data and Information Units SI Material Properties • • E = 2E11 Pa I = (4/3)E-8m4 Finite Element Modeling • • • 20 bar elements 1 rigid element 26 nodes The mesh is shown in the following figure: Boundary Conditions Constraints • Nodes 1 and 4: Fully constrained in all directions. This test is a linear statics analysis of a straight. cantilever beam with plane bending and a rigid element. It provides the input data and results for benchmark test SSLL05/89 from “Guide de validation des progiciels de calcul de structures.neu. . Guide de validation des progiciels de calcul de structures. Loads • Node 3: Set nodal force = 1000 N in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Node # Node 6 Node 3 Node 1 Node 1 Node 4 Node 4 Displacement Reaction Force Displacement Y (T2 Translation) Displacement Y (T2 Translation) Force Y (N) (T2 Constraint Force) Moment Rz (Nm) (R3 Constraint Moment) Force Y (N) (T2 Constraint Force) Rz moment (Nm) (R3 Constraint Moment) Bench Value -0.00% 0.00% Reference • Societe Francaise des Mecaniciens.125 -0.125 500 500 500 500 FEMAP Structural -0.125 -0.00% 0. (Paris. Afnor Technique.00% 0. SSLL05/89.1990. .) Test No.00% 0.125 500 500 500 500 Difference 0.00% 0. 3 Finite Element Modeling Test 1 (ssll07a) • • 90 bar elements 91 nodes Test 2 (ssll07b) • • 90 curved beam elements 91 nodes .” Test Case Data and Information Units SI Material Properties E = 2E11 Pa ν = 0. It provides the input data and results for benchmark test SSLL07/89 from “Guide de validation des progiciels de calcul de structures.neu (curved beam) This test is a linear statics analysis (three–dimensional problem) of a curved pipe with transverse bending and bending–torque loading.neu (linear beam) ssll07b.Transverse Bending of a Curved Pipe The complete model and results for this test case are the following files: • • ssll07a. The mesh for Test 1 is shown in the following figure: Boundary Conditions Constraints • Fully constrain node 91 in all translations and rotations. Loads • Create a nodal force at node 1 = 100 N in Z direction The boundary conditions are shown in the following figure: . 01% 3.02% 0.23% 1.) Test No. .8109 -96.02% 0.1180 -96. second end • • Mf=Bar End BX2 Moment Mt=Bar End BX1 Moment Curved Beam Element (ssll07b) List beam forces on element 166. Solution Type Statics Results Node # Node 1 Node 1 θ=15° Point Displacement Moment Displacement Z (T3 Translation) Displacement Z (T3 Translation) Mt (Nm)* Mt (Nm)* Mf (Nm) Mf (Nm) Bench Value 0.13464 76. SSLL07/89.3680 -95. Guide de validation des progiciels de calcul de structures.35% Mf = bending moment Mt = torsional moment *See “Post Processing” below Post Processing Bar Element (ssll07a) List beam forces on element 167. second end • • Mf=Bar End BX2 Moment Mt=Bar End BX1 Moment Reference • Societe Francaise des Mecaniciens.13462 1 2 74.1990.6709 75. Afnor Technique.44% 1.5925 1 2 1 2 Test Number FEMAP Structural 0.13465 0. (Paris.2869 Difference 0. and Z translations. This test is a linear statics analysis (plane problem) of a thin arc with plane bending.Plane Bending Load on a Thin Arc The complete model and results for this test case are in file ssll08.3 Finite Element Modeling • • 11 nodes 10 bar elements The mesh is shown in the following figure: Boundary Conditions Constraints • • Node 2: Constrain the X. Y. Node 1: Constrain the Y and Z translation only.neu.” Test Case Data and Information Units SI Material Properties E = 2E11 Pa ν = 0. It provides the input data and results for benchmark test SSLL08/89 from “Guide de validation des progiciels de calcul de structures. . 05% 1.1990.9342E-2 5. Loads • Force=100N in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Node # Node 2 Node 1 Node 7 Node 1 Displacement Rz (rad) (R3 Rotation) Rz (rad) (R3 Rotation) Y (m) (T2 Translation) X (m) (T1 Translation) Bench Value -3.71% 0. (Paris.9206E-2 5.) Test No.0774E-2 -1.1097E-2 3.3913E-2 FEMAP Structural -3. . SSLL08/89. • Nodes 3-11: Constrain in the Z translation only.1097E-2 -1.0774E-2 3.33% Reference • Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures.05% 0. Afnor Technique.3735E-2 Difference 1. It provides the input data and results for benchmark test SSLL11/89 from “Guide de validation des progiciels de calcul de structures.neu.Nodal Load on an Articulated Rod Truss The complete model and results for this test case are in file ssll11.” Test Case Data and Information Units SI Material Properties • E = 1. . and Z translations only. This test is a linear statics analysis of a plane truss with an articulated rod. Y.962E11 Pa Finite Element Modeling • • 4 nodes 4 rod elements The mesh is shown in the following figure: Boundary Conditions Constraints • Nodes 3 and 17: Constrained in the X. 6004E-3 Difference 0.00% ~0. . Guide de validation des progiciels de calcul de structures.00% 0.08839E-3 3.47902E-3 -5. Loads • Node 2: Set Nodal force = 9. (Paris.08839E-3 3.47903E-3 -5.60084E-3 FEMAP Structural 0.81E3 N in -Y direction The boundary conditions are shown in the following figure: Solution Type Statics Results Node # Node 18 Node 18 Node 2 Node 2 Displacement X (m) (T1 Translation) Y (m) (T2 Translation) X (m) (T1 Translation) Y (m) (T2 Translation) Bench Value 0.26517E-3 0.1990.) Test No. • Nodes 2 and 18: Constrained in the Z translation only.26517E-3 0.00% ~0. Afnor Technique. SSLL11/89.00% Reference • Societe Francaise des Mecaniciens. 1E11 Pa Finite Element Modeling Test 1 (ssll14a) • • 4 bar elements 5 nodes Test 2 (ssll14b) • • 10 linear beam elements 11 nodes The mesh for Test 1 is shown in the following figure: . It provides the input data and results for benchmark test SSLL14/89 from “Guide de validation des progiciels de calcul de structures.Articulated Plane Truss The complete model and results for this test case are in the following files: • • ssll14a.” Test Case Data and Information Units SI Material Properties • E = 2.neu (10 bar elements) This test is a linear statics analysis of a straight cantilever beam with plane bending and tension–compression.neu (4 bar elements) ssll14b. Boundary Conditions Test 1 (ssll14a) • Constraints Nodes 1 and 4: Constrain in the X. F2 = -10. • Loads (ssll14b) Set forces and moments to the following numeric values: p = -3. and Z translations. 3.000N/m (on element 4).000N (on node 2).000N (on node 8). Y. 3. 5-13: Constrain in the Z translation only.000Nm (on node 2) Test 2 (ssll14b) • Constraints Nodes 1 and 4: Constrain in the X. and Z translations. F2 = -10. F1 = -20. • Loads Set forces and moments to the following numeric values: p = -3.000N (on node 2). M = -100.000Nm (on node 2) The boundary conditions are shown in the following figure: Solution Type Statics .000N/m (on elements 5-7). F1 = -20. M = -100. 8: Constrain in the Z translation only. Y. Nodes 2. Nodes 2.000N (on node 8). SSLL14/89.1990. Results Node # 1 Displacement Reaction Force Bench Value Test Number 1 2 1 2 1 2 FEMAP Structural 33233.0 reaction (N) (T2 Constraint Force) horizontal (x) reaction (N) 20239.4 (T1 Constraint Force) Y (m) (T2 Translation) -0. Afnor Technique. Reference • Societe Francaise des Mecaniciens.10% 2.) Test No.1 33233.50% 5.2 20609.82% 1.03106 -0. (Paris.3 -0.1 20609.03161 Difference 5.83% 1.03072 Note: The software takes shear effect into account.50% 1. Guide de validation des progiciels de calcul de structures.90% 1 8 V vertical (Y) 31500. . Beam on an Elastic Foundation The complete model and results for this test case are in file ssll16.” Test Case Data and Information Units SI Material Properties • • • E = 2.1E11 Pa K = 8. This test is a linear statics analysis (plane problem) of a straight beam with plane bending and an elastic support.neu. Finite Element Modeling • • • 50 bar elements 49 DOF spring elements 51 nodes The mesh is shown in the following figure: . It provides the input data and results for benchmark test SSLL16/89 from “Guide de validation des progiciels de calcul de structures.4E5 N/m2 Each spring stiffness is set to: K*L/ (number of DOF spring elements). and Z translations. Loads • Set forces. Nodes 2-49: Constrain in the Z translation and X and Y rotations only. p = -5000 N/m (elements 1-50) . M= -15000 Nm (node 1). moments. Boundary Conditions Constraints • • Nodes 1 and 51: Constrain in the X. M = 15000 Nm (node 51). Y. and distributed loads on element to the following numeric values: F = -10000 N (node 26) . The distributed loads are shown below: . 003045 11674 -0. Bench Value -0. The forces and moments are shown below: Solution Type Statics Results Node 51 Displacement Force. Moment rotation(rad) Rz (R3 rotation) reaction force (N) Y (T2 Constraint Force) disp.78% 0. (Paris.1990.003041 11646 -0.36% 0.42270E-2 33286 Difference 0.41% 1.63% 26 26 . Guide de validation des progiciels de calcul de structures.423326E-2 33840 FEMAP Structural -0. second end Reference • Societe Francaise des Mecaniciens. SSLL16/89. Y (m) (T2 Translation) M moment (Nm)* (Bar End BX3 Moment) *On element 26.) Test No. Afnor Technique. Mechanical Structures .Linear Statics Analysis with Plate Elements The linear statics analysis test cases from the Societe Francaise des Mecaniciens include these plate element test cases: • • • • • • • • • • • • • "Plane Shear and Bending Load on a Plate" "Infinite Plate with a Circular Hole" "Uniformly Distributed Load on a Circular Plate" "Torque Loading on a Square Tube" "Cylindrical Shell with Internal Pressure" "Uniform Axial Load on a Thin Wall Cylinder" "Hydrostatic Pressure on a Thin Wall Cylinder" "Gravity Loading on a Thin Wall Cylinder" "Pinched Cylindrical Shell" "Spherical Shell with a Hole" "Uniformly Distributed Load on a Simply-Supported Rectangular Plate" "Shear Loading on a Plate" "Uniformly Distributed Load on a Simply-Supported Rhomboid Plate" . neu. This test is a linear statics analysis (plane problem) of a plate with plane bending.Plane Shear and Bending Load on a Plate The complete model and results for this test case are in file sslp01.” Test Case Data and Information Units SI Material Properties E = 3E10 Pa ν = 0. It provides the input data and results for benchmark test SSLP01/89 from “Guide de validation des progiciels de calcul de structures.25 Finite Element Modeling • • 100 linear quadrilateral plate elements 126 nodes The mesh is shown in the following figure: Boundary Conditions Constraints • Nodes 121-126: Fully constrain in all translations and rotations. . ) Test No.1990. Guide de validation des progiciels de calcul de structures.3413 FEMAP Structural 0.y) Centerline Displacement Y (mm) (T2 Translation) Bench Value 0.3408 Difference 0.15% The displacements are shown in the following figure: Reference • Societe Francaise des Mecaniciens. SSLP01/89. Afnor Technique. . Loads • • Set a shear force with parabolic distribution on width and constant distribution on thickness Resultant force: p = 40 N. The boundary conditions are shown in the following figure: Solution Type Statics Results Node # 3 Point Coordinates (L. (Paris. ” Test Case Data and Information Units SI Material Properties E = 3E10 Pa ν = 0.neu. It provides the input data and results for benchmark test SSLP02/89 from “Guide de validation des progiciels de calcul de structures.Infinite Plate with a Circular Hole The complete model and results for this test case are in file sslp02. This test is a linear statics analysis (plane problem) of a plate with tension–compression and a membrane effect.25 Finite Element Modeling Mapped meshing (with biasing) • • 100 linear quadrilateral plate elements 121 nodes The mesh is shown in the following figure: . Nodes 111-121: Constrain in X translation and Y and Z rotations only. Nodes 12-110: Constrain in Z translation only. Loads • Tension force P = 2.5 N/mm**2 (in plane force of 2500 N/m) The boundary conditions are shown in the following figure: Solution Type Statics . Boundary Conditions Constraints • • • Nodes 1-11: Constrain in Y translation and X and Z rotations only. 61 4.) Test No. .0) Node # 1 σθ Stress Bench Value 7.1990.40% 111  a. π - 4 Plate Top Y Normal Stress (N/mm**2) 2.5 Plate Top Y Normal Stress Plate Top Y Normal Stress -2. SSLP02/89. Guide de validation des progiciels de calcul de structures. Afnor Technique. π - 2 -2.5 2.38 4. Results Point Coordinates (a.80% Reference • Societe Francaise des Mecaniciens. (Paris.26% 56  a.5 FEMAP Structural 7.52 Difference 0. 3 11 Finite Element Modeling Test 1 (ssl03a) .Uniformly Distributed Load on a Circular Plate The complete model and results for this test case are in the following files: • • ssls03a. It provides the input data and results for benchmark test SSLS03/89 from “Guide de validation des progiciels de calcul de structures.neu (linear quadrilateral) ssls03b.neu (linear triangle) This test is a linear statics analysis (three–dimensional problem) of a circular plate fixed at the edge with transverse bending and a uniform load.” Test Case Data and Information Units SI Material Properties E = 2.Free meshing: • • 38 linear quadrilateral plate elements 50 nodes .1 ×10 Pa ν = 0. .Free meshing: • • 53 linear triangular plate elements 38 nodes Only 1/4 of the plate is meshed. Loads • Uniform elemental pressure p = -1000 Pa. Constrain nodes 4-8 in the X translation and Y and Z rotations. Note: Symmetric conditions are applied to the sides. Boundary Conditions Constraints • • • • Constrain node 1 in all directions except for the Z translation. Constrain nodes 9-13 in the Y translation and X and Z rotations. Test 2 (ssl03a) . Fully constrain nodes 2-3 and nodes 15-21 in all directions. ) Test No.0065 -0.0065 Test Number 1 2 FEMAP Structural -0.0065 Difference 0. SSLS03/89.0065 -0. .1990.00% Reference • Societe Francaise des Mecaniciens.00% 0. (Paris. Test 1 boundary conditions: Solution Type Statics Results Node # Node 1 Node 1 Point Center O Center O T3 Translation (Displacement Z) w (m) Bench Value -0. Afnor Technique. Guide de validation des progiciels de calcul de structures. Torque Loading on a Square Tube The complete model and results for this test case are in file ssls05.1 ×10 Pa ν = 0.” Test Case Data and Information Units SI Material Properties E = 2. This test is a linear statics analysis (three–dimensional problem) of a thin–walled tube loaded in torsion by pure shear at the free end. It provides the input data and results for benchmark test SSLS05/89 from “Guide de validation des progiciels de calcul de structures.neu.3 11 Finite Element Modeling Mapped meshing • • 160 linear quadrilateral plate elements 176 nodes The mesh is shown in the following figure: . 00% 0.10% 0.11E6 Difference 0.988E-7 0.987E-7 0.5N.617E-7 0. Note: This translates into an equivalent nodal force of ±12. Loads • Torque equal to 10 Nm on the free end. Boundary Conditions Constraints • Completely constrain nodes 1-5. 112-115.197E-4 -0. and 167-169 in all translations and rotations.00% 0. The boundary conditions are shown in the following figure: Solution Type Statics Results Node # 193 193 193 208 208 208 Displacement and Stress T2 Translation (m) R1 Rotation (rad) Plate Bottom Minor Stress (Pa) T2 Translation (m) R1 Rotation (rad) Plate Bottom Minor Stress (Pa) Bench Value -0.00% 0.00% 0. 57-60.123E-4 -0.11E6 FEMAP Structural -0.00% .123E-4 -0.11E6 -0.617E-7 0.197E-4 -0.11E6 -0. SSLS05/89.) Test No. Afnor Technique. Guide de validation des progiciels de calcul de structures. Reference • Societe Francaise des Mecaniciens.1990. (Paris. . test 1) ssls06b.Cylindrical Shell with Internal Pressure The complete model and results for this test are in the following files: • • ssls06a.1 ×10 Pa ν = 0.Mapped meshing • • 100 linear quadrilateral plate elements 121 nodes .3 11 Finite Element Modeling Test 1 (ssls06a) . test 2) This test is a linear statics analysis of the thin cylinder loaded by internal pressure.” Test Case Data and Information Units SI Material Properties E = 2.neu (linear quadrilateral. It provides the input data and results for benchmark test SSLS06/89 from “Guide de validation des progiciels de calcul de structures.neu (linear quadrilateral. 126. 190. 231. 315. 89. 358. 106. Constrain node 21 in all directions except for the X translation. Constrain nodes 2-10 in the Z translation and X and Y rotations. 336. 45. 274. 33. 56. 100. 85. 189. 110. 44. 148.Mapped meshing • • 400 linear quadrilateral plate elements 441 nodes Boundary Conditions Constraints for Test 1 (ssls06a) • • • • • Constrain node 1 in all directions except for the Y translation. and 111 in the X translation and Y and Z rotations only. 84. 64. Loads for Test 1 and Test 2 • Internal pressure on the elements = 10000 Pa. 34. 378. 105. 420. and 421 in the X translation and Y and Z rotations only. 88. 273. 399. Constrain nodes 12. . 294. 55. Constraints for Test 2 (ssls06b) • • • • • Constrain node 1 in all directions except for the Y translation. Constrain nodes 22. 63. Test 2 (ssls06b) . 295. Constrain nodes 2-20 in the Z translation and X and Y rotations. Constrain node 11 in all directions except for the X translation. 168. 232. 127. 441 in the Y translation and X and Z rotations only. Constrain nodes 42. 99. 77. 169. 357. 147. 67. 211. 316. 400. Constrain nodes 22. 23. 252. 43. 379. 78. 253. 337. 121 in the Y translation and X and Z rotations. 210. 66. 20% Plate Top X Normal Stress .0 1 Test Number FEMAP Structural 1. The boundary conditions are shown in the following figure: Solution Type Statics Results Node # 11 σ11 ( Pa ) ) Displacement and Stress Bench Value 0.00E5 1 4.40% 421 Plate Top X Normal Stress σ22(Pa) σ22 ( Pa ) ) 2 4.99E5 0.32 Difference Plate Top Y Normal Stress 21 σ11 ( Pa ) ) 2 -0.98E5 0.139 Plate Top Y Normal Stress 111 σ22 ( Pa ) ) 5. Afnor Technique.1990.43E-6 1 -1.38E-6 0.70% T3 Translation 441 ∆L ( m ) 2 -1. 121 ∆R ( m ) 2.00% T3 Translation All results are averages.37E-6 0.42% T1 Translation 441 ∆R ( m ) 2 2. .00% T1 Translation 121 ∆L ( m ) -1. (Paris. Guide de validation des progiciels de calcul de structures. SSLS06/89.42E-6 0.38E-6 1 2. Reference • Societe Francaise des Mecaniciens.43E-6 0.) Test No. neu (parabolic triangle plate.” Test Case Data and Information Units SI Material Properties E = 2. test 2) This test is a linear static analysis of a thin cylinder loaded axially. It provides the input data and results for benchmark test SSLS07/89 from “Guide de validation des progiciels de calcul de structures.neu (parabolic quadrilateral plate. test 1) ssls07b.3 11 Finite Element Modeling Test 1 • • Meshed by revolving a meshed beam 200 parabolic quadrilateral plate elements .1 ×10 Pa ν = 0.Uniform Axial Load on a Thin Wall Cylinder The complete model and results for this test are in the following files: • • ssls07a. . Constrain node 1 in the Y and Z translations and the X and Z rotations. Constrain the nodes along the other long edge in the X translation and the Y and Z rotations. Constrain the nodes along the top short edge in the Z translation only. • 661 nodes Test 2 • • Meshed by free meshing on 1/8 of a cylinder 400 parabolic triangular plate elements Boundary Conditions Constraints • • • • Constrain the nodes along one long edge in the Y translation and X and Z rotations. q = 10000 N/m The boundary conditions are shown in the following figure: Solution Type Statics Results Node # 641 σ11 ( Pa ) Displacement and Stress Bench Value 5.00E5 2 5.00E5 Difference 0.00E5 1 Test Number FEMAP Structural 5.00E5 0.00% Plate Top Y Normal Stress 641 σ11 ( Pa ) 5. • Constrain node 21 in the X and Z translations and Y and Z rotations.00% Plate Top Y Normal Stress . Loads • Uniform axial elemental pressures. ) Test No.52E-6 0. (Paris.0 Plate Top X Normal Stress 641 ∆R ( m ) -7.0 2 0. Guide de validation des progiciels de calcul de structures. 641 σ22 ( Pa ) 0.14E-7 1 -7. .0% T1 Translation 641 ∆L ( m ) 9.1990.52E-6 1 9.14E-7 0.0% T3 Translation All results are averages.14E-7 2 -7.52E-6 2 9.0 Plate Top X Normal Stress 641 σ22 ( Pa ) 0. Reference • Societe Francaise des Mecaniciens. Afnor Technique.0 1 0.0% T3 Translation 641 ∆L ( m ) 9.0% T1 Translation 641 ∆R ( m ) -7.14E-7 0.52E-6 0. SSLS07/89. 1 ×10 Pa ν = 0.Hydrostatic Pressure on a Thin Wall Cylinder The complete model and results for this test case are in file ssls08.” Test Case Data and Information Units SI Material Properties E = 2.3 11 Finite Element Modeling • • 200 parabolic quadrilateral plate elements 661 nodes Cylinder is meshed by revolving a meshed beam.neu. The mesh is shown in the following figure: . It provides the input data and results for benchmark test SSLS08/89 from “Guide de validation des progiciels de calcul de structures. This test is a linear statics analysis of a thin cylinder loaded by hydrostatic pressure. Constrain the nodes on side B (from node 1 to node 641) in the Y translation.and X and Z rotation. Boundary Conditions Constraints • • Constrain the nodes on side A (from node 21 to node 661) in the X translation and Y and Z rotations. p = p0*Z/L with p0=20000 Pa The boundary conditions are shown in the following figure: Solution Type Statics . Loads • Internal elemental pressures. 1990. (Paris.00% T3 Translation Node 321 ψ ( rad ) 1.19E-6 0. .19E-6 1. Afnor Technique.38E-6 2. SSLS08/89.38E-6 0. Guide de validation des progiciels de calcul de structures.40% Plate Top X Normal Stress Node 321 x=L/2 ∆R ( m ) 2.0E5 4.98E5 0.0054E5 Difference Plate Top Y Normal Stress Node 321 x=L/2 σ22 ( Pa ) 5.0 FEMAP Structural -0.) Test No.00% R2 Rotation ψ represents the rotation of a generator Reference • Societe Francaise des Mecaniciens.86E-6 1.00% T1 Translation Node 1 x=L ∆L ( m ) -2.486E-6 0. Results Node Node 321 Point Any σ11 ( Pa ) Displacement and Stress Bench Value 0. This test is a linear statics analysis of a thin cylinder loaded by its own weight.” Test Case Data and Information Units SI Material Properties E = 2.neu.3 γ = 7.Gravity Loading on a Thin Wall Cylinder The complete model and results for this test case are in file ssls09.1 ×10 Pa ν = 0. It provides the input data and results for benchmark test SSLS09/89 from “Guide de validation des progiciels de calcul de structures.85 ×10 Pa kg mass = 8002 -----3 m 11 11 Finite Element Modeling • • 65 linear quadrilateral plate elements (mapped meshing) 84 nodes . Loads • Body load: Translational acceleration in the Z direction . Nodes 33-36: Constrain in the Z translation only. 21-32: Constrain the X translation and Y and Z rotations. Node 4: Constrain in the X and Z translations and the Y and Z rotations. 5-16: Constrain in the Y translation and X and Z rotations. Nodes 3. Node 2: Constrain in all directions except for the X translation and Y rotation. The mesh is shown in the following figure: Boundary Conditions Constraints • • • • • Nodes 1. The boundary conditions are shown in the following figure: Solution Type Statics Results Node # Node 2 Point x=0 σ11 ( Pa ) Displacement and Stress Bench Value 3.0 -1578 to 1578 Plate Top Y Normal Stress .82% Plate Top X Normal Stress Node 1 Any σ22 ( Pa ) 0.14E5 FEMAP Structural 3.02E5 Difference 3. 1990.12E-7 -1.99E-6 2. (Paris.) Test No.49E-7 -4.00 R2 Rotation Reference • Societe Francaise des Mecaniciens. Node 2 x=0 ∆R ( m ) -4.00% T3 Translation Node 10 x-L ψ ( rad ) -1.39E-7 2.00% T1 Translation Node 1 x=L z∆ ( m ) 2.99E-6 0. . Afnor Technique. Guide de validation des progiciels de calcul de structures.12E-7 0. SSLS09/89. 5x10 Pa ν = 0. It provides the input data and results for benchmark test SSLS20/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties E = 10. pinching as shown.Pinched Cylindrical Shell The complete model and results for this test case are in the following files: • • ssls20a.315 6 Finite Element Modeling Test 1 (ssls20a) .neu (linear quadrilateral plate) This test is a linear statics analysis of a cylindrical shell with nodal forces. F.Free meshing • • 296 linear triangle plate elements 173 nodes .neu (linear triangle plate) ssls20b. To set free boundary conditions. Test 2 (ssls20b) . Loads • Nodal forces Fy = -25 N at point D . Node 1: Fully constrain except for the X translation. Node 4. use symmetry about XY. Nodes 14-26: Constrain the Z translation and the X and Y rotations.Mapped meshing • • 140 linear quadrilateral plate elements 165 nodes Boundary Conditions Constraints • • • • • • Free conditions. Node 3: Fully constrain except for the Y translation. 5-13: Constrain in the Y translation and the X and Z rotations. 27-35: Constrain in the X translation and the Y and Z rotations. XZ and YZ planes. Node 2. ) Test No.1990.3E-3 Difference 0. SSLS20/89.53% Reference • Societe Francaise des Mecaniciens.44% 0. Guide de validation des progiciels de calcul de structures. Afnor Technique.9E-3 1 2 Test Number FEMAP Structural -114.4E-3 -113.9E-3 -113. The boundary conditions are shown in the following figure: Solution Type Statics Results Point D D Displacement Displacement Y (Node 3) (T2 Translation) Displacement Y (Node 3) (T2 Translation) Bench Value -113. (Paris. . linear triangular plate) ssls21c.neu (Test 3.Spherical Shell with a Hole The complete model and results for this test case are in the following files: • • • ssls21a.285x10 Pa ν = 0.neu (Test 1. It provides the input data and results for benchmark test SSLS21/89 from “Guide de validation des progiciels de calcul de structures.neu (Test 2.3 7 Finite Element Modeling Test 1 (ssls21a) • • 100 linear quadrilateral plate elements 121 nodes . parabolic quadrilateral plate) This test is a linear statics analysis of a spherical shell with a hole with nodal forces. linear quadrilateral plate) ssls21b.” Test Case Data and Information Units SI Material Properties E = 6. Free condition . Boundary Conditions Constraints • • • Constrain nodes 1-11 in the X translation and Y and Z rotations. Test 2 (ssls21b) • • 200 linear triangular plate elements 121 nodes Test 3 (ssls21c) • • 100 parabolic quadrilateral plate elements 341 nodes All tests are executed with mapped meshing. Constrain nodes 111-121 in the Z translation and X and Y rotations. (Paris.3E-3 103.6E-3 Difference 9.7E-3 98.0. s Note: To set free boundary conditions. use symmetry about XY and YZ planes.91% 10. Afnor Technique.0E-3 1 2 3 Test Number FEMAP Structural 103. .32% 4.0) T1 Translation u (m) node 111 node 111 node 421 Bench Value 94. Loads • Nodal forces F = 2 Newtons Due to the symmetric boundary conditions.) Test No. Guide de validation des progiciels de calcul de structures.89% Reference • Societe Francaise des Mecaniciens. SSLS21/89. The boundary conditions are shown in the following figure: Solution Type Statics Results Point A(R.0E-3 94.1990. only half of the load is applied.0E-3 94. It provides the input data and results for benchmark test SSLS24/89 from “Guide de validation des progiciels de calcul de structures.neu (Test 3.3 7 Finite Element Modeling Test 1 (ssls24a): length/thickness=1 • 100 linear quadrilateral plate elements . very fine mesh) This test is a linear statics analysis of a plate with pressure loading and simple supports.” Test Case Data and Information Units SI Material Properties E = 1.neu (Test 1.neu (Test 2. coarse mesh) ssls24b. fine mesh) ssls24c.0x10 Pa ν = 0.Uniformly Distributed Load on a Simply-Supported Rectangular Plate The complete model and results for this test case are in the following files: • • • ssls24a. • 121 nodes Test 2 (ssls24b): length/thickness=2 • • 200 linear quadrilateral plate elements 231 nodes Test 3 (ssls24c): length/thickness=5 • 500 linear quadrilateral plate elements . Loads • Set pressure = 1 N/m**2 in the -Z direction . • 561 nodes Boundary Conditions Constraints • • Fully constrain node 1 in all translations and rotations. Constrain the nodes on all edges in the Z translation only. 00444 0.01110 1 2 3 Test FEMAP Structural 0.1417 .01110 0.03% 0.0 α 0.06% 2.00453 0.0 α Parameter Bench Value 0. The boundary conditions are shown in the following figure: Solution Type Statics Results Center Node 61z direction (T3 Translation) 116z direction (T3 Translation) 281z direction (T3 Translation) Length/ Thickne ss 1.0 α 5.01402 Difference 2.0% 1. 0 β 2874 1 2905 1.00% 2. Guide de validation des progiciels de calcul de structures.0 α 7476 3 7332 1. Reference • Societe Francaise des Mecaniciens. .1990. Note that the plate top surface corresponds to the side of the plate with negative global z coordinates.61% 5. 61x component top surface (Plate Top X Normal Stress) 116x component top surface (Plate Top Y Normal Stress) 281x component top surface (Plate Top Y Normal Stress) 1. The correct values are extracted from “Formulas for Stress and Strain (Roark/Young)”. (Paris.) Test No. SSLS24/89.0 β 6102 2 6065 0. Afnor Technique.93% βqb Max σ = σ b = ----------2 t – αqb Max y = --------------3 Et 4 2 Where: q= distributed load b = dimension t = thickness E = elastic modules β values of reference from the “Guide de Validation” are incorrect. It provides the input data and results for a test similar to benchmark test SSLS25/89 from “Guide de validation des progiciels de calcul de structures.neu (Test 1) ssls25b.” Test Case Data and Information Units SI Material Properties E = 36.neu (Test 2) This test is a linear statics analysis (three–dimensional problem) of a plate with pressure and transverse bending.0x10 Pa ν = 0.3 6 Finite Element Modeling • • Length/thickness=2 linear quadrilateral plate elements Test 1 (ssls25a) θ = 30° .Uniformly Distributed Load on a Simply-Supported Rhomboid Plate The complete model and results for this test case are in the following files: • • ssls25a. Constrain the nodes along the edges of the mesh in the Z translation. Test 2 (ssls25b) θ = 45° Boundary Conditions Constraints • • Fully constrain node 231 in all translations and rotations. . Loads • Elemental pressure = 1 N/m**2 in the -Z direction Solution Type Statics Results Test Case Test 1 ssls25a ssls25a β = 0.894x10E-3m Y stress (Plate Top Y Nor.27% lation) at node 116 -3.3.761x10E3N/m2 Z displacement (T3 Trans.1.53% lation) at node 116 -2.108 θ = 45° β = 0.137x10E-3m Y stress (Plate Top Y Nor.70x10E3N/m2 Z displacement -3.0x10E-3m Y stress FEMAP Structural Difference Z displacement (T3 Trans.39x10E3N/m2 .539 -5.277x10E-3m Y stress -5.349x10E3N/m2 Test 2 ssls25b ssls25b α = 0.118 θ = 30° Bench Center location Value Z displacement -3.76% mal Stress) at node 116 -5.0.07% mal Stress) at node 116 -5.570 Parameters α = 0.4. The correct values are extracted from “Formulas for Stress and Strain (Roark/Young). SSLS25/89. (Paris.” table 26. case number 14a. Max σ =βqb 2 4 αqb Max y = -----------3 Et Where: q= distributed load b = dimension t = thickness E = elastic modules Values of reference from the “Guide de validation” are incorrect. Afnor Technique.) Test No. . Reference • Societe Francaise des Mecaniciens.1990. Guide de validation des progiciels de calcul de structures. Mindlin (element formulation) • • 6 linear quadrilateral plate elements 14 nodes Test 2 (ssls27b) .neu (Test 1) ssls27b.25 7 Finite Element Modeling Test 1 (ssls27a) .” Test Case Data and Information Units SI Material Properties E = 1.Kirchhoff (element formulation) • 6 linear quadrilateral plate elements .neu (Test 3) This test is a linear statics analysis of a thin plate with torque and shear loading.Shear Loading on a Plate The complete model and results for this test case are in the following files: • • • ssls27a.neu (Test 2) ssls27c.0x10 Pa ν = 0. It provides the input data and results for benchmark test SSLS27/89 from “Guide de validation des progiciels de calcul de structures. Mindlin (element formulation) • • 48 linear quadrilateral plate elements 75 nodes All tests are executed with mapped meshing. D The boundary conditions are shown in the following figure: A C D Solution Type Statics . Boundary Conditions Constraints • Fully constrain the nodes on side AD in all translations and rotations. Loads • • Create a nodal force Fz = -1N at point B. • 14 nodes Test 3 (ssls27c) . Create a nodal force -Fz = 1N at point C. 335E-2 3.38% 6. Guide de validation des progiciels de calcul de structures. (Paris.) Test No.83% 4.537E-2 3.750E-2 Difference 50. Results at Location C Displacement Node (Total T3 Translation) 14 14 75 Bench Value 3.02% Reference • Societe Francaise des Mecaniciens.382E-2 3.537E-2 3. SSLS27/89. .537E-2 1 2 3 Test Number FEMAP Structural 5. Afnor Technique.1990. Mechanical Structures .Linear Statics Analysis with Solid Elements The linear statics analysis test cases from the Societe Francaise des Mecaniciens include these solid element test cases: • • • • • "Solid Cylinder in Pure Tension" "Internal Pressure on a Thick-Walled Spherical Container" "Internal Pressure on a Thick-Walled Infinite Cylinder" "Prismatic Rod in Pure Bending" "Thick Plate Clamped at Edges" . Solid Cylinder in Pure Tension The complete model and results for this test case are in the following files: • • • • sslv01a. It provides the input data and results for benchmark test SSLV01/89 from “Guide de validation des progiciels de calcul de structures.0x10 Pa ν = 0. free meshing) This test is a linear statics analysis of a solid cylinder with tension–compression.” Test Case Data and Information Units SI Material Properties E = 2.30 11 Finite Element Modeling Test 1 (sslv01a) .neu (linar brick. free meshing) sslv01b.neu (linear quadrilateral axisymmetric solid. mapped meshing) sslv01c. mapped meshing) sslv01d.neu (parabolic tetrahedron.Free meshing • • 155 parabolic tetrahedron elements 342 nodes .neu (linear triangular axisymmetric solid. Mapped meshing • • 192 linear brick elements 259 nodes Test 3 (sslv01c) .Free meshing • • 28 linear triangular axisymmetric solid elements 24 nodes .Mapped meshing • • 48 linear quadrilateral axisymmetric solid elements 65 nodes Test 4 (sslv01d) . Test 2 (sslv01b) . 173-199: Constrain in the X translation. 153. 234. 81. 117. . 126. 17-19: Constrain in the Y and Z translations. Constrain node 37 in the X. and 306 in the X translation. 18. 72. Y. 14-16: Constrain in the X and Z translations. 252. 108. Constraints (sslv01b) • • • • • • Constrain node 1. 198. 243. 23-25. Constrain nodes 9. and 29-35 in the Z translation. 216. 127. 279. and Z translations. Nodes 5. 64-72: Constrain in the Z translation. Boundary Conditions Constraints • Uniaxial deformation of the cylinder section Constraints (sslv01a) • • • • • • • Nodes 1. and 307 in the X and Y translation. 59-63: Constrain in the X and Y translations. and 36 in the X and Z translation. Nodes 4. 144. and Z translations. Constrain nodes 54. 288. 99. 33-45. 46-58. Constrain nodes 2-8. 200-226: Constrain in the Y translation. 10. 261. 189. 172. 20-26. 297. Nodes 6. Constrain nodse 82. Node 3: Constrain in the X. 20-22. 11-17. 217. Nodes 7-13. 27.19. 171. and 28 in the Y and Z translation. 63. 162. Nodes 2. Y. 207. 226. Constrain node 65 in the X and Z translations. 39. 181. 136. and 298 in the Y translation. 190. 55. 271. 163. 109. Constraints (sslv01c) • • Constrain nodes 13. 244. 280. 6. 145. 154. 91. 208. and 52 in the Z translation. 235. 5. 199. 100. 289. 253. 26. • Constrain nodes 46. Constraints (sslv01d) • • Constrain node 1 in the X and Z translation Constrain nodes 2. 73. 64. . 118. and 7 in the Z translation. 5E-3 1.5E-3 1.00% 0.00% 0.00% .5E-3 1. Tests 1 and 2 Loads.5E-3 1. F/A = 100 MPa Loads.00% 0.00% 0.5E-3 1. Loads (all tests) • • Set uniformly distributed force -F/A on the free end in the Z direction Elemental pressure.5E-3 1.00% 0.00% 0.5E-3 Difference 0.5E-3 1.5E-3 1. Tests 3 and 4: Solution Type Statics Results Node # 6 279 1 4 4 307 53 Displacements T3 Translation T3 Translation T3 Translation T3 Translation T3 Translation T3 Translation T3 Translation Bench Value 1.5E-3 1.5E-3 1.5E-3 1.5E-3 1.5E-3 1 2 3 4 1 2 3 Test # FEMAP Structural 1. 00% 4 T1 Translation -0.00% 9 T1 Translation -0.00% 9 T3 Translation 0.15E-3 0.00% 5 T2 Translation -0.15E-3 0.00% 25 T1 Translation -0.15E-3 3 -0. .15E-3 0.5E-3 0.00% 279 T2 Translation -0.00% 189 T3 Translation 1E-3 2 1E-3 0. (Paris.15E-3 0.15E-3 0.00% 189 T1 Translation -0.15E-3 4 -0.5E-3 0.00% Reference • Societe Francaise des Mecaniciens.00% 99 T2 Translation -0. Afnor Technique.5E-3 0.15E-3 3 -0.00% 41 T3 Translation 0.00% 41 T1 Translation -0. 3 T3 Translation 1.15E-3 0.15E-3 2 -0.00% 6 T2 Translation -0.15E-3 4 -0.00% 99 T3 Translation 0.15E-3 0.00% 29 T1 Translation -0.15E-3 0.00% 37 T3 Translation 1E-3 1 1E-3 0.15E-3 0.) Test No.15E-3 1 -0.15E-3 2 -0.00% 29 T3 Translation 0.15E-3 0.00% 1 T1 Translation -0.5E-3 2 0.15E-3 1 -0. Guide de validation des progiciels de calcul de structures.15E-3 3 -0.5E-3 0.00% 25 T3 Translation 1E-3 4 1E-3 0.5E-3 1 0.5E-3 0.15E-3 2 -0.5E-3 4 1.00% 37 T1 Translation -0.15E-3 1 -0.15E-3 0.5E-3 3 0.15E-3 4 -0.15E-3 0.1990.5E-3 4 0.00% 5 T3 Translation 1E-3 3 1E-3 0. SSLV01/89/89. Mapped meshing • 1600 linear brick elements .0x10 Pa ν = 0. It provides the input data and results for benchmark test SSLV03/89 from “Guide de validation des progiciels de calcul de structures. linear axisymmetric solids) sslv03d.Internal Pressure on a Thick-Walled Spherical Container The complete model and results for this test case are in the following files: • • • • sslv03a.neu (Test 2. parabolic axisymmetric solids) This test is a linear statics analysis of a thick sphere with internal pressure. linear solids) sslv03b.neu (Test 4.30 5 Finite Element Modeling Test 1 (sslv03a) .neu (Test 1. parabolic solids) sslv03c.” Test Case Data and Information Units SI Material Properties E = 2.neu (Test 3. Mapped meshing • • 250 parabolic brick elements 1256 nodes Test 3 (sslv03c) .Mapped meshing • 400 linear quadrilateral axisymmetric solid elements . • 1898 nodes Test 2 (sslv03b) . Constraints .Tests 1 and 2: . • 451 nodes Test 4 (sslv03d) .Mapped meshing • • 400 parabolic quadrilateral axisymmetric solid elements 1301 nodes Boundary Conditions Constraints • The equivalent of the center of the sphere being fixed is modeled via symmetric boundary conditions. Constraints .Tests 3 and 4: .Tests 3 and 4: Loads • Uniform radial elemental pressure = 100 MPa The boundary conditions are shown in the following figure: Pressure -Tests 1 and 2: Pressure . 04 4.20 3.81 72.43 2 73.43 2 3 4 1 -104.33% 4.00% .70% 1 Axisym C1 Azimuth Stress u (m) T3 Translation 0.70 3.50 2.40E-3 0.43 4 69.19% 0.07 Difference 9.18% Solid Y Normal Stress 41 σ θ ( MPa ) 71.50 -94.43 3 69.4E-3 1 0.12% Axisym C1 Azimuth Stress 41 σ θ ( MPa ) 71.33 -95.50% 5. Solution Type Statics Results Results for Point R = 1m Point r=1 m Node # 1 σ Π ( MPa ) Displacement Stress Bench Value -100 Test Number 1 FEMAP Structural -90.85% Solid Y Normal Stress 1 σ θ ( MPa ) 71.93% 1 41 41 1 Solid Z Normal Stress Solid Z Normal Axisym C1 Radial Stress Axisym C1 Radial Stress σ θ ( MPa ) -100 -100 -100 71. 40E-3 0.53% 1 1 Solid Y Normal Stress Axisym C1 Radial Stress Axisym C1 Radial Stress 21.43 3 4 1 -.70% .649 N/A 1 1 1826 Solid Z Normal Stress Axisym C1 Radial Stress Axisym C1 Radial Stress σ θ ( MPa ) 0 0 21.041 Difference N/A Solid Z Normal Stress 2221 σ Π ( MPa ) 0 2 -.4E-3 2 3 4 0.43 3 4 21.40E-3 0.39 21.18 N/A N/A 1.50% 0.00% Results for Point R = 2m Point r=2 m Node # 1826 Displacement Stress 0 σ Π ( MPa ) Bench Value Test Number 1 FEMAP Structural -.4E-3 0. 1 41 41 u (m) T3 Translation u (m) T3 Translation u (m) T3 Translation 0.43 21.233 -.58 0.76 1.00% 2.4E-3 0.41E-3 0.43 2 21.19% 0.16% Solid Y Normal Stress 2221 σ θ ( MPa ) 21.430 21. 1826 2221 1 1 u (m) T3 Translation u (m) T3 Translation u (m) T3 Translation u (m) T3 Translation 1.5E-4 1.5E-4 1.5E-4 1.5E-4 1 2 3 4 1.50E-4 1.50E-4 1.53E-4 1.50E-4 0.00% 0.00% 2.00% 0.00% All results are averaged. Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLV03/89. Internal Pressure on a Thick-Walled Infinite Cylinder The complete model and results for this test case are in the following files: • • • • sslv04a.neu (solid, linear brick) sslv04b.neu (solid, parabolic brick) sslv04c.neu (solid, axisymmetric quadrilateral) sslv04d.neu (solid, axisymmetric parabolic) This test is a linear statics analysis of a thick cylinder with internal pressure. It provides the input data and results for benchmark test SSLV04/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties E = 2.0x10 Pa ν = 0.30 5 Finite Element Modeling All tests are executed with mapped meshing. Test 1 (sslv04a) - Mapped meshing • • 400 solid (linear brick) elements 902 nodes Test 2 (sslv04b) - Mapped meshing • • 240 solid (parabolic brick) elements 1873 nodes FE Model - Tests 1 and 2: Test 3 (sslv04c) - Mapped meshing • • 600 axisymmetric (linear quadrilateral solid) elements 656 nodes Test 4 (sslv04d) - Mapped meshing • • 600 axisymmetric (parabolic quadrilateral solid) elements 1911 nodes FE Model - Tests 3 and 4: Boundary Conditions Constraints (sslv04a) • • Nodes 1-41, 452-492: Constrain in the X translation. Nodes 411-451, 862-902: Constrain in the Z translation. Constraints (sslv04b) • • Nodes 1-61, 1038-1098, 2075-2135: Constrain in the X translation. Nodes 977-1037, 2014-2074, 3051-3111: Constrain in the Z translation. Constraints (sslv04c) • Nodes 1-41: Constrain in the Z translation. Constraints (sslv04d) • Nodes 1-81: Constrain in the Z translation. Loads (all tests) • • Unlimited cylinder Internal elemental pressure p = 60 MPa Boundary Conditions - Tests 1 and 2: Boundary Conditions - Tests 3 and 4: Solution Type Statics Results All results are averaged. Results for R=0.1m Test Case sslv04a Point r=0.1 m σ r ( MPa ) Displacement Stress Bench Value -60 Node # 411 FEMAP Structural -57.07 Difference 4.88% sslv04b sslv04c sslv04d sslv04a Solid X Normal Stress Solid X Normal Stress Axisymm C1 Radial Stress Axisymm C1 Radial Stress σ θ ( MPa ) -60 -60 -60 100 977 616 1831 411 -60.97 -58.03 -59.98 99.69 1.62% 3.28% 0.03% 0.31% Solid Z Normal Stress sslv04b σ θ ( MPa ) 100 977 100.98 0.98% sslv04c sslv04d sslv04a Solid Z Normal Stress Axisymm C1 Azimuth Stress Axisymm C1 Azimuth Stress τ max ( MPa ) 100 100 80 616 1831 411 100.77 99.98 79.35 0.77% 0.02% 0.81% Solid Max Shear Stress sslv04b sslv04a sslv04b sslv04c sslv04d Solid Max Shear Stress u (m) T1 Translation T1 Translation T1 Translation T1 Translation 80 59E-6 59E-6 59E-6 59E-6 977 411 977 616 1831 80.97 59E-6 59E-6 59E-6 59E-6 1.21% 0.00% 0.00% 0.00% 0.00% Results for R=0.2m Test Case sslv04a Point r=0.2m σ r ( MPa ) Displacement Stress 0 Bench Value Node # 451 FEMAP Structural -.006 Difference NA sslv04b sslv04c sslv04d sslv04a Solid X Normal Stress Solid X Normal Stress Axisymm C1 Radial Stress Axisymm C1 Radial Stress σ θ ( MPa ) 0 0 0 40 1037 656 1911 451 -.250 -.253 .002 39.70 NA NA NA 0.75% sslv04b sslv04c sslv04d sslv04a Solid Z Normal Stress Solid Z Normal Stress Axisymm C1 Aximuth Stress Axisymm C1 Aximuth Stress τ max ( MPa ) 40 40 40 20 1037 656 1911 451 40.25 40.61 39.90 20.10 0.62% 1.53% 0.25% 0.50% Solid Max Shear Stress sslv04b sslv04a sslv04b sslv04c sslv04d Solid Max Shear Stress u (m) T1 Translation T1 Translation T1 Translation T1 Translation 20 40E-6 40E-6 40E-6 40E-6 1037 451 1037 656 1911 20.25 40E-6 40E-6 39.9E-6 40E-6 1.25% 0.00% 0.00% 0.25% 0.00% Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. SSLV04/89. neu (Test 2. parabolic tetrahedrons) sslv08c.Free meshing • • 198 solid (linear tetrahedron) elements 76 nodes Test 2 (sslv08b) . linear bricks) sslv08d.30 5 Finite Element Modeling Test 1 (sslv08a) .neu (Test 3. parabolic bricks) This test is a linear statics analysis of a solid rod with bending.Free meshing • • 198 solid (parabolic tetrahedron) elements 409 nodes . solid elements.neu (Test 4 solid elements. solid elements. linear tetrahedrons) sslv08b.” Test Case Data and Information Units SI Material Properties E = 2.0x10 Pa ν = 0. solid elements.neu (Test 1. It provides the input data and results for benchmark test SSLV08/89 from “Guide de validation des progiciels de calcul de structures.Prismatic Rod in Pure Bending The complete model and results for this test case are in the following files: • • • • sslv08a. FE Model .Tests 3 and 4: Boundary Conditions Constraints (sslv08a) • • • Nodes 29.Mapped meshing • • 48 solid (linear brick) elements 117 nodes Test 4 (sslv08d) .Tests 1 and 2: Test 3 (sslv08c) . 40: Constrain in the Z translation. and Z translations. 33: Constrain in the X and Z translations. . Node 57: Constrain in the X. Y. 34. 39. Nodes 30-32.Mapped meshing • • 48 solid (parabolic brick) elements 381 nodes FE Model . Constraints (sslv08c) • • Nodes 1-4. Constraints (sslv08d) • • • Nodes 1-8. Y. 6-9: Constrain in the Z translation. Constraints (sslv08b) • • • Nodes 127. and Z translations. Nodes 11: Constrain in the X. Nodes 128-130. Node 5: Constrain in the X. 132-146. and Z translations. 10. 14-21: Constrain in the Z translation. and Z translations. 188-195: Constrain in the Z translation only. Loads (all tests) • Set moment Mx equal to (4/3)E+7 N. 12. Y. Y. Node 187: Constrain in the X. 131: Constrain in the X and Z translations. Nodes 9.m Boundary Conditions .Tests 1 and 2: . 13: Constrain in the X translation. 268E6 10.1480E-4 0.70% 0.15E-4 0.93% 1.15E-4 FEMAP Structural -4.044E-4 1.Tests 3 and 4: Solution Type Statics Results Test # 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 5 5 75 245 26 90 77 251 19 40 76 249 5 5 75 245 Node # Displacement/ Stress Solid Z Normal Stress (Pa) Solid Z Normal Stress (Pa) Solid Z Normal Stress (Pa) Solid Z Normal Stress (Pa) T2 Translation T2 Translation T2 Translation T2 Translation T3 Translation T3 Translation T3 Translation T3 Translation T1 Translation T1 Translation T1 Translation T1 Translation Bench Value -10E6 -10E6 -10E6 -10E6 4E-4 4E-4 4E-4 4E-4 2E-4 2E-4 2E-4 2E-4 0.010E-4 7.10% 26.00% 1.00% 0.10% 27.33% 0.30% 0. Boundary Conditions .73% .15E-4 0.1514E-4 0.449E-6 0.50% 50.1511E-4 Difference 57.460E-4 2E-4 2E-4 2.07E6 10.00% 0.00% 0.00% 0.964E-4 4E-4 4E-4 4.03E6 10.15E-4 0.01E6 2.00% 0.00% 0.34% 0. 20% 0. Guide de validation des progiciels de calcul de structures.60% 1.2620E-6 -0.15E-4 -6. Afnor Technique.15E-4 -0. .1509E-4 -0.1990. (Paris.73% Reference • Societe Francaise des Mecaniciens.33% 0.1511E-4 58. SSLV08/89.15E-4 -0.) Test No.1480E-4 -0.15E-4 -0. 1 2 3 4 8 8 73 241 T1 Translation T1 Translation T1 Translation T1 Translation -0. neu (Test 1.neu (Test 1. linear plate. parabolic brick. length/thickness =100) sslv09b10.neu (Test 1. length/thickness =50) sslv09b75.neu (Test 2. parabolic brick. linear plate. parabolic brick.neu (Test 2. linear plate.neu (Test 1. length/thickness =10) sslv09b20. length/thickness =50) sslv09a75.30 11 Finite Element Modeling Test 1 .Thick Plate Clamped at Edges The complete model and results for this test case are in the following files: • • • • • • • • • • sslv09a10.Mapped meshing • • 25 parabolic brick elements 228 nodes . length/thickness =20) sslv09b50.neu (Test 2. parabolic brick. length/thickness =75) sslv09a100. length/thickness =20) sslv09a50.neu (Test 2. It provides the input data and results for benchmark test SSLV09/89 from “Guide de validation des progiciels de calcul de structures. length/thickness =100) This test is a linear statics analysis of a square thick plate with pressure and transverse bending. linear plate. parabolic brick.1x10 Pa ν = 0. length/thickness =75) sslv09b100.neu (Test 2.neu (Test 1.” Test Case Data and Information Units SI Material Properties E = 2. linear plate. length/thickness =10) sslv09a20. 01 .02 length/thickness =75. t=0. 20.1 length/thickness =20. • length/thickness =10. 50. 100 Test 2 .05 length/thickness =50. t=0. 100 Test 2 is done using plate elements with the following thickness values: • • • • • length/thickness =10. t=0. 50.Mapped meshing • • • 25 linear quadrilateral plate elements 36 nodes length/thickness =10. t=0. 75. 20.01333 length/thickness =100. t=0. 75. and A’D’ in all translations and rotations. Boundary Conditions Constraints – Test 1 • • • • Fully constrain the nodes on edges AB. Constrain the corner nodes at C in all translations and rotations except for the Z translation. AD. Constrain the nodes on edge BC and B’C’ in the X translation and Y and Z rotations. A’B’. Constrain the nodes on edge BC in the X translation and Y and Z rotations. Constrain the nodes on edge DC in the Y translation and X and Z rotations.5E5 N in -Z direction Boundary conditions for Test 1: . Constraints – Test 2 • • • • Fully constrain the nodes on edges AB and AD in all translations and rotations. Constrain the corner nodes at C and C’ in all translations and rotations except for the Z translation. Constrain the nodes on edge DC and D’C’ in the Y translation and X and Z rotations. Loads • Load case 1: Elemental pressure p = 1E6 Pascals in -Z direction • Load case 2: Point C Nodal force F = 2. 42995E-3 -.426662E-3 -.26861E-1 -.25352E-2 -.29146 Difference 12.29146E-3 -.76231E-4 -.00% 6.Load Case # ness 10 10 20 20 50 50 75 75 100 100 Pressure Force Pressure Force Pressure Force Pressure Force Pressure Force 242 242 242 242 242 242 242 242 242 242 Reference FEM -.27641E-1 -.38% 0.346276E-1 -.98% 4. Boundary conditions for Test 2: Solution Type Statics Results Test Case 1 (T3 Translation at location C) Length/ Node Thick.95% 6.27794 FEMAP Structural -.11837 -.15% 4.259820E-1 -.114411 -.65520E-1 -.523376E-3 -.81900E-2 -.32% 46.12296 -.735942E-4 -.52416E-3 -.6552E-4 -.612191E-1 -.56% 8.53833E-3 -.63389E-1 -.00% 4.36433E-1 -.778247E-2 -.242500E-2 -.80286E-2 -.96% 6.268120 File Name sslv09a10 sslv09a10 sslv09a20 sslv09a20 sslv09a50 sslv09a50 sslv09a75 sslv09a75 sslv09a100 sslv09a100 Analytical -.00% .23317E-2 -.35738E-1 -. 36433E-1 -.70% 3.381471E-1 -.81900E-2 -.302292 Analytical -.395973E-3 -.797294E-4 -.97% 3. SSLV09/89.20% 3.86% 8. (Paris.69% 35.849953E-2 -.564973E-3 -.37454E-1 -.72% Reference • Societe Francaise des Mecaniciens.676175E-1 -.) Test No. Afnor Technique.260199E-2 -.69% 11.59% 3.29579 FEMAP Structural -.35% 3.12296 -.66390E-1 -.65520E-1 -. Test Case 2 (T3 Translation at location C) Part Name sslv09b10 sslv09b10 sslv09b20 sslv09b20 sslv09b50 sslv09b50 sslv09b75 sslv09b75 sslv09b10 0 sslv09b10 0 Length/ Node Thick.41087E-3 -.78% 4.29146 Difference 21.Load Case # ness 10 10 20 20 50 50 75 75 100 100 Pressure Force Pressure Force Pressure Force Pressure Force Pressure Force 1 1 36 36 36 36 36 36 1 1 Reference FEM -.27641E-1 -. Guide de validation des progiciels de calcul de structures.285676E-1 -.6552E-4 -.1990.78661E-4 -.127845 -.12525 -.29146E-3 -.25946E-2 -.83480E-2 -.55574E-3 -. .23317E-2 -.52416E-3 -.28053E-1 -. Mechanical Structures .Normal Modes/Eigenvalue Analysis The normal modes/eigevanlues test cases from the Societe Francaise des Mecaniciens include: • • • • • • • • • • • • • • • "Lumped Mass-Spring System" "Short Beam on Simple Supports" "Axial Loading on a Rod" "Thin Circular Ring" "Cantilever Beam with a Variable Rectangular Section" "Thin Circular Ring Clamped at Two Points" "Vibration Modes of a Thin Pipe Elbow" "Cantilever Beam with Eccentric Lumped Mass" "Thin Square Plate (Clamped or Free)" "Simply-Supported Rectangular Plate" "Thin Ring Plate Clamped on a Hub" "Vane of a Compressor .Pipes with Flexible Elbows" "Rectangular Plates" .Clamped-free Thin Shell" "Bending of a Symmetric Truss" "Hovgaard’s Problem . Lumped Mass-Spring System The complete model and results for this test case are in file sdld02.neu. . This test is a normal modes/eigenvalue analysis of an elastic link with lumped mass.” Test Case Data and Information Units SI Material Properties Spring constant Finite Element Modeling • • • 8 mass elements 9 DOF springs 8 nodes The mesh is shown in the following figure: Boundary Conditions Constraints • Constrain all the nodes (1-8) in all translations and rotations except for the X translation. It provides the input data and results for benchmark test SDLD02/89 from “Guide de validation des progiciels de calcul de structures. 00% 0.9155 20.5664 29.5664 29.3840 27.3474 Bench Value (Hz) FEMAP Structural (Hz) 5.00% 0.9113 31.00% 0.00% 0.9113 31.5274 10.4642 for mode 8.4606 24.00% .00% 0.SVI method Results The mode shapes results are exact.3474 Difference 0.00% 0. Frequency Results: Normal Mode 1 2 3 4 5 6 7 8 5.4606 24.8868 15.4642 for mode 1 and 0.3840 27. The multiplication coefficient is 0.8868 15.00% 0.5274 10.9155 20. The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue . 4082 0.6527 -0.4642 -0. SDLD02/89.0000 0. Mode Shapes Results: Normal Mode 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 P1 P2 P3 P4 P5 P6 P7 P8 P1 P2 P3 P4 P5 P6 P7 P8 Point 0.3473 -0.8794 -0.4642 0. p.1612 0.4082 0.3473 0.1990.1612 Bench Value FEMAP Structural 0.0000 -1.8794 0.3030 0.3030 -0.4642 0.4642 0.3473 Reference • Societe Francaise des Mecaniciens.8794 1.6527 0. 178. .3030 0.0000 1.4082 -0.1612 -0. Afnor Technique.0000 0.) Test No.1612 0.4082 0.8794 1.3473 0.3030 0. (Paris.6527 0.6527 0. Guide de validation des progiciels de calcul de structures. 3 kg ρ = 7800 -----3 m 11 Finite Element Modeling Problem 1 (sdll01a) • • 10 bar elements 11 nodes .neu sdll01b.neu This test is a modal analysis of a straight short beam with simple supports both inline and offset.” Test Case Data and Information Units SI Material Properties E = 2x10 Pa ν = 0. It provides the input data and results for benchmark test SDLL01/89 from “Guide de validation des progiciels de calcul de structures.Short Beam on Simple Supports The complete model and results for this test case are in the following files: • • sdll01a. except for the X translation and Z rotation. Node 2: Constrain in all directions and rotations. Loads • no load case The boundary conditions for both problems are shown in the following figure: . except the Z rotation. master node 3 to slave node 1) Boundary Conditions Constraints • • • Node 1: Constrain in all directions and rotations. Constrain all other nodes in the Z translation and the X and Y rotations. Problem 2 (sdll01b) • • 10 bar elements 2 rigid elements (master node 4 to slave node 2. 24% 3.2 0. (Paris.2 Bench Value (Hz) FEMAP Structural (Hz) 394.912 0.50% 5.2 1591.924 1498.08% 6.38% 2.555 1267.03% 0.28% Difference Reference • Societe Francaise des Mecaniciens.171 2904. Afnor Technique.16% 0. SDLL01/89.096 3833.1990.) Test No.3 922. Solution Type Normal Modes/Eigenvalue – SVI method Results Problem 1: Frequency Results Normal Mode Bending 1 Tension 1 Bending 2 Bending 3 Tension 2 Bending 4 Bench Value (Hz) 431.555 1265.33% 1.9 2629.2 3126.8 902.10% 0.837 FEMAP Structural (Hz) 431.295 2870.226 1503.773 4377.003 4493.93% 2.65% Difference Problem 2: Frequency Results Mode number 1 2 3 4 5 392.661 3797. . Guide de validation des progiciels de calcul de structures.0 2800.4 1641.0 3291. Axial Loading on a Rod The complete model and results for this test case are in the following file: • • sdll05a. It provides the input data and results for benchmark test SDLL05/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties E = 2x10 Pa kg ρ = 7800 ------m3 11 Finite Element Modeling • • 10 bar elements 11 nodes The mesh is shown in the following figure: .neu sdll05b.neu This test is a modal analysis of a simply–supported beam with stress stiffening. Node 2: Leave the X translation and Z rotation free and constrain the node in all other translations and rotations. Boundary Conditions Problem 1 (sdll05a): • • Node 1: Leave the Z rotation free and constrain the node in all other translations and rotations.SVI method . Load Set 1 (node 2): Define a nodal force = to 1E5N in the -X direction. Ensure that Stress Stiffening is turned on in the analysis set. Node 2 : Leave the X translation and Z rotation free and constrain in all other translations and rotations. Problem 2 (sdll05b): • • • Node 1: Leave the Z rotation free and constrain the node in all other translations and rotations. Solution Type Normal Modes/Eigenvalue . 351 22.399 108.61 Difference 0. Afnor Technique.40% 0.702 114.080 FEMAP Structural (Hz) 28. (Paris.10% 0. .434 109.43% Reference • Societe Francaise des Mecaniciens. SDLL05/89.807 22.672 114.) Test No. Guide de validation des progiciels de calcul de structures.16% 0.1990. Results Frequency Results: Normal Mode sdll05a sdll05a sdll05b sdll05b Mode 1 Mode 3 Mode 1 Mode 3 Bench Value (Hz) 28. It provides the input data and results for benchmark test SDLL09/89 from “Guide de validation des progiciels de calcul de structures.Cantilever Beam with a Variable Rectangular Section The complete model and results for this test case are in the following file: sdll09a.” b0 b0 β = ----b1 b1 Test Case Data and Information Units SI Material Properties E = 2x10 Pa kg ρ = 7800 ------m3 11 Finite Element Modeling • • 10 beam elements (tapered) 11 nodes .neu This test is a modal analysis of a straight cantilever beam with a variable section. Constrain all other nodes in the Z translation and X and Y rotations only.SVI method . The mesh is shown in the following figure: Boundary Conditions • • • Constrain node 1 in all directions. no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue . Guide de validation des progiciels de calcul de structures.89 1092.1990.24 1112.34% 0.28 FEMAP Structural (Hz) 54. SDLL09/89.70% 1. Results Frequency Results Normal Mode 1 2 3 4 5 Bench Value (Hz) 54.13 171. (Paris.74% 4 Reference • Societe Francaise des Mecaniciens.) Test No.94 384.18 171.70 688.92 β Difference 0.40 697.20% 1.09% 0. Afnor Technique. .36 381. neu.Thin Circular Ring The complete model and results for this test case are in file sdll11. It provides the input data and results for benchmark test SDLL11/89 from “Guide de validation des progiciels de calcul de structures. This test is a modal analysis of a thin curved beam.3 kg ρ = 2700 -----3 m 10 Finite Element Modeling • • 36 bar elements 36 nodes The mesh is shown in the following figure: .” Test Case Data and Information Units SI Material Properties E = 7.2x10 Pa ν = 0. Loads • no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue .20% 0. 21. 14 0 318.36 511 900.46 1590 Bench Value (Hz) FEMAP Structural (Hz) 0 318.59% 0.SVI method Results Frequency Results Normal Mode Modes 1-6 Modes 7.00% 0. 12 Modes 13. 10 Modes 11.32% . Boundary Conditions Constraints • • Unconstrained (free) conditions Create 1 constraint set (Kinematic DOF set) to fully constrain the 3 nodes shown below (nodes 7. 30).99 508 900.03% 1. 8 Modes 9.19 1569 Difference 0. 1990. Modes 15.21 2774. 16 1726.29% Modes 17. .91 0. Afnor Technique. SDLL11/89.) Test No. 18 2792.14% Reference • Societe Francaise des Mecaniciens. Guide de validation des progiciels de calcul de structures.62% Modes 19. (Paris.56 0.55 1721. 20 3184 3116 2. This test is a modal analysis of a thin curved beam.3 kg ρ = 2700 -----3 m 10 Finite Element Modeling • • 29 bar elements 29 nodes The mesh is shown in the following figure: .neu.Thin Circular Ring Clamped at Two Points The complete model and results for this test case are in file sdll12.2x10 Pa ν = 0.” Test Case Data and Information Units SI Material Properties E = 7. It provides the input data and results for benchmark test SDLL12/89 from “Guide de validation des progiciels de calcul de structures. 3 575.SVI method Results Frequency Results Normal Mode 1 2 3 4 5 6 7 235.25% 0.80% 2.59% 0.1 1102.80% Difference .5 Bench Value (Hz) FEMAP Structural (Hz) 235.54% 0.9 575.6 1751.0 0. Boundary Conditions • • • Points A and B (nodes 1 and 2): Fully constrained in all directions All other nodes: Constrained the Z translation and X and Y rotations only.03% 0.0 2801.7 1405.8 2536.0 1740. no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue .3 1105.7 1398.1 2557.27% 0.6 2723. ) Test No. . Reference • Societe Francaise des Mecaniciens.1990. SDLL12/89. (Paris. Afnor Technique. Guide de validation des progiciels de calcul de structures. neu sdll014c.neu sdll014b. It provides the input data and results for benchmark test SDLL14/89 from “Guide de validation des progiciels de calcul de structures. and a thin curved beam.Vibration Modes of a Thin Pipe Elbow The complete model and results for this test case are in the following files: • • • sdll014a.” C A L B L D Test Case Data and Information Units SI .neu This test is a modal analysis of a straight cantilever beam. 3 kg ρ = 7800 -----3 m 11 Finite Element Modeling Problem 1 (sdll14a) where L=0 and Problem 2 (sdll14b) where L=0.1x10 Pa ν = 0.6: • • 18 bar elements 19 nodes Problem 3 (sdll14c) where L=2: • • 28 bar elements 29 nodes The FE model is shown below: . Material Properties E = 2. Boundary Conditions Problem 1 (sdll14a): • Fully constrain points C and D (nodes 1 and 2) in all translations and rotations. Solution Type Normal Modes/Eigenvalue . Constrain point C (node 3) in the Y and Z translations.SVI method . Problem 2 (sdll14b) and Problem 3 (sdll14c): • • • Fully constrain points C and D (nodes 1 and 4) in all translations and rotations. Constrain point B (node 2) in the X and Z translations. SDLL14/89.9 24.4 24.6 Difference 0.22% Problem 3 (sdll14c) Frequency Results: Normal Mode 1 2 3 4 17. (Paris.58% 0.27% 0.7 24.8 25.67 L 2 Difference 1.01% Reference • Societe Francaise des Mecaniciens.61% 1. .00% 0.) Test No.00% 1.88% Problem 2 (sdll14b) Frequency Results: Normal Mode 1 2 3 4 33. Guide de validation des progiciels de calcul de structures.23 119 125 227 FEMAP Structural (Hz) 44.80% 0.11 119 126 225 L 0 Difference 0.00% 2.30% 0. Afnor Technique.3 27 Bench Value (Hz) FEMAP Structural (Hz) 17.9 26.1990.4 94 100 180 Bench Value (Hz) FEMAP Structural (Hz) 33.12% 1.3 94 99 184 L 0. Results Problem 1 (sdll14a) Frequency Results: Normal Mode 1 2 3 4 Bench Value (Hz) 44. ” Test Case Data and Information Units SI Material Properties E = 2.neu This test is a modal analysis of a straight cantilever beam and a mass element.neu sdll15b.Cantilever Beam with Eccentric Lumped Mass The complete model and results for this test case are in the following files: • • sdll15a.1x10 Pa kg ρ = 7800 -----3 m 11 Finite Element Modeling Problem 1 (sdll15a) • • • 10 bar elements 1 mass element at point B 11 nodes A B . It provides the input data and results for benchmark test SDLL15/89 from “Guide de validation des progiciels de calcul de structures. Problem 2 (sdll15b) • • • • 10 bar elements 1 rigid element from point B to point C 1 mass element at point C 12 nodes A C B Boundary Conditions Constraints: • Fully constrain point A (node 1) in all translations and rotations.SVI . Solution Type Normal Modes/Eigenvalue . 10 1 2 3 4 5 6 7 8 Bench Value (Hz) 1.46% 4.07 50.54 59.69% wc=T3 translation at point C wb= T3 translation at point B uc=T1 translation at point C vb= T2 translation at point B .148 2.02 76.67% 0.66% 3.06% 0.46 13.6 7 8 9. Results Frequency Results: Normal Mode 1.030 0.28% 3.00% 1.48 80.54% 0.635 1.922 FEMAP Structural 1.61 63.53% 0.68 31.53 1.4 5.00% 1.12% 0.2 3.00% 0.97 61.52% 0.882 -0.148 2.76% 1.84 98.640 13.82 yc 0 Difference 0.59 28.20 1.93 FEMAP Structural (Hz) 1.75 76.030 0.30% 1 Mode Shapes Results: yc 1 1 2 3 4 • • • • Normal Mode Modal Displacement wc/wb uc/vb uc/vb wc/wb Bench Value 1.90 31.47 103.96 61.636 1.37 13.65 15.47 80.01% 0.52 28.65 16.845 -0.956 Difference 0.31% 2.00% 2.642 13.91 48. . (Paris. SDLL15/89. Guide de validation des progiciels de calcul de structures.) Test No. Afnor Technique. Reference • Societe Francaise des Mecaniciens.1990. ” Test Case Data and Information Units SI Material Properties E = 2.neu This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a thin plate.neu sdls01b.Thin Square Plate (Clamped or Free) The complete model and results for this test case are in the following files: • • sdls01a.3 kg ρ = 7800 -----3 m 11 Finite Element Modeling • • 100 linear quadrilateral plate elements 121 nodes The mesh is shown in the following figure: A D B C . It provides the input data and results for benchmark test SDLS01/89 from “Guide de validation des progiciels de calcul de structures.1x10 Pa ν = 0. 7266 21. and 111) in all translations and rotations. Solution Type Normal Modes/Eigenvalue .76% . • Problem 2 (sdls01b) : Free plate. 11.5542 FEMAP Structural (Hz) 8. Boundary Conditions • Problem 1 (sdls01a): Constrain the nodes along side BC in all translations and rotations.9586 Difference 0.SVI method Results Problem 1 (sdls01a) Frequency Results: Normal Mode 1 2 3 Bench Value (Hz) 8.1474 53. Create a constraint set (Kinematic DOF set) to constrain the three nodes shown below (nodes 1.6719 21.63% 0.74% 0.3042 53. 07% Reference • Societe Francaise des Mecaniciens.4165 59.0471 68.7814 135.2984 77.5160 FEMAP Structural (Hz) 32.7119 49.1990.4467 77. Guide de validation des progiciels de calcul de structures.11 Bench Value (Hz) 33.21% 0.0785 Difference 2.1873 83.05% 0.19% Problem 2 (sdls01b) Frequency Results: Normal Mode 7 8 9 10. SDLS01/89.) Test No.0513 87.38% 4.7448 136.05% 5.9104 47.4558 61.12% 3. Afnor Technique. (Paris. 4 5 6 68. .783 0. ” Test Case Data and Information Units SI Material Properties E = 2.Simply-Supported Rectangular Plate The complete model and results for this test case are in file sdls03.neu. This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a thin plate.3 kg ρ = 7800 -----3 m 11 Finite Element Modeling • • 150 linear quadrilateral plate elements 176 nodes The mesh is shown in the following figure: .1x10 Pa ν = 0. It provides the input data and results for benchmark test SDLS03/89 from “Guide de validation des progiciels de calcul de structures. 13 138. 119. Constrain these nodes in all directions except for the Z translation.78% 2.94 Difference 1.21 67. Create a constraint set to define the Master (ASET) DOFs on nodes 47. no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue .62 123. Boundary Conditions • • • Constrain the Z translation of the nodes on all sides of the plate.30 187.51 197.SVI method Results Frequency Results: Normal Mode 4 5 6 7 8 9 35.75% .95% 4.60% 1.90% 0.21 108.96 121.32 Bench Value (Hz) FEMAP Structural (Hz) 35.63 68. 55.51 109.32 142.18% 1. Reference • Societe Francaise des Mecaniciens. . (Paris. Afnor Technique. Guide de validation des progiciels de calcul de structures.1990.) Test No. SDLS03/89. 1x10 Pa ν = 0.Thin Ring Plate Clamped on a Hub The complete model and results for this test case are in file sdls04.” Test Case Data and Information Units SI Material Properties E = 2.neu.3 kg ρ = 7800 -----3 m 11 Finite Element Modeling Mapped meshing • • 400 linear quadrilateral plate elements 440 nodes The mesh is shown in the following figure: . It provides the input data and results for benchmark test SDLS04/89 from “Guide de validation des progiciels de calcul de structures. This test is a normal modes/eigenvalue analysis (three–dimensional problem) of an annular thin plate. 9 10.19 Difference 0. 5 6. Boundary Conditions Constraints • Fully constrain all the nodes on the inner ring as shown below. 3 4.57% .51 532.19% 0.45 158. 11 12.38 226. Loads • no load case The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue – SVI Results Frequency Results: Normal Mode 1 2. 17 18 Bench Value (Hz) 79.05% 0.05 89.85 FEMAP Structural (Hz) 79.09 89.79 not available not available not available not available not available 518.04 527.58% 2.64 113.04 433.26 81. 7 8. 13 14.41 81.02 317. 15 16.01% 0.63 112. 09 576.18% 23 609. (Paris. Guide de validation des progiciels de calcul de structures. 22 559. SDLS04/89. 19.30% 21.1990.48% Reference • Societe Francaise des Mecaniciens.) Test No. .91 6. Afnor Technique.63 0. 20 528.70 612.90 3.61 561. 0685x10 Pa ν = 0. fine mesh) This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a cylindrical thin shell. coarse mesh) slds05b.Clampedfree Thin Shell The complete model and results for this test case are in the following files: • • sdls05a.Coarse Mesh Mapped meshing • • 100 linear quadrilateral plate elements 121 nodes .neu (linear quadrilateral.” Test Case Data and Information Units SI Material Properties E = 2.3 kg ρ = 7857. It provides the input data and results for benchmark test SDLS05/89 from “Guide de validation des progiciels de calcul de structures.2 -----3 m 11 Finite Element Modeling .Vane of a Compressor .neu (linear quadrilateral. Fine Mesh Mapped Meshing • • 225 linear quadrilateral plate elements 256 nodes The fine mesh is shown in the following figure: . The coarse mesh is shown in the following figure: Finite Element Modeling . Afnor Technique.9 386.0 FEMAP Structural coarse mesh (Hz) 85.0 395.5 549.0 351.7 138. SDLS05/89. .0 537.8 FEMAP Structural fine mesh (Hz) 85. Boundary Conditions Fully constrain the nodes on one side as shown in the following figure: Solution Type Normal Modes/Eigenvalue .1990.6 138.7 Normal Mode 1 2 3 4 5 6 Reference Societe Francaise des Mecaniciens.5 259.3 248.7 386.) Test No. (Paris.6 134.0 343.8 345. Guide de validation des progiciels de calcul de structures.2 249.0 531.SVI method Results Frequency Results: Bench Value (Hz) 85. neu.” Test Case Data and Information Units SI Material Properties E = 2.Bending of a Symmetric Truss The complete model and results for this test case are in file sdlx01.3 kg ρ = 7800 -----3 m 11 Finite Element Modeling • • 24 bar elements 24 nodes The mesh is shown in the following figure: .1x10 Pa ν = 0. It provides the input data and results for benchmark test SDLX01/89 from “Guide de validation des progiciels de calcul de structures. This test is a normal modes/eigenvalue analysis (plane problem) of a straight cantilever beam structure. 00% 0.3 179.20% 0. Boundary Conditions Constraints • • Fully constrain nodes 1 and 4 in all translations and rotations.00% 0.3 96.4 43.28% Difference .10% 0.2 102.8 56.00% 0.4 43. The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue – SVI Results Frequency Results: Normal Mode 1 2 3 4 5 6 7 8 9 8.29% 0.4 175.3 96. Constrain nodes 2-3 and 5-24 in the Z translation and X and Y rotations.8 29.8 29.1 174.00% 0.2 102.3 0.00% 0.8 Bench Value (Hz) FEMAP Structural (Hz) 8.8 56.6 147.8 178.7 147. ) Test No.64% 320.44% 266. .75% 335. Afnor Technique.7 1.0 206.1990.9 0. (Paris. Guide de validation des progiciels de calcul de structures.4 268.1 0.10% Reference • Societe Francaise des Mecaniciens. SDLX01/89.4 0. 10 11 12 13 206.0 338.0 322. 658x 10 Pa ν = 0. This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a straight.3 kg ρ = 13404.106 -----3 m Units SI Finite Element Modeling • • 25 bar elements 26 nodes The mesh is shown in the following figure: .Pipes with Flexible Elbows The complete model and results for this test case are in file sdlx02. thin curved cantilever beam. It provides the input data and results for benchmark test SDLX02/89 from “Guide de validation des progiciels de calcul de structures.neu.Hovgaard’s Problem .” Test Case Data and Information Material Properties · 11 E = 1. SVI Results Frequency Results: Normal Mode 1 2 3 4 5 6 7 8 9 10.36 47.15 Bench Value (Hz) FEMAP Structural (Hz) 10.65% Difference Reference • Societe Francaise des Mecaniciens.1990. The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue . Boundary Conditions • Fully constrain nodes 1 and 6 in all translations and rotations.61% 3.16% 1.40 19.) Test No. SDLX02/89.18 19.34 123.69% 0.43% 0.87 25.20 125.09 52. (Paris.54 25. Afnor Technique.53 127.01% 9. Guide de validation des progiciels de calcul de structures.35% 2.11 122.71 51.86 75.84 85.47 48.80 82.09% 6.94 80.64 2.79% 2. . This test is a normal modes/eigenvalue analysis (three–dimensional problem) of a thin plate with rigid body modes.neu.” Test Case Data and Information Units SI Material Properties · 11 E = 2.3 kg ρ = 7800 -----3 m Finite Element Modeling • • 300 linear quadrilateral plate elements 320 nodes The mesh is shown in the following figure: .Rectangular Plates The complete model and results for this test case are in file sdlx03.1x 10 Pa ν = 0. It provides the input data and results for benchmark test SDLX03/89 from “Guide de validation des progiciels de calcul de structures. The boundary conditions are shown in the following figure: Solution Type Normal Modes/Eigenvalue . (Paris.34% 0. Boundary Conditions Constraints • Constraint Set 1 (Kinematic DOF Set): Fully constrain nodes 2. Guide de validation des progiciels de calcul de structures. .76% 3.68% 0.24% 0.35% Reference • Societe Francaise des Mecaniciens. SDLX03/89.11% 0. and 84 in all translations and rotations.SVI Results Frequency Results: Normal Mode 7 8 9 10 11 12 584 826 855 911 1113 1136 Bench Value (Hz) FEMAP Structural (Hz) 586 824 854 904 1072 1140 Difference 0. 69.) Test No.1990. Afnor Technique. Convection" "Wall .Convection" "Hollow Sphere .Fixed Temperatures.Fixed Temperatures" "Hollow Cylinder .Steady State Heat Transfer Analysis The stationary thermal test cases for steady-state heat transfer analysis from the Societe Francaise des Mecaniciens include: • • • • • • • • • "Hollow Cylinder .Flux Density" "Hollow Cylinder with Two Materials . Convection" "L-Plate" "Hollow Sphere with Two Materials -Convection" .Fixed Temperatures" "Wall .Stationary Thermal Tests .Convection" "Cylindrical Rod . 5 linear quadrilateral axisymmetric solid elements Test 2 . This test is a steady–state heat transfer analysis of a 2D axisymmetric cylinder with fixed temperatures.” Test Case Data and Information Units SI Material Properties W λ = 1 ---.Fixed Temperatures The complete model and results for this test case are in file htpla01. It provides the input data and results for benchmark test TPLA01/89 from “Guide de validation des progiciels de calcul de structures.Hollow Cylinder .°C m Finite Element Modeling Two tests: • • Test 1 .5 parabolic quadrilateral axisymmetric solid elements The meshes are shown in the following figure: Boundary Conditions • One temperature set: .neu. Internal temperature Ti = 100°C External temperature Te = 20°C Solution Type Steady–State Heat Transfer . Results Temperature Results (0 degrees Celsius): Radius(m) 0.51 50.00 FEMAP Structural 5 parabolic quads.30 0.54 35.39 1701.13 1526.04 20.1990.64 1526.39 1482.34 0.00 82.31 0.33 0.91 1674.13 1526.33 0.83 1504.00 FEMAP Structural 5 linear quads.98 66.38 Reference • Societe Francaise des Mecaniciens. 5 parabolic quads.84 1504.35 Bench Value 1729.68 1622.70 1674.31 0.54 35.00 82. TPLA01/89.00 Total Heat Flux Results (W/m**2): Radius (m) 0.98 66.32 0.98 66. Guide de validation des progiciels de calcul de structures.30 0.11 1621.32 0.78 FEMAP FEMAP Structural Structural 5 linear quads.04 20.69 1622.34 0. 100.69 1674.00 82.32 1573.32 1573.79 1572.35 Bench Value 100. 100. .51 50.54 35. (Paris. 1701.) Test No.04 20. Afnor Technique.51 50. Convection The complete model and results for this test case are in file htpla03.2 parabolic axisymmetric quadrilateral solid elements The meshes are shown in the following figure: .°C m Finite Element Modeling Three tests: • • • Test 1 .” Test Case Data and Information Units SI Material Properties W λ = 40 ---. It provides the input data and results for benchmark test TPLA03/89 from “Guide de validation des progiciels de calcul de structures.10 linear axisymmetric quadrilateral solid elements Test 2 .Hollow Cylinder . This test is a steady–state heat transfer analysis of a 2D axisymmetric cylinder with convection.neu.2 linear axisymmetric quadrilateral solid elements Test 3 . Boundary Conditions Elemental Convection • Convection on internal surface (nodes 3.27 FEMAP Structural 10 linear quads.17 FEMAP Structural 2 parabolic quads. 17): W he = 142.0 -----.35 FEMAP Structural 2 linear quads.°C 2 m Ti = 20°C Solution Type Steady–State Heat Transfer Results Temperature and Element Total Heat Flux Ti (°C) Bench Value 272.°C 2 m Ti = 500°C • Convection on external surface (nodes 12.0 -----. 272. 15. 272. 272.35 . 14. 16): W hi = 150. 13 ---L m Reference • Societe Francaise des Mecaniciens.40 27824.82 ⋅ 2 ⋅ π ⋅ 0.10 204.51 31792.66 31746.300 = 64416.1990.15 27853.69 204. (Paris.  2 m ϕ -. . TPLA03/89.90 W ϕe  -----.= 34173.) Test No.05 34160.51 33637. Afnor Technique. Te (°C) W ϕi  ------  2 m 205. Guide de validation des progiciels de calcul de structures.8 So: ϕ W -.= ϕ2πR L 26508.7 26276.00 204. 33 ---. This test is a steady–state heat transfer analysis of a 2D axisymmetric rod with fixed temperatures and flux density.neu. It provides the input data and results for benchmark test TPLA05/89 from “Guide de validation des progiciels de calcul de structures.Flux Density The complete model and results for this test case are in file htpla05.°C m Finite Element Modeling • • 20 linear quadrilateral axisymmetric solid elements 42 nodes The mesh is shown in the following figure: .Cylindrical Rod .” Test Case Data and Information Units SI Material Properties W λ = 33. Boundary Conditions Nodal Temperatures • z = 0 (nodes 1 and 3): Set temperature to 0°C • z = 1 (nodes 2 and 4): Set temperature to 500°C Elemental Heat Flux • Cylindrical surface (elements 1-20): W Set flux ϕ to – 200 ------m2 The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer . 00 500.00% 0.01% 0.97 303.9 1. TPLA05/89.97 155.00 224.1 0.6 0.4 0.00% ~0.00% Results are post–processed on the internal surface.00 56.0 Bench Value 0.) Test No.97 99. .13% 0.05% 0.3 0.50% 0.00 24.98 395. Afnor Technique.7 0. Guide de validation des progiciels de calcul de structures.8 0.00 4.00 156.00 FEMAP Structural 0.00 396.00 Difference 0.50% 0. Reference • Societe Francaise des Mecaniciens. Results Temperature Results (degrees C): Node # Node 3 Node 41 Node 39 Node 37 Node 35 Node 33 Node 31 Node 29 Node 27 Node 25 Node 4 z (m) 0.03% 0.00 -4.00 -4.98 500.0 0. (Paris.97 223.2 0.02 3.00 100.00 304.1990.5 0.00% 0.02% ~0.97 55.98 23. neu.0 ---.°C m Finite Element Modeling • • 7 linear quadrilateral axisymmetric solid elements 16 nodes .” Test Case Data and Information Units SI Material Properties • Material 1: W λ 1 = 40.Convection The complete model and results for this test case are in file htpla08.0 ---. It provides the input data and results for benchmark test TPLA08/89 from “Guide de validation des progiciels de calcul de structures.Hollow Cylinder with Two Materials .°C m • Material 2: W λ 2 = 20. This test is a steady–state heat transfer analysis of a 2D axisymmetric cylinder with two materials and convection. The mesh is shown in the following figure. Boundary Conditions Elemental Convection • Convection on internal surface: W hi = 150.0 ------ °C 2 m Ti = 70°C • Convection on external surface: W hi = 200.0 ------ °C 2 m Ti = ( – 15° )C Solution Type Steady–State Heat Transfer Results Node # Node 9 Node 14 Node 16 Node 9 Temperature/ Element X Heat Flux Ti (°C) Tm (°C) Te (°C) W ϕi  ------   2 m Bench Value 25.42 17.69 12.11 6687.44 FEMAP Structural 25.42 17.69 12.11 6577.88 Difference 0.00% 0.00% 0.00% 1.64% Node 14 W ϕm  ------  2 m 5732.09 5733.33 0.02% Node 16 W ϕe  ------   2 m 5422.25 5496.59 1.37% ϕ -- = ϕ2πR L So: ϕ W -- = 5733.33 ⋅ 2 ⋅ π ⋅ 0.35 = 12608.25 ---L m Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLA08/89. Wall - Convection The complete model and results for this test case are in file htpl03.neu. This test is a steady–state heat transfer analysis of a 1D wall with fixed convection. It provides the input data and results for benchmark test TPLL03/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information Units SI Material Properties W λ = 1.0 ---- °C m Finite Element Modeling • • 1 linear quadrilateral plate element 4 nodes The plate element thickness is set to 1m. The mesh is shown in the following figure: Boundary Conditions Elemental Convection • Convection on internal surface: W hA = 20.0 ------ °C 2 m TA = – 20.0°C • Convection on external surface: W hB = 10.0 ------ °C 2 m TB = 500°C • Convection coefficient is defined as energy / (length*time*temperature) in the current system of units. The boundary conditions are shown in the following figure: A B Solution Type Steady–State Heat Transfer Results Temperature Results (Degrees Celsius): Node # Node 1 (Temp) Node 4 (Temp) Node 1 (Flux) Temperature Flux TA (°C) TB (°C) ϕ (W/m**2) 21.71 416.58 834.2 Bench Value FEMAP Structural 21.71 416.57 834.3 Difference 0.00% ∼0.00% 0.01% Reference • Societe Francaise des Mecaniciens, Guide de validation des progiciels de calcul de structures, (Paris, Afnor Technique,1990.) Test No. TPLL03/89. Wall - Fixed Temperatures The complete model and results for this test case are in file htpl01.neu. This test is a steady–state heat transfer analysis of a 1D wall with fixed temperatures. It provides the input data and results for benchmark test TPLL01/89 from “Guide de validation des progiciels de calcul de structures.” Test Case Data and Information The mesh is shown in the following figure: Units SI Material Properties W λ = 0.75 ---- °C m Finite Element Modeling • • 5 beam (line 2) elements 6 nodes 0 52.00 0.0 84.04 0.03 0.02 0.01 0.0 20.00% 0.0 52.0 68.00% .0 68. Boundary Conditions Nodal Temperatures • Internal temperature Ti = 100°C ( node 1 ) • External temperature Te = 20°C ( node 6 ) The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer Results Temperature Results (Degrees Celsius): Node # Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 0.00% 0.0 20.05 Length: x (m) Bench Value 100.0 84.00% 0.00% 0.0 Difference 0.00% 0.0 FEMAP Structural 100.0 36.0 36. (Paris. Afnor Technique.) Test No.1990. Guide de validation des progiciels de calcul de structures. The flux calculated with the software is exact: Ω ϕ = 1200 ----2 µ Reference • Societe Francaise des Mecaniciens. . TPLL01/89. It provides the input data and results for benchmark test TPLP01/89 from “Guide de validation des progiciels de calcul de structures. 12 parabolic quadrilateral plate elements The mesh is shown in the following figure: . 12 linear quadrilateral plate elements 53 nodes.L-Plate The complete model and results for this test case are in the following files: • • htpp01a.neu (linear quadrilateral) htpp01b.°C m Finite Element Modeling Two tests: • • 21 nodes.neu (parabolic quadrilateral) This test is a steady–state heat transfer analysis of a 2D L–plate with fixed temperatures.0 ---.” Test Case Data and Information Units SI Material Properties W λ = 1. 13 1.816 7.64 . 7.883 5.869 5.495 2.861 5.519 2.18 0.10 0.43 0. 7. Boundary Conditions Nodal Temperatures • AF side: Set temperature to 10°C • DE side: Set temperature to 0°C The boundary conditions are shown in the following figure: F E C D A B Solution Type Steady–State Heat Transfer Results Temperature Results (Degrees Celsius): FEMAP Bench Values Structural linear quads.845 FEMAP Structural parabolic quads.834 Node 8 9 10 % Difference 1.03 % Difference 0.502 2. 667 0.514 8.661 0.972 2.015 0.283 0.294 0.680 5.881 2.34 9.16 9.667 6.14 8.961 0. Guide de validation des progiciels de calcul de structures. TPLP01/89.00 2.505 0.990 0.316 9.519 0.669 0.640 8. 19 18 20 17 6 16 21 15 14 5 8.) Test No.20 8.53 Reference • Societe Francaise des Mecaniciens.108 1.11 8.666 0.667 0.10 8.19 5.25 2. (Paris.04 5.06 6.30 9.71 2.61 2.026 0.963 0.669 0. Afnor Technique.35 9.1990.24 8.14 8.877 0.018 8.009 8. .959 2.001 9.996 0.24 9.00 6.015 0. It provides the input data and results for benchmark test TPLV02/89 from “Guide de validation des progiciels de calcul de structures.Fixed Temperatures. This test is a steady–state heat transfer analysis of a 3D sphere with fixed temperatures and convection.Hollow Sphere . Convection The complete model and results for this test case are in file htpv02.°C m Finite Element Modeling • • 500 solid (brick and wedge) elements 666 nodes The test is executed on 1/8 of a mapped meshed sphere.0 ---. The mesh is shown in the following figure: .neu.” Test Case Data and Information Units SI Material Properties W λ = 1. °C 2 m Ti = 100°C(elements 401-500) Nodal Temperature • Set external surface temperature Te to 20°C(nodes 1-111) The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer . Boundary Conditions Elemental Convection • Convection on internal surface: W hi = 30 -----. 48% 0.47 817.33 0.00 54.35 566 455 344 233 122 11 Node # 65.18% 0.07% 0.47 771. .92 20.65 821. TPLV02/89.31 0.32 27.11% 0.21 797.90 871.74 45.00% Element X Heat Flux results (W/m**2): Radius r (m) 0.32 0.45% 3.3 0.1990. (Paris.31 0.32 0.94 20. Afnor Technique.24 36.35 922.84 45.32% Reference • Societe Francaise des Mecaniciens.) Test No.34 0. Results Temperature results (Degrees C): Radius r (m) 0.36 27.87 54.43% 0.31 36.15% 0.33 0.43% 0. Guide de validation des progiciels de calcul de structures.35 566 455 344 233 122 11 Node # Bench Value 1050.43 FEMAP Structural 1019.00 Bench Value FEMAP Structural 64.34 987.11 Difference 2.3 0.00 Difference 0.85 867.20% 0.92% 0.00 983.34 0.57 926. neu (linear brick) htpv04b.0 ---.neu (parabolic tetrahedron) htpv04c.0 ---.” Test Case Data and Information Units SI Material Properties • Material 1: W λ 1 = 40.°C m • Material 2: W λ 2 = 20. It provides the input data and results for benchmark test TPLV04/89 from “Guide de validation des progiciels de calcul de structures.°C m Finite Element Modeling Three tests: .Hollow Sphere with Two Materials Convection The complete model and results for this test case are in the following files: • • • htpv04a.neu (axisymmetric solid) This test is a steady–state heat transfer analysis of a 3D sphere with two materials and convection. .888 nodes. 700 solid (brick and wedge) elements • Test 2 . 4 axisymmetric solid parabolic quadrilateral elements The test is executed on 1/8 of a mapped meshed sphere. 2192 solid parabolic tetrahedron elements • Test 3 .3818 nodes.23 nodes. • Test 1 . 0 -----.0 -----.°C 2 m Te = ( – 9° )C The boundary conditions are shown in the following figure: Solution Type Steady–State Heat Transfer . Boundary Conditions Elemental Convection • Convection on internal surface: W hi = 150.°C 2 m Ti = 70°C • Convection on external surface: W he = 200. 06 17. Afnor Technique.84 N5 13. . Results Temperature Results (Degrees Celsius): FEMAP Structural linear brick (htpv04a) N1 25.18 FEMAP Structural parabolic tetrahedron (htpv04b) N19 25.01 N6 17.1990.15 FEMAP Structural axisymmetric solid (htpv04c) N2 25.03 N556 17.75 N5 13.06 N9 17.17 Temperature Bench Value 25.84 13.) Test No. Guide de validation des progiciels de calcul de structures. TPLV04/89. (Paris.84 N778 13.16 Ti (C°) Tm (C°) Te (C°) Reference • Societe Francaise des Mecaniciens. Thermo-mechanical Test .Linear Statics Analysis The stationary thermal-mechanical test cases for linear statics analysis from the Societe Francaise des Mecaniciens include: • "Thermal Gradient on a Thin Pipe" . It provides the input data and results for benchmark test HSLA01/89 from “Guide de validation des progiciels de calcul de structures. This test is a thermo–mechanical linear statics analysis of a thin pipe with thermal gradient and plane strain.” Test Case Data and Information Units SI Material Properties · 11 E = 1x 10 Pa ν = 0.Thermal Gradient on a Thin Pipe The complete model and results for this test case are in file hsla01.neu.3 10 Coefficient of expansion: α = 1x ---------C° –5 Finite Element Modeling • • 500 axisymmetric (linear quadrilateral solid) elements 561 nodes The mesh is shown in the following figure: . Nodal Temperature • Radial temperature ( 1 – ( r – Ri ) ) T = Ti ⋅ ------------------------------. Boundary Conditions Constraints • Constrain nodes 1-11 in the X and Z translations.with Ti=100°C ( Re – Ri ) The boundary conditions are shown in the following figure: Solution Type Statics . 85E6 -74.89E6 1. Results Point r = Ri σ r ( Pa ) Stress 0 Bench Value FEMAP Structural -0.65E6 68.20E6 -3.36% Post Processing Value Definition = the axisymmetric C1 radial stress at node 265 σr = the axisymmetric C4 Azimuth stress at node 265 σθ =the axisymmetric C1 radial stress at node 270 σr =the axisymmetric C1 Azimuth stress at node 270 σθ = the axisymmetric C1 radial stress at node 275 σr .53E6 Difference -74.40E6 -0.18% 1.78E6 σ θ ( Pa ) 0.22% r=(Re+Ri)/2 σ r ( Pa ) -3.52% 1.95E6 1.306E6 σ θ ( Pa ) r=Re σ r ( Pa ) 0 68.07E6 σ θ ( Pa ) 0. Value Definition = the axisymmetric C2 Azimuth stress at node 275 σθ Reference • Societe Francaise des Mecaniciens.) Test No. HSLA01/89. Afnor Technique. .1990. Guide de validation des progiciels de calcul de structures. (Paris. 171 B Bar elements 76. 42. 76. 323. 268. 288. 6. 95. 300. 274. 12. 156. 192. 18. 95. 347. 356 Hovgaard’s Problem 326 hsla01. 9.neu 331 htpla03. 353 Flux density 337 Free annular membrane 152 Free cylinder 165 G Gravity loading 232 H Heated beam 15 Hemisphere point loads 44 Hollow cylinder 331.neu 350 .neu 334 htpla05. 194. 307. 340 Hollow sphere 353. 192.neu 337 htpla08. 356 Curved beam elements 196 Curved pipe 196 Cylindrical rod 337 Cylindrical shell 39. 186. 206. 168.neu 340 htpp01a. 98. 12. 307 Cantilever mass 78 Cantilevered plate 105 Cantilevered solid beam 186 Cantilevered square membrane 144 Cantilevered tapered membrane 148 Cantilevered thin square plate 124.neu 344 htpla01. 307 Beam elements 294.neu 361 htpl01. 340 Axisymmetric vibration 165. 101. 83. 199.neu 347 htpl03. 196. 101. 323 Bending load 210 C Cantilever 92 Cantilever beam 4. 347 Bending 27. 140. 334. 326 Beam 4. 331. 337. 297. 78. 344. 182 Anti-symmetric modes 108 Articulated plane truss 203 Articulated rod truss 201 Articulated supports 192 Axial distributed load 6 Axial loading 291 Axisymmetric solid elements 165. 294. 255. 194. 288. 334. 353. 15. Index A Annular membrane 152 Annular plate 117. 92. 196. 171. 294. 101. 18 E Elastic foundation 206 Elliptic membrane 34 F Fixed temperatures 331. 9. 161 Circular hole 212 Circular plate 215 Circular ring 98 Clamped beams 194 Clamped thick rhombic plate 136 Clamped thin rhombic plate 121 Clamped-free thin shell 320 Compressor 320 Convection 334. 199. 291. 206. 303. 221 D Deep simply-supported beam 95 Deep simply-supported solid beam 174 Displacement 15 Distorted mesh 124 Distributed loads 9. 340. 174. 203. 68. 225.neu 356 htpv04c. 71.neu 117 nf001ac. 203. 6.neu 76 mstvn007.neu 34 le1101a. 9.neu 30 mstvn002. 49.neu 34 le103. 192.neu 44 le302. 232.neu 86 .neu 58 le1102b. 247. 242. 12. 78. htpp01b.neu 39. 212. 218.neu 21 mstv1014.neu 356 htpv04b. 229. 98 Internal pressure 221.neu 47 le601.neu 58 le1101b. 24. 221.neu 53 le1003.neu 15 mstv1008. 268 K Kirchhoff formulation 251 L le1001.neu 24 mstv1015. 42.neu 356 Hydrostatic pressure 229 I Infinite plate 212 In-plane vibrations 83.neu 58 le1105b. 261.neu 353 htpv04a. 42 le202b. 39.neu 58 le1103b.neu 58 le1106b.neu 12 mstv1007.neu 27 mstv1016.neu 44 le303.neu 44 le304.neu 58 le1106a. 18 Linear Statics 4.neu 53 le101.neu 34 le102. 42 le201b. 53. 18.neu 58 le201a. 194.neu 49 le602. 58.neu 4 mstv1002. 307 Membrane 21 Membrane loads 21 Mindlin formulation 251 Moment load 12 mstv1001.neu 39.neu 18 mstv1009.neu 350 htpv02. 21. 201.neu 58 le1102a.neu 39.neu 49 Linear beam 6. 239. 199. 251. 361 L-Plate 350 Lumped mass 285.neu 58 le1104b. 236.neu 58 le1103a. 30. 268. 307 M Mass elements 65. 285.neu 44 le501. 42 le301. 34.neu 39.neu 58 le1105a. 27. 15. 196.neu 78 N Natural frequency 78 ne014ll. 261.neu 83 nf002ac. 210.neu 6 mstv1003. 274.neu 9 mstv1004.neu 58 le1104a.neu 47 le502.neu 65 mstvn003. 42 le202a. 44.neu 68 mstvn004. 215.neu 73 mstvn006.neu 53 le1002.neu 71 mstvn005. neu 129 nf021apl.neu 121 nf015ll.neu 114 nf013pl.neu 168 nf043lc.neu 111 nf012pl.neu 182 .neu 182 nf053ll.neu 171 nf043pc.neu 133 nf021bpl.neu 108 nf011bpl.neu 152 nf033pc.neu 174 nf052lc.neu 171 nf043pl.neu 174 nf051pl.neu 105 nf011all.neu 121 nf015pl.neu 165 nf041ll.neu 89 nf004a.neu 144 nf031llc.neu 111 nf013lc.neu 105 nf011blc.neu 165 nf041pc.neu 144 nf031pl.neu 144 nf031pc.neu 174 nf051pc.neu 165 nf042lc.neu 108 nf0121c.neu 168 nf042pc.neu 178 nf053lc.neu 168 nf042ll.neu 168 nf042pl.neu 133 nf0221c.neu 108 nf011bll.neu 117 nf014pc.neu 105 nf011apc.neu 174 nf051ll.neu 165 nf041pl.neu 129 nf021all.neu 114 nf013pc.neu 133 nf021bll.neu 144 nf032lc.neu 152 nf033ll.neu 136 nf023lc.neu 171 nf043ll.neu 182 nf053pc.neu 148 nf032pc.neu 148 nf032ll.neu 148 nf033lc.neu 178 nf052pl.neu 152 nf033pl.neu 117 nf014pl.neu 140 nf031ll.neu 114 nf013ll.neu 114 nf014lc.neu 121 nf021alc.neu 136 nf022pc.neu 136 nf022pl.neu 105 nf011apl.neu 140 nf023pc.neu 111 nf012ll.neu 178 nf052ll.neu 98 nf011alc.neu 178 nf052pc. nf003ac.neu 129 nf021blc.neu 136 nf022ll.neu 133 nf021bpc.neu 152 nf041lc.neu 148 nf032pl.neu 108 nf011bpc.neu 171 nf051lc.neu 129 nf021apc.neu 95 nf006ac.neu 117 nf015lc.neu 111 nf012pc.neu 140 nf023pl.neu 92 nf005ac.neu 140 nf023ll.neu 121 nf015pc. 152. 114. 344.neu 317 sdls05a. 92. 124. 221. 140. 95. 218.neu 182 nf071a. 133. 117.neu 186 nf072bc.neu 101 nf071c. 105.neu 294 sdll11. 105.neu 156 nf074c. 129. 133.neu 156 nf073cc. 121. 255 R Rectangular plates 328 Rhombic plate 121.neu 156 nf073dc. 156. 152. 83. 279. 285. 274 Pure tension 24. 136 Rhomboid plate 247 Rigid elements 65. 225.neu 311 sdls01b. 268 Prismatic rod 274 Pure bending 27. 136.neu 288 sdll01b. 210 Plane strain elements 34 Plane truss 203 Plate elements 34.neu 285 sdll014a.neu 186 nf072bl. nf053pl. 71. 328. 178. 328 O Off-center point masses 92 Out-of-plane vibration 98 P Patch test 39. 326. 194 Rod elements 201 S sdld02. 68. 291.neu 156 nf073cl. 42 Pinched cylindrical shell 236 Pin-ended cross 83 Pipes 326 Plane bending 199.neu 161 nf074l.neu 307 sdls01a. 350 plate elements 144 Pressure 53.neu 101 nf072ac. 323.neu 320 sdls05b. 294.neu 326 sdlx03. 221.neu 291 sdll09a. 121.neu 307 sdll15b. 297. 49.neu 328 Shear loading 251 . 161.neu 186 nf072al. 136.neu 311 sdls03. 314.neu 101 nf071b. 114.neu 323 sdlx02.neu 288 sdll05a. 174. 182.neu 156 nf073bc. 42. 317. 215. 242. 201 Normal Modes/Eigenvalue 65. 39. 161. 317. 320.neu 303 sdll014b.neu 300 sdll15a. 101. 239. 168. 210.neu 291 sdll05b. 140. 148. 156. 311. 236. 232.neu 161 Nodal loads 4.neu 297 sdll12. 78. 307.neu 320 sdlx01. 108.neu 314 sdls04. 144. 229. 171.neu 156 nf073dl. 300. 303. 124. 165. 108.neu 156 nf073al. 247. 314. 212.neu 303 sdll014c.neu 156 nf073bl. 44. 186.neu 186 nf073ac. 98. 229. 251. 117.neu 303 sdll01a. 148. 320. 76. 129. 311. 274.neu 242 ssls25a.neu 255 sslv03a.neu 236 ssls21a.neu 242 ssls24c.neu 279 .neu 239 ssls21b.neu 279 sslv09a100.neu 210 sslp02.neu 268 sslv04c.neu 203 ssll14b.neu 261 sslv03d.neu 221 ssls07a. 314 Simply-supported rhomboid plate 247 Simply-supported solid annular plate 182 Simply-supported solid square plate 178 Simply-supported thick annular plate 140 Simply-supported thick square plate 133 Simply-supported thin square plate 114 Single DOF 65 Skew plate normal pressure 49 Solid cylinder 58.neu 239 ssls21c.neu 215 ssls03b. 361 Solid sphere 58 Solid square plate 178 Solid taper 58 Spherical shell 239 Spring elements 65.neu 239 ssls24a. 285 Square tube 218 ssll02.neu 196 ssll08.neu 274 sslv08b.neu 279 sslv09a20.neu 203 ssll16.neu 261 sslv03b.neu 201 ssll14a. 255.neu 218 ssls06a.neu 236 ssls20b.neu 229 ssls09.neu 247 ssls27a.neu 212 ssls03a. 268. 288 Simply-supported annular plate 117. 186.neu 279 sslv09a75.neu 225 ssls08. 206.neu 192 ssll05.neu 251 ssls27c. 171 Simply-supported rectangular plate 242.neu 261 sslv04a. 68.neu 199 ssll11. 182.neu 221 ssls06b. 356. 178.neu 268 sslv04b. 58.neu 251 sslv01a. 255 Solid elements 53. 174.neu 274 sslv08d. 71.neu 274 sslv08c.neu 247 ssls25b.neu 255 sslv01b.neu 268 sslv04d.neu 242 ssls24b.neu 255 sslv01c.neu 225 ssls07b.neu 206 sslp01. 353.neu 232 ssls20a. 279.neu 274 sslv09a10.neu 279 sslv09b10.neu 251 ssls27b.neu 268 sslv08a. Short beam 192.neu 261 sslv03c.neu 255 sslv01d.neu 194 ssll07a.neu 279 sslv09a50.neu 196 ssll07b.neu 215 ssls05. 347 . 68. 347. 83.neu 279 Steady-State Heat Transfer 331.neu 279 sslv09b50. 156. 68 Undamped free vibrations 76 Uniform axial load 225 Uniform radial vibration 168 Uniformly distributed load 215. 108 Thin square plate 124. 340. 353 Tension 24 Thermal gradient 361 Thermal strain 15 Thick annular plate 140 Thick hollow sphere 168 Thick plate 279 Thick plate pressure 53 Thick square plate 129. 225. 161.neu 279 sslv09b20. 98. 347. 247 V Vibrations 65. 356 Strain energy 30 Stress 15 Symmetric modes 105 Symmetric truss 323 T Tapered beam elements 294 Tapered membrane 148 Temperatures 58. 229. 353. 331. 232 Three DOF 71 Torque loading 218 Torsional system 71 Transverse bending 196 Truss 30 Two DOF 68 U Undamped free vibration 65. 344. 168. 165. sslv09b100.neu 279 sslv09b75. 350. 133 Thick-walled infinite cylinder 268 Thick-walled spherical container 261 Thin arc 199 Thin circular ring 297. 300 Thin pipe 361 Thin pipe elbow 303 Thin ring plate 317 Thin shell 320 Thin shell beam wall 27 Thin square cantilevered plate 105. 242. 334. 311 Thin wall cylinder 24. 76. 171. 337. 303 W Wall 344.

Femap Structural - Verification Guide

Comments

Description