June 9, 2018 | Author: Marko Šimić | Category: Matrix (Mathematics), Eigenvalues And Eigenvectors, Normal Mode, Buckling, Parallel Computing



DYNADynamic Analysis SOFiSTiK 2016 DYNA Dynamic Analysis DYNA Manual, Version 2016-0 Software Version SOFiSTiK 2016 c 2015 by SOFiSTiK AG, Oberschleissheim, Germany. Copyright SOFiSTiK AG HQ Oberschleissheim Bruckmannring 38 85764 Oberschleissheim Germany Office Nuremberg Burgschmietstr. 40 90419 Nuremberg Germany T +49 (0)89 315878-0 F +49 (0)89 315878-23 T +49 (0)911 39901-0 F +49(0)911 397904 [email protected] www.sofistik.de This manual is protected by copyright laws. No part of it may be translated, copied or reproduced, in any form or by any means, without written permission from SOFiSTiK AG. SOFiSTiK reserves the right to modify or to release new editions of this manual. The manual and the program have been thoroughly checked for errors. However, SOFiSTiK does not claim that either one is completely error free. Errors and omissions are corrected as soon as they are detected. The user of the program is solely responsible for the applications. We strongly encourage the user to test the correctness of all calculations at least by random sampling. Front Cover Project: MILANEO, Stuttgart, Germany | Client: Bayerische Hausbau and ECE | Architect: RKW Rhode Kellermann Wawrowsky | Structural Engineering for Bayerische Hausbau: Boll und Partner | Photo: Dirk Münzner Contents | DYNA Contents Contents i 1 Task Description 1-1 2 Theoretical Principles 2.1 Integration of the Equations of Motion . . . . . . . . . . . . . 2.2 Computation of the Eigenvalues and the Modal Damping 2.3 Modal Analysis for Time-dependent Loading . . . . . . . . . 2.4 Modal Excitation through Ground Acceleration . . . . . . . 2.5 Modal Analysis of a Steady-state Excitation . . . . . . . . . 2.6 Excitation through a Spectrum . . . . . . . . . . . . . . . . . . 2.7 Sign of corresponding forces . . . . . . . . . . . . . . . . . . . 2.8 Kinematic Constraints . . . . . . . . . . . . . . . . . . . . . . . . 2.9 Elastic Stiffnesses . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Geometric Stiffness and P-delta . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1 2-1 2-3 2-4 2-4 2-6 2-8 2-9 2-10 2-11 2-11 Literature 2-13 3 3-1 3-1 3-1 3-3 3-5 3-9 3-12 3-14 3-16 3-17 3-20 3-21 3-23 3-26 3-30 3-32 3-34 3-36 Input Description 3.1 Input Language . . . . . . . . . . . . . . . . . . . . . 3.2 Input Records . . . . . . . . . . . . . . . . . . . . . . 3.3 SYST – System Parameters . . . . . . . . . . . . . 3.4 CTRL – Calculation Parameters . . . . . . . . . . 3.4.1 SOLV Equation solver . . . . . . . . . . . 3.4.2 CORE Parallel computation control . . 3.5 GRP – Selection of Element Groups . . . . . . . 3.6 MAT – General Material Properties . . . . . . . . 3.7 BMAT – Elastic Support / Interface . . . . . . . . 3.8 SMAT – SBFEM - Material Properties . . . . . . 3.9 MASS – Lumped Masses . . . . . . . . . . . . . . 3.10 EIGE – Eigenvalues and Eigenvectors . . . . . . 3.11 MODD – Modal Damping . . . . . . . . . . . . . . . 3.12 STEP – Parameter of the Step-wise Integration 3.13 LC – Load Case . . . . . . . . . . . . . . . . . . . . . 3.14 CONT – Contact and Moving Load Function . . 3.15 HIST – Results within Time . . . . . . . . . . . . . SOFiSTiK 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . .7 Displacements . .1 Nodes . . . . . . . . Output Description 4. .2 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Internal Forces and Moments . ECHO – Extent of Output . . . . . . . . . . . . . . . . . . . . . . . . . . .5 Natural Frequencies . . . . . . . . . 4. . . . . 4. .17 4 ii EXTR – Evaluation of Max. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. . . .4 Elements . . . . . . . . . . . . . 4. . . . . . . . . . . . . . . . . . . . . . . . . . 3-39 3-45 4-1 4-1 4-1 4-1 4-2 4-2 4-2 4-3 4-3 4-3 SOFiSTiK 2016 . . . . . . . . . . . . . .DYNA | Contents 3. . 4.3 General Parameters . . .9 Time Variations . . . . . Functions and Loads 4. . . . . . . . . . . . . .6 Load Cases. . . . . . . . 4. . . . . . . . . . . 4. . . . . . . . . . . . . . . . .16 3. . . . . . . . . . .8 Internal Forces and Moments . . . . . . . . . . . . . . . . . SOFiSTiK 2016 1-1 . warping torsion and bedding profiles (piles) • Truss. • Static analysis of load cases after second-order theory • Computation of the natural frequencies of three-dimensional structures. • Computation of the buckling eigenvalues of three-dimensional structures.g. Only the truss. by the program SOFiMSHA. as well as planar and axisymmetric structures. boundary and FLEX elements • Infinite half space elements (SBFEM) • Damping elements • Shell elements • 3D-solid elements For the explicit integration not all features are supported. • Steady-state oscillations and excitation through spectra. cable.Task Description | DYNA 1 Task Description The program DYNA can be used for static and primarily for dynamic analysis of three-dimensional structures. The following elements can be processed by DYNA: • Point masses (with off diagonal components) • Three-dimensional prismatic bending beams with haunches. It can perform the following tasks (Special licenses may be needed): • Static analysis of load cases acting upon three-dimensional structures. • Implicit direct integration of the equations of motion for structures with arbitrary damping • Explicit direct integration of the nonlinear equations of motion • Interaction with load trains and wind loading • Soil structure interaction with the SBFEM • Integration of the equations of motion by superposition of the mode shapes. SOFiMSHC or SOFiPLUS.and cable elements • Spring elements. The static system is stored in the database after its generation e. Soil) are not available. All interactions (Wind. Loadtrain. The results of the dynamic analysis including the mode shapes are stored in the database as displacements and stresses with a load case number. For speed reasons almost all algorithms follow what is called IN-CORE solutions. For the purposes of a dynamic analysis.DYNA | Task Description spring and the 3D volume (BRIC) element are available. the program may output the maximal and the minimal of all displacements. and eventually the time variation of selected degrees of freedom or internal forces and moments. 1-2 SOFiSTiK 2016 . But geometric and material nonlinearity are supported. The mode shapes can also be transferred from the database after a calculation with the program ASE. The size of the problem is therefore limited by the amount of available main memory. Modal solutions transferring the eigenvalues from ASE are not subjected to this limitations. velocities or accelerations as well as internal forces and moments. velocity and acceleration vectors. 2. The violation of the discrete maximum principle may lead in case of very small time steps to oscillations of the solutions. but can not be applied to rotational masses and kinematic constraints with rotational degrees of freedom. The material properties are converted to mass. all matrices have the same structure. to diagonalise the mass and the damping matrix.1) where u displacement m mass c viscous damping k stiffness p(t) external loading The method of finite elements replaces the continuous vector fields by discrete displacement. but produce in general more accurate results. however.2) In general. This is permitted in most cases without large errors. The first step is to subdivide the time in discrete time steps. For these reasons the program provides an input entry for the type of matrix assembly in the CTRL MCON record. The consistent mass matrices imposes a larger numerical effort and bigger memory requirements. The times steps in such case must not be smaller that the time needed by the wave to propagate through a single element.1 Integration of the Equations of Motion For the most general approach the direct integration of the differential equations a second discretisation in time has to be applied. damping and stiffness matrices: mj · ¨j + cj · ˙j + kj · j = p (t) (2.Theoretical Principles | DYNA 2 Theoretical Principles The general dynamic problem is given by the differential equation: ¨+c· ˙ + k ·  = p (t) m· (2. It is common. However there is another disadvantage. Then the simplest form is to assume a constant SOFiSTiK 2016 2-1 . 25(0.5) Then we have the choice between five different possibilities to select how or for which time t + θ · Δt the equilibrium equation is fulfilled. The method is well suited to be parallelized.0. β ≥ 0. β = (1 − α)2 / 4) This method has been developed to introduce a numerical damping without 2-2 SOFiSTiK 2016 . δ ≥ 0. • Newmark-Method (θ = 1.3) According to the Newmark method the following expressions hold for the velocity and the displacement at the end of the time interval νt : ˙ (t + Δt) = (t) ˙ ¨ ¨ (t + Δt)]  + Δt · [(1 − δ) · (t) +δ· (2.50. • Wilson-Theta-Method (θ ≥ 1. but it is only stable if the time step is below a certain critical value which is approximately equal to the wave speed divided my the minimum mesh size. However a more enhanced precision is obtained using a linear approximation for the acceleration .4) ˙ ¨ ¨ (t + Δt)]  (t + Δt) = (t) + Δt · (t) + Δt 2 · [(1/ 2 − β) · (t) +β· (2. Figure 2. • α -Method Hilber-Hughes-Taylor (θ < 1. δ = (1 − 2α)/ 2. Thus small errors may enlarge especially for the accelerations. In the literature the parameter β is given as α but this has been changed to avoid conflicts with the next method. In the literature parameter δ is often given as γ.1: Integration in Time • Explicit Integration (θ = 0. ¨ ¨ 0) + (t) = (t t − t0 Δt ¨ 0 + Δt) − (t ¨ 0 )] · [ (t (2.DYNA | Theoretical Principles acceleration during each time step.0) As the variation of the acceleration along the time step is constant it is possible to calculate all values highly efficient explicitly by the mass matrix. but keeps the amplitudes to a higher accuracy.5 + δ)2 ) The default of the parameters has no numerical damping at all.37) This value is a modification of the Newmark method where the numerical damping enlarges the period to a greater extent. In those cases the value of δ should be enlarged.0. 2.Theoretical Principles | DYNA degrading the order of accuracy. damping must be diagonal itself or proportional to the mass and/or the stiffness matrix: c=·m+b·k (2. the calculation of which is relatively extensive.6a) . Thus we have a formal equivalent to the Crank-Nicholson method (see program HYDRA) • Modal Analysis The system of equations to be solved can be significantly simplified if the solution is calculated in the subspace of a few eigenvectors.  6= j (2. This requires knowledge of the eigenvalues and the eigenvectors. This results in significant simplification of the equations of motion (decoupling). The value α is taken from the input value θ as α = (θ − 1.  6= j (2. The algorithms find the lowest eigenvalues of the structure along with the corresponding mode shapes V . The fact that the contributions of the higher eigenvalues can usually be neglected leads to a reduction of the vector space dimension.6b) By use of these conditions both the mass and the stiffness matrix in the eigenvalue space become pure diagonal matrices. The implicit methods lead to a system of equations for the displacements or accelerations at t + Δt . The computation of the real eigenvalues is done either by a simultaneous inverse vector iteration or by the Lanczos method. the modal damping (d) and the SOFiSTiK 2016 2-3 .2 Computation of the Eigenvalues and the Modal Damping The description of a problem by means of its eigenvalues is a transformation in another vector space. But then it is possible to integrate the linear equations exactly.7) A decoupled system can be solved in such case yielding the natural frequencies ω as well as the generalised masses (M). Compared to the explicit methods. The following orthogonality conditions are always satisfied: V T · m · V j = 0 V T · k · Vj = 0 .0). the time step may be chosen considerably larger. In order for the damping matrix to become diagonal too. Specific errors (oscillations) may be introduced however by a time step chosen to small with a consistent mass matrix. Nonlinear effects may be treated in a simplified way if the modes contain the nonlinear displacement possibilities. It is especially suited for non linear problems. the resulting modal damping d (Lehr’s damping factor) is also a diagonal matrix: dn = 1 2  ·  ωn  + b · ωn = δn (2. The solution at each time moment results from superposition of the computed mode shapes. In that case there are three possibilities: • Modal Analysis with complex Eigenvalues (rather large effort) • Direct integration of the modal equations • Energetic equivalent modal damping or diagonalisation. 2. load vectors will be created which applied as a static load case would yield the same response of the structure. this is used in DYNA.7) is used. The proportionality of the damping is then no longer given and the damping matrix Cn does not become a diagonal matrix.8c) (2.3 Modal Analysis for Time-dependent Loading As long as the conditions (2.DYNA | Theoretical Principles generalised loads (P): Mn = V Tn · m · V n Kn = Cn = Pn = V Tn V Tn V Tn (2. Thus its use is for special non-linear cases or for verification purpose only. This procedure.8b) (2. the equation of motion can be solved decoupled and integrated exactly. whereas the accelerations are given as absolute values in the original system.8d) · c · V n = 2 · d · ω · Mn · p(t) The mode shapes are scaled in such a way that Mn become equal to 1. 2-4 SOFiSTiK 2016 . 2. described in many design codes is not required within a software intended for dynamic analysis.9) 2π In a complex system the individual elements may have quite different damping properties.8a) · k · V n = ω · Mn 2 (2.6)-(2. The displacements and velocities are computed in the reference system.7) are fulfilled.0.4 Modal Excitation through Ground Acceleration A ground acceleration is analysed with a reference system accelerated along. When (2. as all other dependant results for a eigenform are directly evaluated and stored. When calculating an eigenform. 3 2-5 .Theoretical Principles | DYNA One obtains by this procedure the load vector: ¨ (t) p(t) = −m · r ·  (2.00 4.00 1.2: eigenforms we obtain for a horizontal acceleration the modal loads with different signs and the largest contribution from the third Eigenform: Mode 1 2 3 R*V-Factor -2.00 6.00 6.00 5.11) 0.00 1. Excitations at particular base points can be defined by this vector as well. ¨ (t) P = V Tm · p(t) = Lm ·  (2.g.00 7.00 3.10) one can obtain the modal loads. influence line of the reaction force).278E+00 9.8d) to the load vector (2.10) The vector r defines the displacements of the individual nodes.00 2.00 3. The vector can be defined through the input of its individual components or it can be read from the database (e.00 1.00 0. If we consider for example the first three modes of a column with an intermediate support: −1.00 6.00 0. when the base point is subjected to a unit displacement.00 2.00 3.00 1.00 4.00 It is very important to keep in mind.226E-01 2.00 m 1.747E+00 SOFiSTiK 2016 [o/o] 30.0 44.00 2.00 −1. Applying equation (2.00 m 7.00 5.00 7. which can also be represented as the product of the acceleration with the so-called participation factors L.00 1.4 5. that those modal loads describe the participation of the eigenforms and thus may have quite different values.00 m Figure 2.00 5.00 4.00 2. 13) The contribution of each mode shape is then given by ƒ (t) = 2-6  T · p0 ω2 ·r sn (Ω · t − ϕ) 2 1 − r 2 + 4 (d · r)2 (2. If the user wants to see those load vectors in detail he may use SOFiLOAD and the command ACCE NODE LINF i where i is the load case number of the corresponding eigenform and an acceleration has to be defined from the value ω2 times the modal response (Y ) taken from the DYNA results printout.401E+01 82. those bulk values are not available for the user.DYNA | Theoretical Principles 4 6. (2. However the resultant forces of those.12) The given formula respective the load vector is a very nice picture if we have only one principal mode. Even the maximum obtained acceleration is not a suitable measure for an unfavourable action on any member. we encounter a severe problem. 2. The number of eigenvectors used in practical analyses should be such that at least 90 percent of the total mass is taken into account. As DYNA calculates the forces and moments of the Eigenforms in a much more efficient and mathematical correct way.5 Modal Analysis of a Steady-state Excitation The steady-state excitation is given by a harmonic excitation: p (t) = p0 · sn (Ω · t − ) (2. Many design codes use equivalent loads to calculate the forces and moments for every mode. Beside the inefficient evaluation of all those data there is no such thing like an unfavourable load in a single node.0 5 -6.14) SOFiSTiK 2016 . the base shear is evaluated and superposed like all other results according to the definitions of CTRL STYP.5 ------------------------Qu.505E-01 2. = Mϕ · L M · S. They are given by the relation: HE.2 The sum of the squares of the participation factors represents the mass of the system in the activated direction. However if we have multiple modes and multiple directions.345E-08 0.Sum 1. Theoretical Principles | DYNA where r= Ω ω . All frequencies used in DYNA are always there for those of the undamped oscillation. DYNA can selectively omit this component or add it if it’s unfavourable. ϕ =  + rctn  2·d·r  1 − r2 (2. introduced through the starting conditions and gradually reduced due to damping. The oscillation contains an additional r-multiple component.15) These classical response functions have a region below the resonance frequency where the structure follows the loading with a dynamic enlarging factor and a region above the resonance where it is no longer possible for the structure to follow the loading.3: Response These response functions yield the true response including the shift of the resonance peak due to damping effects. yielding in a steady decay of the counter phase response until zero for high frequencies. An accurate calculation of the maximum stressing taking into consideration the phase shift can be carried out only for the final transient oscillation state by neglecting the transient components. Figure 2. In all other cases only a statistical super- SOFiSTiK 2016 2-7 . The superposition of these oscillations results in a floating effect. which can be accurately registered by time integration. 6 Excitation through a Spectrum In this case the factors f(t) with unknown phase shift are defined by their maximum value only. It should be especially noted that the method without modal dampings will yield different values to SRSS only for multiple eigenvalues.16) (2. but the CQC method is no guarantee for correct results either. and they are usually prescribed in tables as functions of natural frequency and damping. The CQC (Complete Quadratic Combination) method by Wilson.18) The maximum displacements and stresses must be superimposed according to probability theory.20) For the case of shear within a quadratic section it can be easily shown. 2.19) (2. or the Sum of the Absolute Values or the Square Root of the Sum of Squares (SRSS) can be used for this purpose.0. For an earthquake analysis the response spectra define the acceleration dependant of the Perios and Damping or the behaviour factor. The SRSS method is known to be rather faulty in case of multiple eigenvalues. 2-8 SOFiSTiK 2016 . The acceleration in X-direction exits the two diagonal Eigenforms with the same amount of 25 % of the total shear. q= ƒ ·S v u t 1+ = π2 ∗ ƒ ·S 2δ σ2 1 · X + 2 · X 2 + 3 · X 3 (1 + b · X c )d ƒ ƒ ·L ƒ ·z X= = or ƒm V V σ2 (2. as this is on the safe side and is appropriate if the coherence effects are introduced by the loading itself. While the dynamic response is obtained from a normalized power spectrum. q= rX X q · ρj · qj Æ  3 8 d dj d + r · dj · r 2 ρj = € Š 2  1 − r 2 + 4d dj r 1 + r 2 + 4 d2 + dj2 r 2 (2. which error is introduced by the SRSS Method.DYNA | Theoretical Principles position as in the case of spectrum excitation can be carried out. the background contribution is always assumed to be 1. In order to compute the response frequency and damping are interpolated from the spectra.17) (2. For the wind the response is obtained by a background and a resonance response. 7 Sign of corresponding forces For every type of superposition yielding only positive values. the sign of the corresponding forces and moments should not be neglected. the internal forces and moments vary depending on the sign of the horizontal force. this is not true and uneconomical in most cases. The same method may be also used for the directional superposition for the most unfavourable direction. 2.Theoretical Principles | DYNA Eigenfor m 2 a = Eigenfor m 1 + Eigenfor m 1 Eigenfor m 2 Figure 2. Although it is quite common to use positive values for all results. yet in every case it has to be observed that the sign of the moment and normal force in one of the column are identical. Figure 2.4: Shear within a quadratic section The SRSS-Method yields 35 % for all 4 walls. while different in the other one.5: Plane framework SOFiSTiK 2016 2-9 . while the method used in other programs with independent extreme values may yield results considerably to large. while the CQC Method will give 50 % for the x-walls and zero for the y-walls which is the correct value. For example if we look at a plane horizontally loaded framework. The correct sign of the corresponding forces will yield correct results. Three load cases with accelerations in orthogonal directions may be analyzed together in a single DYNA run and combined with the SRSS method. then we should thus always add the mode shapes only completely with a global factor. If we now assemble the maximum moment of different mode shapes. Exactly this is available from the mode shapes. then it is sufficient that all mode shapes are either added or subtracted according to the sign of the leading force. then the associated normal forces must have different signs. When we intend to add the absolute values.DYNA | Theoretical Principles If we extremize for the maximum moment. So we are replacing the rule of combination SUMj = X. . . sj . s < 0 j  The same can be used for the method SRSS (Square Root of Sum of Squares) the rule: v uX sj 2 SUMj = t (2. which necessitate the use of a consistent. s ≥ 0 j (2.21)  by the general form for the vector of internal forces and for the maximum value of force j: SUM = X ƒ · S . ƒ =   +1. DYNA takes this effect into account automatically for standard kinematic constraints. however. These require a certain expertise. mass matrix.e. results in off diagonal mass matrix components. These do not need not only more memory place. 2. but 2-10 SOFiSTiK 2016 . (2. because the selection of the reference nodes is critical.23)  is replaced through SUM = X  ƒ · S . The same holds for kinematic constraints too. In any case the leading force value will be positive thence it must be introduced as an alternating load in the final design superposition. While a force at a distance a generates a moment P · . the inertia of an eccentric mass is given by m · 2 . sj ƒ  = qP 2  sj (2.22)  −1. not diagonalised. This. i.24) Last but not the same can be done for the CQC-method.8 Kinematic Constraints Frequent use of condensations is made in dynamic analysis. which then requires special care in the description of the constraints.10 Geometric Stiffness and P-delta For beam and truss elements a load case can be read. When modelling rigid floor disks one should place the reference node as close as possible to the gravity or the shear centre in order to get the most realistic results. which can be used for the determination of the geometric stiffnesses. The spring and boundary elements are in the classical form given and do not distinguish from those ones in programs ASE or STAR2. That is considered at: – variable stiffnesses and location of centre of gravity – variable locations of shear centre – shear deformations over correction terms – optional warping force torsion – elastic bedding for pile elements – all beam loads from database The element always produces however only internal forces and moments for internal sections if requested bei CTRL BEAM 1. 2. The memory capacity can thus be quickly exceeded in cases of large systems or strongly recursive kinematic constraints. the user therefore can switch to the use of a diagonalised mass matrix. The second order theory effects are exact in those cases where the axial force does not change due to SOFiSTiK 2016 2-11 . But as these matrices are not always acceptable. Deformations along the beam element will never be calculated. The QUAD shell element corresponds to the simple accretion without nonconforming parts. The beam element is a real finite element with a displacement accretion with Hermitical function of second redundancy (therefore cubical polynomials).9 Elastic Stiffnesses DYNA employs very compact formulations of the element stiffnesses. (Hughes and/or Bathe-Dvorkin) 2. Kinematic constraints increase the band width considerably.Theoretical Principles | DYNA can lead also to oscillation of solution through violation of the discrete maximum principle at small time steps that perform disturbingly. One part is included in the general stiffness (this is the value defined with the element itself) and the difference from the actual primary estate to that general value is then used to form the geometric stiffness for the buckling analysis. the primary estate will be taken as general prestress. So it is generally foreseen for cables to split the prestress in two parts. while those of members under compression will decrease until they reach the value of zero for the buckling load. as this might generate negative eigenvalues in a buckling analysis.DYNA | Theoretical Principles geometric nonlinear effects. 2-12 SOFiSTiK 2016 . For cable elements the complete separation of geometric stiffness is not always a good approach. On the other side a buckling factor is defined as the factor of the loading. The eigenfrequency of member with tension will thereby increase. If that general value is not defined and option CTRL PLC does not select otherwise. Thus this approach includes not only but exceeds the so called P-delta effects. SOFiSTiK 2016 2-13 . Betonkalender. Ldl: a consise sparse cholesky factorization package. Baudynamik.edu/research/sparse/ldl. [2] F. Davis. 1978.ufl.cise. Müller.P. Teil II. 2003-2012. http://www.Literature | DYNA Literature [1] Timothy A. DYNA | Literature 2-14 SOFiSTiK 2016 . The default unit for each category is defined by the currently active (design code specific) unit set. The specified unit in square brackets corresponds to the default for unit set 5 (Eurocodes. Implicit units are categorised semantically and denoted by a corresponding identity number (shown in green). This input default can be overridden as described above. [mm] 1011 Implicit unit.5[m] ). NORM UNIT 5). Input is always required in the specified unit. 2. for example. geodetic elevation. Input defaults to the specified unit.2 Input Records The following record names are defined: Record Items SYST TYPE NCS PROB CTRL OPT VAL VAL2 GRP NO VAL MODD MAT BMAT SMAT PHYS CS PLC STAT CS FACS HING RADA RADB FACP FACM WIND LMAX NCSP NO E MUE G K GAM GAMA ALFA EY MXY OAL OAF SPM TITL NO C CT CRAC YIEL MUE COH DIL GAMB REF MREF H NO LC EX EY EZ RHOX RHOY Table continued on next page. an explicit assignment of a related unit is possible (eg. SOFiSTiK 2016 3-1 . 3. section length and thickness.1 Input Language The input is made in the CADINP language (see general manual SOFiSTiK: ’Basics’). Valid categories referring to the unit ŠlengthŠ are. [mm] Explicit unit.Input Description | DYNA 3 Input Description 3. Alternatively. Three categories of units are distinguished: mm Fixed unit. END and PAGE are described in the general manual SOFiSTiK: ’Basics’.DYNA | Input Description Record MASS EIGE Items RHOZ ALF BET NO MX MY MZ MXY MXZ MYZ MB NEIG TYPE NITE MITE MXX MYY MZZ LMIN STOR LC DEL LCUP MODD NO D A B STEP N DT INT A B BET THE EIGB EIGT EIGS DTF STHE LC NO FACT DLX DLY DLZ MODB TITL CONT TYP REF NR V TMIN LCUV LCUT TYPE FROM TO STEP RESU LCST XREF YREF ZREF DUMP EXTR TYPE MAX MIN STYP ACT ECHO OPT VAL LCUR HIST The records HEAD. A description of each record follows: 3-2 SOFiSTiK 2016 . with a primary load case the default is TH2. but stress induced geometric stiffness and 3rd order theory (large deformations but small strains). DYNA can use also the FE-meshes of a specific section. GRP SYST Item Description Unit Default TYPE Type of System REST use existing main system SECT use subsystem of section SNO Section number LT REST − - LT * LT LINE CS Geometric type of the analysis LINE linear analysis TH2 2nd order theory TH3 3rd order theory Physical type of the analysis LINE linear analysis NONL non linear analysis (all) NSPR non linear analysis (Spring) NMAT non linear analysis (Material) Construction stage − - PLC Primary load case − - STAT State of analysis SERV serviceability ULTI ultimate limit CALC general nonlinear LT - SNO PROB PHYS The system for the analysis has to exist in the database. The physical type of the analysis may be linear or including the nonlinear properties of the spring elements and/or the full material non linearity (explicit inte- SOFiSTiK 2016 3-3 . This may be selected with SYST SECT nnn. Option TH3 is currently only available for explicit integration. STEP. The geometric type of the analysis may be linear or according 2nd order theory (small deformations.3 SYST – System Parameters See also: CTRL. The FE-system of the sections is saved in separate data base in a sub-directory. The stresses for the geometric stiffness are taken from the primary load case.Input Description | DYNA 3. where nnn is the number of that section. Thus without a primary load case the analysis is always linear. The definition of the state presets the selection of stress strain laws and safety factors according to the INI-file of the selected design code. 3-4 SOFiSTiK 2016 . The analysis uses the properties for construction stage CS and the stresses and deformations according CTRL PLC from load case PLC.DYNA | Input Description gration only). MASS. V2 Usage of primary load case 0= 1= 2= 3= V3 Usage of primary load case stiffness for beams (default n=7).4 CTRL – Calculation Parameters See also: ECHO. EXTR CTRL Item Description Unit Default OPT Calculation parameter LT ! VAL Value of the parameter − ! V2 Secondary value of the parameter − - V3 Secondary value of the parameter − - V4 Secondary value of the parameter − - V5 Secondary value of the parameter − - V6 Secondary value of the parameter − - CTRL defines parameters of calculation. Non-linear stiffness created by AQB will be taken into account. STEP. where: +1 = +2 = SOFiSTiK 2016 only for geometric stiffness. GRP. while a tensile stress field will increase the eigenvalue. but no iteration will take place for changes of the initial stress. MODD. CONT. For an eigenfrequency analysis. EIGE. LC. default). axial force bending moments 3-5 . Thus. HIST. for a buckling eigenvalue the specification of this value is mandatory! As the dynamic analysis is then based on the tangential stiffness. These are: PLC Primary load case When entering a primary load case you will have initial stress stiffness included in the analysis. added to results (beam elements only. loadings should always be defined as incremental loads. creates inverse loading (beam elements only) Option 1 and 2 together. thus we have second order or pi-deltaeffects. a compressive stress field will reduce the eigenvalues until zero at the buckling limit.Input Description | DYNA 3. These results may be used for an animated sequence.) The initial stress stiffness for lateral torsional buckling is applied. As the characteristic length becomes zero in that case. we do not obtain torsional stresses directly at a warping support condition. the 2nd order Saint Venant theory for torsion is applied 1= yes. alias: BTYP +1 = with all sections (static analysis only) +4 = classical Timoshenko beam +8 = non-conforming Timoshenko beam (Default) +12 = classical beam with shear correction factors Deactivation / activation of the extrapolation of contact point displacement 0= deactivation 1= activation Warping torsion and lateral torsional buckling 0= no.DYNA | Input Description +4 = V4 Options for geometric stiffness of cables (default 0) 1= 2= RLC torsion do not set the general prestress value for cables from the primary load case for buckling eigenvalues. 2= yes. unless the section is warp free. (CM ≈ 0. Via V2 you may control by adding the options: +1 = Displacements (default) +2 = Results of elements +4 = Velocities and accelerations +8 = Loadpatterns for travelling load trains value = user defined load case number (> 9999) BEAM CONT WARP BETA Formulation of beam element (Bitpattern).0. Please use this option only for very special cases. Treatment of buckling length after buckling Eigenvalues 0= 3-6 save SOFiSTiK 2016 . suppress the coordinate update Result load case for Histories With input of a result case RLC you will save results to the database after every time step interval of an direct integration with individual load cases starting at RLC+1. even if CM ≈ 0. It has to be marked however. definition however only in very special cases) HLC Number of interim results for transient analysis of wind histories (only for internal purpose) SRES Steady-state response SOFiSTiK 2016 3-7 .Input Description | DYNA 1= superposition The estimate of the buckling length will be saved only for those beam elements where the estimate is less than the limit value LMAX specified in record GRP. QUAD BRIC SPRI MCON Formulation of QUAD elements 0= conforming elements with “bbar” correction 1= nonconforming elements 2= four assumed strains + drilling degrees 3= five assumed strains + drilling degrees BRIC Formulation of QUAD elements 0= conforming elements with “bbar” correction 1= nonconforming elements Formulation of Spring elements (Bitpattern) +1 = apply eccentricity effects (default) +2 = account for nonlinear effects +32 = do not extrapolate displacements in time +64 = do not extrapolate damping forces in time Formulation of the mass matrix 1= Diagonal mass matrix (default) 2= Consistent mass matrix for system Consistent translatoric element matrices (default if such relevant kinematic constraints exist) 3= Consistent element. that there are many cases not applicable for a buckling length approach and that the second order analysis will be more suitable in most cases. CCON Formulation of the damping matrix (same as MCON. A constraint rotation must be considered therefore with the definition of the cross section.and system matrices including rotational masses (default if CTRL WARP 1) Hint Rotational masses for torsion are always referred on the shear centre. (2) CQC Complete Quadratic Combination (3) SRSi SRSS with sign aligned to mode i. The resulting Moment is always taken to the reference of the origin of the global coordinate system to allow the superposition of different levels. CQCi CQC with sign aligned to mode i.DYNA | Input Description STYP 0= Simplified analysis of phases by sign only 1= As above. SOFiSTiK 2016 . (2) SRSS The square root of the sum of squares is computed. (1) SRSS The square root of the sum of squares is computed. (0) ADD All functions are added algebraically. but account for transient components of initial conditions (to be used only in very special cases) 2= Exact account of phases (default) Superposition of results of spectra and stationary response MAX The functions are evaluated separately followed by a max/min selection. (3) The default is dependant on the type of analysis. (1) SUM All functions are added by absolute values. V2 Default for EXTR and the evaluation of the resultant shear base values: ADD All functions are added algebraically. BLEV 3-8 Height ordinate of a layer for which the resultant base shear should be calculated during the response spectra evaluation (may be defined multiple times). (0) SUM All functions are added by absolute values. as the effort for solving them is very small compared to the triangulization of the equation system.4. • Direct Sparse Solver These types of solvers correspond to state of technology.Input Description | DYNA 3. The advantage of the direct solvers is especially given in case of multiple right hand sides. Which solver is used best depends highly on the type of the system and requires knowledge of relevant system parameters. The current implementation works best on a skyline oriented matrix. SOFiSTiK provides a number of solvers. The programs SOFIMSHA/C by default always create a sequence which is suitable for the direct sparse solver (3).1 SOLV Equation solver SOLV Description VAL Selection of equation solver 1 Direct Skyline Solver (Gauss/ Cholesky) 2 Iterative Sparse Solver 3 Direct Sparse LDL Solver 4 Direct Parallel Sparse Solver (PARDISO) Unit Default − 3 For solving the equation systems of the Finite-Element problem. but it may also provide reduced computing time compared to the previous two types especially in case of large volume structures. A quite efficient version based on the work of DAVIS [1] is available as well as a direct parallel solver PARDISO. The storage needed depends on the internal optimization of the node numbers and may become quite large for 3D structures. This optimization step is usually performed during system generation. Thus they are the first choice for any dynamic analysis or in case of many load cases. • Iterative Solver (Conjugate Gradients) One advantage of the iterative solver lies in its reduced requirements for storage. The solvers (1) or (2) however require a skyline oriented numbering which may be obtained using the option (CTRL OPTI 1) or (CTRL OPTI 2) during system generation. The correct SOFiSTiK 2016 3-9 . Following types are available: • Direct Skyline Solver (Gauss/Cholesky) This is the classical solver of the FE-Method. the solvers need an optimized sequence of equation numbers. In order to minimize computational effort. 4. The equation solvers are selected using the parameter (CTRL SOLV).DYNA | Input Description setting will be checked and a warning will be issued in case a correct numbering is not available. For the preconditioning. The iterative (CTRL SOLV 2) and the parallel sparse solver (CTRL SOLV 4) can be run in parallel providing an additional reduction in computing time.2 describing the input parameter (CTRL CORE). More information about parallelization can be found in subsection 3. A parallelization basically requires a license of type ”HISOLV”. followed by optional additional parameters. The first value defines the type of the solver. Iterative equation solver SOLV VAL Description 2 Iterative equation solver Unit Default − ! V2 Maximum number of iterations − * V3 Tolerance in numeric digits (5 to 15) − * V4 Type of preconditioning: 0 Diagonal Scaling (not recommended) 1 Incomplete Cholesky 2 Incomplete Inverse − 1 V5 Threshold value of preconditioning − * V6 Maximum bandwidth in preconditioning − * The iterative solver uses a conjugate gradient method in combination with preconditioning. Direct Skyline Solver (Gauss/ Cholesky) SOLV VAL Description 1 Direct Skyline Solver (Gauss/ Cholesky) Unit Default − ! No additional parameters are required. following variants are supported: 3-10 SOFiSTiK 2016 . However it is mandatory to optimize the equation numbers in SOFIMSHA/C using (CTRL OPTI 1) or (CTRL OPTI 2) in order to minimize computation time as well as storage requirements. Input Description | DYNA • Diagonal scaling (V4=0) Although this is the fastest method with the least memory requirements. It shows however better performance in case of more densely populated matrices (Recommended threshold V5: 0. This applies to the convergence-rate as well as the time required for computing the inverses. it will need a considerable high amount of iterations and is therefore not recommended in most cases. Compared to a full triangulization with the Cholesky method. The mesh generators SOFiMSHA/C generate by default an equation numbering required for this type of solver which minimizes the so-called Fill In of the matrix. changing the default setting V3 is not recommended. Therefore.01). The optimum choice depends on the type of the structure and may only be found by some tests. In any case the analyst should carry out a proper assessment of the computation results. • Incomplete Cholesky (V4=1) This type of preconditioning performs a partial triangulization of the input matrix.direct parallel sparse solver SOFiSTiK 2016 3-11 . PARDISO . Direct Sparse LDL Solver (Default) SOLV VAL Description 3 Direct Sparse LDL Solver Unit Default − ! Additional parameters are not required. Hint The correctness of the solution of the iterative solver depends primarily on the tolerance threshold. the Incomplete Cholesky saves time by ignoring the so called Fill-In during decomposition. • Incomplete Inverse (V4=2) This type of preconditioning is generally inferior to the Cholesky method. For any kind of preconditioning the number of matrix entries taken into account during preconditioning can be reduced either by giving a relative threshold value at V5 or via a maximum bandwidth size at V6. 4. Additionally. Hence.2 CORE Parallel computation control CORE Description VAL Number of used threads Unit Default − * SOFiSTiK supports parallel computing for selected equation solvers.DYNA | Input Description SOLV WERT Description 3 Direct parallel sparse solver Unit Default − ! This solver PARDISO uses processor optimized high performance libraries from the Intel Math Kernel Library MKL. some programs offer parallel element processing capabilities – independent of the chosen equation solver (CTRL SOLV). It does not require an a priori optimization of the equation numbers during system generation. Hint Parallel computing requires availability of a HISOLV license (ISOL granule). availability of an adequate SOFiSTiK license is obligatory. 3. Activation of parallel computing By default parallel computing is triggered automatically where it is feasible. the number of adopted threads is determined as follows (listed with increasing priority): a) The software retrieves the information about the number of available physical processor cores on the system. Thus. It usually provides the least computing times. a usage in combination with the program ELLA is not possible. On the other hand however. This number defines the default number of 3-12 SOFiSTiK 2016 . this solver does not allow reusing the factorized stiffness matrix in other programs. the equation optimization in SOFiMSHA/C could also be deactivated using (CTRL OPTI 0) in order to save memory during system generation. Parallel computing requires corresponding harware and operation system support. In addition. Number of available threads for parallel computing If parallel computing is active. b) This default can be modified via the environment variable SOF_NUM_THREADS. an explicit statement CTRL CORE NN (or as relative input CTRL CORE NN[%]) temporarily assigns the number of available threads for the respective run. HISOLV HISOLV 3-13 .a. Iterativ 2 Sparse LDL (default) 3 Sparse Parallel (Pardiso) 4 SOFiSTiK 2016 HISOLV HISOLV – n. which is also available as sofistik. depends on the actual analysis option (parallel processing must be supported for the specific task) and the availability of an adequate license.def parameter. The decision if a parallel computation is triggered. c) Finally.Input Description | DYNA threads that are used when a parallel computation is activated.a. Parallel options for equation solvers License Solver CTRL SOLV Serial Parallel Skyline Gauss/ Cholesky 1 – n. Parallel computing can be suppressed by explitly setting the number of available threads to 1 (or 0). Hint Neither option b) nor option c) state an explicit parallel computation request. The geometric initial stress stiffness will not be multiplied with the factor RADB in general.g. CONT.0 WIND Options for Wind-Loading − - LMAX Limiting Slenderness for buckling length − - NSCP Node number for the scaling point of the SBFEM Method − * All elements are used if nothing is input.0 HING blocked degrees of beam hinges Lt16 - RADA Mass proportional damping 1/ sec 0.5 GRP – Selection of Element Groups See also: ECHO.0 RADB Stiffness proportional damping sec 0. if only some groups get a damping assigned to. EIGE.0 MODD Modal damping − 0. The elements of a group can be provided with two damping types. LC. This effect has to be especially taken care of. EXTR Item Description NO Group number VAL Selection OFF YES FULL SOIL GRP Unit Default − ! LT FULL CS do not use use.DYNA | Input Description 3. air or water). HIST. only the specified groups get activated. the value RADA represents an external damping proportional to the mass and thus the excursion (e. Only for the cable the prestress defined with the element is contributing 3-14 SOFiSTiK 2016 .0 FACM Factor of the masses of the group − 1. MASS. When there is input. but do not print use and print the results elements define boundary to halfspace for SBFEM Number of the construction stage − - FACS Factor of the group stiffness − 1. MODD. CTRL.0 FACP Factor of the primary stresses − 1. STEP. The value RADB represents an internal damping proportional to the stiffness (material damping). C = RADA · m + RADB · K kNsec/ m = 1/ sec · Nsec2 / m + sec · kN/ m For a modal analysis it is possible to specify a modal damping for every group. This value is then converted using the element masses to an approximate equivalent modal damping of the total eigenform. Without definition of NSCP the scaling point will be located on the upper center of all soil interface nodes. More explanations for the damping you will find at MODD The description of the half space with the “Scaled Boundary Element Method” (SBFEM) allows to define the respective static and dynamic properties of the infinite space accounting for the radiation damping properties. GRP selects the boundary elements of a 2D Analysis or the QUAD elements of a 3D analysis defining the boundary of the half space. SOFiSTiK 2016 3-15 . The local z axis must show into the direction of the half space.Input Description | DYNA to the damping. 2 G Shear modulus kN/ m2 * K Bulk modulus kN/ m2 * GAM Specific weight kN/ m3 25 GAMA Specific weight under buoyancy kN/ m3 * ALFA Thermal expansion coefficient 1/ ˇrK E-5 EY Anisotropic elastic modulus Ey kN/ m2 E MXY Anisotropic poisson’s ratio m-xy − MUE OAL Meridian angle of anisotropy about the local x axis Descent angle of anisotropy about the local x axis deg 0 deg 0 − 1. MAT has older item names for the orthotropic parameters. The differences between the two records are mainly the used dimensions.6 MAT – General Material Properties MAT Item Description Unit Default NO Material number − 1 E Elastic modulus kN/ m2 * MUE Poisson’s ratio (between 0. while MAT uses (kN/m2 ) analogue to NMAT. (MPa) and has additional strength values.0 Lt32 - OAF SPM Material safety factor TITL Material name Materials which can be used for SVAL or QUAD and BRIC elements may be defined with the record MAT and MATE.49) − 0.DYNA | Input Description 3. The number of the material must not be used for other materials. MATE is analogue to CONC.STEE etc. 3-16 SOFiSTiK 2016 .0 and 0. For pure supporting materials. MATE/CONC/BRIC) properties for elastic support. This step is also necessary if one wants to define just the constants. Zimmermann/Pasternak). among SOFiSTiK 2016 3-17 . It facilitates the definition of elastic supports by an engineering trick which. For a QUAD element it is thus possible to select for a foundation the properties of the plate and the soil within a single element number.g. YIEL Maximum stress of interface kN/ m2 - MUE Friction coefficient of interface − - COH Cohesion of interface kN/ m2 - DIL Dilatancy coefficient − 0. CRAC Maximum tensile stress of interface kN/ m2 0. However for this case a direct definition of a value at the element is much more straight forward. CT Elastic constant tangential to surface Ct kN/ m3 0. BMAT is the second step transforming the elasticity constants from a material to support constants by including a geometric dimension and a specify geometry rule.7 BMAT – Elastic Support / Interface BMAT Item Description Unit Default NO Material number − 1 C Elastic constant normal to surface Cs kN/ m3 0.Input Description | DYNA 3. GAMB Equivalent mass distribution t/ m2 0 TYPE Reference LT - PESS Plane stress condition PAIN Plane strain condition HALF Circular disk at half space CIRC Circular hole in infinite disk SPHE Spherical hole in infinite space NONE no reference MREF Number of a reference material − NO H Reference dimension (thickness H or radius R) m ! BMAT defines for an existing material (e. The bedding approach works according to the subgrade modulus theory (Winkler. If subgrade parameters are assigned to the material of a geometric edge (GLN). BEAM or QUAD and the more general description of BORE profiles) The determination of a reasonable value for the foundation modulus often presents considerable difficulty. spring elements will be generated along that edge based on the width and the distance of the support nodes.g.DYNA | Input Description others.1) E H · (1 − μ) (1 + μ)(1 − 2μ) Ct = E H · 1 (1 + μ) (3. while CT is acting in any shear direction in the QUAD plane.3) Circular hole with radius R in infinite disk with plane strain conditions (bedded pipes or piles): 3-18 SOFiSTiK 2016 . since this value depends not only on the material parameters but also on the geometry and the loading. The bedding effect may be attached to beam or plate elements. The value C is than acting in the main direction perpendicular to the QUAD surface in the local z-direction. The subgrade parameters C and CT will be used for bedding of QUAD elements or for the description of support or interface conditions. A QUAD element of a slab foundation will thus have a concrete material and via BMAT the soil properties attached to the same material number. (see SPRI. ignores the shear deformations of the supporting medium. for modeling elastic support by columns and supporting walls (plane stress condition): Cs = • 1 (1 + μ)(1 − μ) Ct = E H · 1 2(1 + μ) (3. BOUN.2) Equivalent circular disk with radius R on an infinite halfspace: Cs = • H · Planar layer with horizontal constraints for settlements of soil strata (plane strain condition): Cs = • E E R · 2 π(1 + μ)(1 − μ) (3. One must always keep this dependance in mind. when assessing the accuracy of the results of an analysis using this theory. Instead of a direct value you may select a reference material and a reference dimension for some cases with constant pressure based on the elasticity modulus and the Poisson ratio μ[1] : • Planar layer with horizontal constraints e. but in general it will be used as an own element. that before reaching this limit the stiff-ness CT will produce the shear stress only if a deformation is present. the principal deformation component of the interface increases without an increase of the stress.0 has been entered for both friction. If the bedding reaction is applied to a QUAD element. a deformation in the direction of the local z-axis will create compressive (negative) stresses. SOFiSTiK 2016 3-19 . The non-linear effects can only be taken into account by a non-linear analysis. YIEL. the interface fails in both the axial and the lateral direction. while all other effects act upon the principal direction.Input Description | DYNA Cs = • E 1 · R (1 + μ)(1 − 2μ) Ct = Cs (3.6) Non-linear effects are controlled by CRAC. Yield load: Upon reaching the yield stress. The failure load is always a tensile stress. Friction/cohesion: Defining a friction and/or a cohesion coefficient. then the lateral bedding acts only if 0. The friction is an effect of the lateral bedding.coefficient and cohesion. MUE and COH: Cracking: Upon reaching the failure stress. the lateral shear stress can not become larger than: Friction coefficient * normal stress + Cohesion Please note. If the principal interface has failed (CRAC).4) Spherical hole with radius R in infinite 3D elastic continua: Cs = E R · 2 Ct = Cs (1 + μ) (3.5) Including a dilatancy factor describing the volume change induced by shear deformations. we have for the bedding stresses the following equations depending on the normal and transverse displacements: σ = Cs · (s + DL · t ) τ = Ct · t (3. Material Properties SMAT Item Description Unit Default NO Material number − 1 LC Characteristic Length m ! EX Coefficient of elasticity in X-direction − 0 EY Coefficient of elasticity in Y-direction − 0 EZ Coefficient of elasticity in Z-direction − 0 RHOX Coefficient of density in X-direction − 0 RHOY Coefficient of density in Y-direction − 0 RHOZ Coefficient of density in Z-direction − 0 ALF Inhomogenity of elasticity − 0 BET Inhomogenity of density − 0 Record SMAT defines dependency of material values for the SBFEM: – E = Ereƒ · E – ρ = ρreƒ · ρ 3-20  || α Lc  || Lc β + Ey + ρy  |y| α Lc  |y| Lc β + Ez + ρz   |z| α ™ (3.8 SMAT – SBFEM .DYNA | Input Description 3.8) SOFiSTiK 2016 .7) Lc |z| Lc β ™ (3. MXY Rotational mass tm2 0. They are not effective as dead load in static load cases as do the primary masses. CTRL.Input Description | DYNA 3. the dead weight of the material or the cross section should be input as zero. but the have also a group number of the last GRP-record assigned and may be switched on or off with the GRP record. The val- SOFiSTiK 2016 3-21 . MYZ Rotational mass tm2 0. If the dead weight of a structure is not to be applied. MYY Rotational mass tm2 0. They are maintained over several input sets until they are redefined. rotational masses must be defined separately with MASS or CTRL MCON 3. HIST. thus the primary masses from SOFIMSHA are kept. MY Translational mass t MX MZ Translational mass t MX MXX Rotational mass tm2 0.9 MASS – Lumped Masses See also: ECHO. A mass acts usually the same in all three coordinate directions and thus. EXTR Item Description NO MASS Unit Default Node number − ! MX Translational mass t 0. MZZ Rotational mass tm2 0. STEP. LC. MODD. The negative load case number must be input for NO here. MB Rotational mass tm2 0. GRP. EIGE. MASS can be used also to import nodal loads from the database as masses to DYNA. The dead weight of the entire structure is always applied in the form of translational masses. The masses are additional to the primary masses defined in program SOFIMSHA in the database. Rotational masses with inclined axis will have off diagonal masses MXY till MYZ. MXZ Rotational mass tm2 0. CONT. MASS 0 can be used to delete all temporary masses. If necessary. it need to be defined independently only for special cases. 20000 for the Y direction and 30000 for the Z direction. If other load directions are to be converted to masses as well. By contrast the input MASS -30012 0.0.05 0. The second input processes PY loads of the load case 13.01 The mass in global Z direction is reduced to one percent only. these directions have to be specified additionally at NO encoded with the addend 10000 for the X direction. With the input MASS FACT MZ 0. The input MASS -12 creates translational masses from all loads of load case 12 in the direction of the dead weight. For this purpose the literal FACT has to be input for NO. Masses can get also a factor with MASS. Only half of the mass is activated in the y direction. are then the factors for the individual directions of the mass components which are generated from the loads in the dead weight direction. 3-22 SOFiSTiK 2016 . however. with default value of 1. This can be reasonable particularly for larger systems.1 0.1 0.DYNA | Input Description ues MX till MZ.0 creates masses (t) in the x and z direction from all PZ loads (kN) of load case 12.1 MASS -20013 0. where it is favourable to suppress many low frequencies which are not essential for the analysis.0 0. STEP. CONT. All the eigenvectors have to be simultaneously in storage. MODD. While the first uses a well defined positive definite mass matrix. Eigenvalues and forms may represent dynamic vibration modes or buckling eigenforms. one must enter TYPE REST. If the eigenvectors have been already computed. CTRL. the second problem may encounter indefinite geometric stiffness matrices (negative Eigenvalues) and establish problems. LC. SOFiSTiK 2016 3-23 . Special attention must be paid to this when importing eigenvalues from program ASE. The mode shapes can be stored in the database similarly to static load cases and can be then represented graphically as deformed structure. therefore in cases of large problems sufficient memory should be provided.10 EIGE – Eigenvalues and Eigenvectors See also: ECHO. EXTR Item Description NEIG Number of sought eigenvalues TYPE MITE Method for the eigenvalue computation REST Eigenvalues already available SIMU Simultaneous vector iteration LANC Method of Lanczos RAYL Minimum Rayleigh-Quotient BEUL Buckling BESI Buckling (Vector iteration) BELL Buckling (Lanczos) BERA Buckling (Rayleigh) Number of iterations Lanczos vectors Maximum number of iterations and options LMIN Eigenvalue shift STOR EIGE Unit Default − ! LT SIMU − * − * 1/ sec2 0 Number of eigenform to be stored − NEIG LC Load case number of lowest eigenform − 1 LCUP Load case number of highest eigenform − * NITE The input of EIGE requests calculation of the eigenvalues and the mode shapes. In any case you should start with a few Eigenvalues in those cases. Only SIMU and RAYL have some provisions for that type of problem.Input Description | DYNA 3. MASS. GRP. HIST. In this case the numbers of these load cases have to follow the eigenform load cases immediately and may be requested through the explicit input of LCUP. In case of NITE=NEIG. For lateral torsional buckling BURA is the best method in general to suppress the negative eigen values. by contrast to vector iteration. BUSI or BURA). In that case you may however evaluate the buckling eigenform directly via TYPE BUCK (or more specific BULL. 3-24 SOFiSTiK 2016 . The method of Rayleigh is especially useful if only few eigenvalues are required and if there are also negative Eigenvalues. The method of Lanczos is significantly quicker than the vector iteration. The eigenvalue problem can be shifted by one value. The simultaneous vector iteration is used in most cases. 2 · NTE)) is reached or when the highest eigenvalue has only changed by a factor less than 0. As it uses the iterative solver it requires a special license ISOL and a skyline optimization (CTRL OPTI 1) but can handle very large systems with least memory requirements. when a large number of eigenvalues is sought. the geometric initial stiffness is included in the eigenvalue analysis. A good accuracy is achieved when the number of vectors NITE is at least double the number of sought eigenvalues (default). This finds application in structures that are not supported (zero eigenvalue is the smallest value) as well as in checking the number of eigenvalues by means of a Sturm sequence. the higher eigenvalues are usually worthless. For that reason the default value for NITE is the minimum between NEIG+2 and the number of unknowns. The number of skipped eigenvalues is manifested during the shift by the number of sign changes of the determinant. The choice of method for the eigenvalue analysis depends on the number of the eigenvalues. So you will get the frequency zero if you are approaching a buckling case. The number of iterations can be reduced when a somewhat expanded subspace is used for the eigenvalue iteration.DYNA | Input Description A modal evaluation of forces is possible only when all required mode shapes have been stored also as stresses or forces of the elements. The iteration is terminated when the maximum number of iterations (default max (15. On the other side also computed influence areas for the processing of selective foot point excitation or other special cases may be introduced into the analysis.00001 compared to the previous iteration. If a primary load case is selected with CTRL PLC. Input Description | DYNA Number of Eigenvalues Range of Eigenvalues multiple Eigenvalues missing Eigenvalues negative Eigenvalues Memory requirement Speed Vektoriteration Lanczos Rayleigh moderate high few Ritz-Step problematic yes no problems yes sometimes problems yes very rare rare very rare yes does not work only positive moderate high small moderate fast variable Overview of the algorithms SOFiSTiK 2016 3-25 . these values will become effective in just this way. logarithmic dekrement 3-26 δ = og  A1 A2  (3. When using direct integration.describing the ratio of two consecutive amplitudes A1 and A2.11 MODD – Modal Damping See also: ECHO.9) · B · ω In the next pictures you will see the influence of the factors A and B depending on the eigenfrequencies of a SDOF-oscillator. The values are stored in the database. However the modal damping (Lehr’s damping factor). The definition of this value will overwrite any damping definitions in the GRP record or from explicit damper elements! As the values in the literature are mostly given as modal damping values or logarithmic decrements δ we will give some important formulas: d = δ 2π =D+ 1 A · 2 ω + 1 2 (3. EIGE Item Description NO MODD Unit Default Number of the eigenvalue − all D direct Lehr’s damping − 0 A Mass proportional damping 1/ sec 0 B Stiffness proportional damping sec 0 The damping may be specified within the GRP record with different values for each group.10) SOFiSTiK 2016 . GRP. CTRL. following the computation of the eigenvalues. The damping is shown as logarithmic decrement δ. can also be defined separately for each mode by three independent parts (direct value of D. mass proportional A and stiffness proportional B). from the defined damping values by a diagonalisation process.DYNA | Input Description 3. Each Eigenform will then have one distinct modal damping value. For a modal analysis however the modal damping will be calculated. 00 0 800.00 0 200.0 6.00 0 600.0 5.0 3. SOFiSTiK 2016 3-27 .00 0 Zeit 0.00 0 400.Input Description | DYNA − Verschiebun g SY [mm] A1 1600. there is no modal damping.0 10.0 7.00 0 1.0 [sec] Figure 3.4 4 Hint MODD have to be specified as absolute value or with an explicit unit [%] ! For a direct integration without eigenvalues.0 4.00 0 N 1000.8 5 bolted steel constructions 1 7 welded steel constructions 0. thus it is necessary to convert a given damping value to the parameters A and B.1: logarithmic dekrement The decrement δ is related to the modal damping with a factor of 2π .0 8.00 0 A2 1400.0 2. The conversion of parameters A and B can be seen from the next picture.00 0 1200. Usual values for the modal damping D are (M ÜLLER [2]): elastic conditions [%] plastic conditions [%] Reinforced concrete 1-2 7 Prestressed concrete 0.0 9. You have then to specify a combination of A and B given by: (circular frequencies ω = ƒ · 2 · π) A = 2 · ω1 · ω2 · B=2· ξ1 · ω2 − ξ2 · ω1 ω2 2 − ω1 2 ξ2 · ω2 − ξ1 · ω1 ω2 2 − ω1 2 (3.063 i.2 Dekremente [%] 25 A = 0.5 THE = 1.4 DEL = 0. We thus have a decrement of 2 · π · ξ = 2 · π · 0. In General you want to define the damping between two frequencies f1 and f2 with a relatively constant decrement.2: Parameter A and B To achieve a 10 % damping for a frequency of 5 Hz you may either define A as 1.55 ALF = 0.5 20 A = 1.52 10 ALF = 0.e.005 35 A = 0.0 15 ALF = 0.5 1 2 5 10 20 50 Eigenfrequenzen [Hz] ALF = 0.17 DEL = 0.001.0005 50 B = 0.52 5 ALF = 0.3 DEL = 0.4 Figure 3.002 40 B = 0.11) (3.1 30 A = 0.01 = 0.14) Example: A structural steel with bolted connections should have a mean modal damping of 0.001 45 B = 0. the amplitude of a free oscillation should reduce 3-28 SOFiSTiK 2016 .12) If the damping at the start of the interval should be equal to the damping at the end of the interval and by converting to the standard frequencies ω = ƒ · 2 · π we have: A = ξ · 4π · B=ξ· ƒ1 · ƒ2 ƒ1 + ƒ2 1 π · (ƒ1 + ƒ2 ) (3.01 between 2 Hertz and 10 Hertz.0 or B as 0.55 0 0.4 DEL = 0.25 DEL = 0.13) (3.DYNA | Input Description B = 0. 0630 0. DEL = 0. because the equations are integrated exactly. at the bounds of the interval we have the desired damping.0105 0.0525 0.047. SOFiSTiK 2016 3-29 .01 · B= 1 · 0.Input Description | DYNA by 6.15) = 0.021 from B 0.e. Thus: = 0. For a direct integration there is an additional numerical damping effect possible with the selection of the integration constant BET. ƒ −ƒ Factor € ( 22 1 2) Š is given by ƒ2 −ƒ1 A = 4 · π · 0.0105 0.0 Hertz we have only d = 0.0 Hertz from A 0. The default (BET = 0.5.047 i.0630 0.0525 0.026 total 0. DEL and THE.16) To check this we have from the diagram or the formulas: at 2.21 (3. but between we have a little bit less.25.3 % from peak to peak within the range from 2 Hertz to 10 Hertz.083. For 5.0 Hertz at 10.000266 (3.0 Hertz at 5. The same is valid for modal analysis there is also no damping effect. THE = 1) will not have any damping effect.01 π 2 + 10 2 · 10 2 + 10 € (10−2) Š 102 −22 = 0. 4 STEP prescribes the type of time-dependent analysis.1 INT Output interval every INT steps −/ LT 1 A Mass proportional damping 1/ sec 0. When N <1 is input.7 < THE < 1. B Stiffness proportional damping sec 0. DEL = 1/ 2) – THE < 1. GRP.12 STEP – Parameter of the Step-wise Integration See also: ECHO. MASS. EIGE. If the literal TIME or FREQ is input for INT. Three cases must be distinguished: • • STEP N > 0 Analysis of a time segment with duration N · DT by direct (Newmark-Wilson) or analytical modal integration.4 for the Wilson method (BET = 1/ 6.0 for the explicit integration – THE = 1. MODD.0) STEP 0 or record not defined Static analysis (without record EIGE) or statistic analysis of spectra or steady-state excitations.DYNA | Input Description 3. CTRL. CONT. DT is interpreted as total time and the individual time step becomes N · DT . HIST. BET Parameter of the integration method − 1/4 − 1/2 DEL THE relative time value for equilibrium − 1.0 for the Newmark method (Default constant average) – THE ≥ 1.0 for the Hughes-Alpha method (0. EXTR Item Description N STEP Unit Default Number of time steps or divisor − 10 DT Time step or total time (sec) − 0. a response analysis for the oscillation periods or frequencies in the region from 0 to N · DT times the specified load function frequency 2π/ T0 is performed. If 3-30 SOFiSTiK 2016 . – THE = 0. LC. EIGB Optional estimate of bending frequency Hz - EIGT Optional estimate of torsional frequency Hz - EIGS Optional estimate of soil frequency Hz - DTF Number of steps for SBFEM convolution − * STHE Extrapolation factor for SBFEM − 1. Those errors may be introduced by a time step chosen to small together with consistent mass matrices.5 for a damped Newmark-Method • Definition of THE > 1. eg. • STEP N < 0 Analysis of a transient steady-state condition taking phase shifts into consideration.Input Description | DYNA the literal STIM or SFRE is given. the normalisation is based on a constant velocity. A suitable size of the time step depends on the frequency of the expected response. In that or other cases the integration constant should be modified. that the standard Newmark-Method has no numerical damping. A comparison analysis should be performed if in doubt with a step approximately equal to one fourth of the initial time step. Thus small errors may amplify easily. In case of the direct method components with periods smaller than about ten times the time step are damped out of the solution. If the literal VTIM or VFRE is selected. the load is normalised to a constant displacement instead of the acceleration. It should be taken care of the fact.0 for the Hughes-Alpha Method SOFiSTiK 2016 3-31 . Referred to the eigen period if DT not given.4 for the Wilson Method • Definition of THE < 1.: • Definition of DEL > 0. Each load case can be assigned in program SOFiLOAD loadings. 2. CONT. EXTR Item Description NO LC Unit Default Load case number − * FACT Factor for all loads of the load case − 1. EIGE. the item MODB allows to specify the load case number for the loading to the first eigen form. 3-32 SOFiSTiK 2016 . Static or steady-state analysis In case of steady-state analysis the periodical loads are converted to corresponding responses according to Section 2. If spectra are defined.0 MODB Modal base load case number − - TITL Identifier of the load case Lt32 - The loading in DYNA is subdivided in load cases identified by a number. Transient analysis During a time variation analysis (STEP N > 0) all the selected load cases and their functions define the time dependence of the loading and the starting time.13 LC – Load Case See also: ECHO. In case of static analysis the load cases are analysed separately. All functions act with their loads simultaneously upon the structure. MASS. All following eigenforms will be associated to the consecutive load case numbers. STEP. MODD. DYNA allows the extra definition of a contact condition CONT for a moving load. GRP.5. The use of the load cases differs according to the computational procedure: 1. DYNA computes by double interpolation of all the spectra a system response.0 DLZ Dead weight factor in Z direction − 0.DYNA | Input Description 3. HIST. time-functions or a response spectrum. However if every eigenform should obtain a separate loading as in a modal wind analysis. which is then superimposed by statistical methods according to the input for CTRL STYP.0 DLX Dead weight factor in X direction − 0. CTRL. For a modal analysis the general case is to apply the same load vector for all eigenforms.0 DLY Dead weight factor in Y direction − 0. SOFiSTiK 2016 3-33 . The response is 1. If it is zero.Input Description | DYNA In this case there is a special feature for spectral loading: For the load cases the user defined parameter CRIT will be evaluated.0. If defined otherwise the period of the eigenforms will be scaled with that value. Thus for a Wind spectrum this value is to be defined with Ltrb / men / or z/ men / . no evaluation will be taken from the spectra. DYNA | Input Description 3.14 CONT – Contact and Moving Load Function See also: ECHO, CTRL, GRP, MASS, EIGE, MODD, STEP, LC, HIST, EXTR CONT Item Description Unit Default TYPE Selected contact value (obsoleted) LT - REF Ident of a reference axis for load trains − 0 NR Number of an edge element − - V Travel speed m/ sec - YEX Local Eccentricity m 0.0 TMIN Time at start of travel sec 0.0 LCUV Load case for vertical track irregularities − - LCUT Case for transverse track irregularities − - LCUR Case for rotational track irregularities − - Dynamic contact is governed by a changing location of contact point within time, as it is given in the case of a vehicle travelling along a bridge. This record allows the definition of the development in time of the contact point and a mechanism to create loads based on current deformations of the system. For the time dependant location you have to select a sequence of nodes and specify the time value for each node when the contact point is exactly at that point. In most cases the selection of the number NO of a boundary/edge element will select all nodes in the given sequence. However explicit definitions with FUNC (program SOFiLOAD) records and mixing and concatenation of several elements is possible. Defining a travelling speed V will generate all the needed time values from the distance either directly or taken along the reference axis and the optional start time TMIN. If the load case has a load train created within SOFiLOAD, all loads of the train will follow each other with the appropriate distance. If the load train has also structural- or visualisation objects created via the TREX command, the nodes of those objects will receive the current coordinates as displacements and the absolute velocities. Only the point loads are processed by the CONT command. The three load cases LCUV, LCUT and LCUR allow to introduce track irregularities or uneven pavements as additional displacements or rotations for the contact-point. The load functions of these load cases must have the absolute 3-34 SOFiSTiK 2016 Input Description | DYNA displacements as a function of the travelling time of the load reference point. The reference displacement at the contact point is obtained by a linear interpolation between the adjacent nodes. The loading at the contact point is similarly distributed between the adjacent nodes. External nodal loads are placed at the contact point only if the node number is specified as 0. For the definition of a load train moving along a bridge according to DIN FB 101 / EC1 the input may be as follows: PROG SOFILOAD HEAD DEFINE A DEFAULT LANE GEOMETRY ECHO FULL GAX ’AXIS’ 0.0 X 0.0 0.0 R 150 NZ +1.0 ’AXIS’ 3.0 X 30.0 0.0 R 150 LC 191 ; TRAIN RFAT 4 p4 0.0 ; trex 191 901 900 11 1 END PROG DYNA GRP 1,2,3 ; GRP 901 FAKS 0.0 CTRL ELF 1001 7 LET#1 30.0 $ SPEED in m/sec $ STEP 0.01 300.0/#1 $ TOTAL TIME FOR TRAVELING $ LC 191 $ LOAD TRAIN $ CONT REF AXIS NO 10 #1 2.0 $ AUTOMATIC TIMEVALUES IN NODES FROM EDGE $ Further variants may be seen within the example dyna9_travelling_loads.dat and at SOFiLOAD loadtrains.dat. SOFiSTiK 2016 3-35 DYNA | Input Description 3.15 HIST – Results within Time See also: ECHO, CTRL, GRP, MASS, EIGE, MODD, STEP, LC, CONT, EXTR HIST Item Description Unit Default TYPE Result value (see table) LT S FROM Smallest node or element number − 1 TO Largest node or element number − FROM INC Increment or Identifier −/ Lt 1 RESU Output request LT - − * PRIN LCST numerical value printout Number of case to store in database 0 do not save in database XREF Beam section or reference point for the m 0. YREF sum of the spring force components m 0. ZREF or dP/P width m 0. DUMP Filename for a dump of the values Lt48 - The record HIST requests the time history of particular values. These will be saved into the database for the presentation with DYNR, but it is also possible to print the values directly or to save them to an external dump file. Up to 32 values can be addressed per input record. The computed maximum and minimum values of the curves will be printed in any case. Table 3.21: Possible literals for TYPE TYPE Meaning U UX, UY, UZ U-X 3-36 U- U-Z Displacements SOFiSTiK 2016 Input Description | DYNA Table 3.21: (continued) TYPE U-RX Meaning U-RY U-RZ V Rotations VX. VZ V-X V-Y V-Z Velocities V-RX V-RY V-RZ Angular velocity A AX. AY. Calculation of the dynamic stiffness with its real and imaginary part for a range of frequencies Translational degrees of freedom DSRX DSRY DSRZ Rotational degrees of freedom SOFiSTiK 2016 3-37 . AZ AX AY AZ Accelerations ARX ARY ARZ Angular acceleration P PT M Spring forces and moment PX PY PZ Spring force total global components PT/P DP/P Spring force ratios SP Sum of all spring force components SPX SPY SPZ Sum of the spring force components SPRX SPRY SPRZ Sum of the spring moment components TRUS Truss-bar axial force CABL Cable axial force BEAM All Beam forces N VY VZ Beam forces normal and shear MT MY MZ Beam moments torsion and bending SIG TAU SIGV Stresses in sectional points QUAD All Shell forces MXX MYY VXX VYY NXX NYY MXY Shell moments Shell shear forces NXY BRIC Shell membrane forces All continua stresses TXX TYY TZZ Stresses of 3D continuum TXY TXZ TYZ DSX DSY DSZ Shear stresses of 3D continuum (only available for EIGE REST from program ASE). VY. The spring force ratios may be useful for vehicle-structure-interaction. They are defined as follows: PT/P The ratio of the resulting transversal force PT to the main force P of a spring DP/P The ratio of the difference of the main forces of two springs to the mean value of the same spring forces: ΔP P 3-38 = P1 − P2 P1 + P2 (3. For the stresses INC is used to define the identifier of the stress point (SPT) within the section where the stresses should be evaluated. Then the value ΔP will be established from the moment and the plan view distance derived from values XREF to ZREF.DYNA | Input Description For the beam results XREF is used to define the section where the results are evaluated. SOFiSTiK 2016 . A negative definition is taken as the ratio of the section to the total beam length. thus a value of -1.17) INC=0 only between FROM and TO INC>0 change relative to the prestressing force or: For all springs a following rotational spring is searched having the same nodes.0 selects the end of the beam. GRP. STEP.. SRS9 harmonised SRSS CQC9 harmonised CQC The default value (CQC) may be changed with CTRL STYP V2.. CONT.16 EXTR – Evaluation of Max. MODD. Internal Forces and Moments See also: ECHO. HIST EXTR Item Description Unit Default TYPE Structural magnitude LT ! MAX Load case number for maximum − 0 MIN Load case number for minimum − 0 LT CQC 0 STYP print only Superposition type statistical/steady-state ADD sum of values SUM sum of absolute values SRSS square root of sum of squares CQC Complete Quadratic Combination harmonised SRSS SRS1 CQC1 harmonised CQC . EIGE. The values of the first line activate all possible internal forces and moments as maximum value only. ACT Action names of the results See below LT The following literals are possible for TYPE.Input Description | DYNA 3. CTRL. LC. MASS. No corresponding internal forces are computed in this case. SOFiSTiK 2016 3-39 . 23: For nodes TYPE Designation U Displacement V Velocity A Acceleration Table 3.25: For truss elements (TRUS) TYPE Designation TRUS Forces in truss elements 3-40 SOFiSTiK 2016 .DYNA | Input Description Table 3.24: For beams (BEAM) TYPE Designation BEAM Maximum values for beam elements (not usable for superposition) N Normal force VY Shear force Vy VZ Shear force Vz MT Torsional moment MY Bending moment My MZ Bending moment Mz MB Warping moment MT2 Secondary torsional moment Table 3. 27: For springs (SPRI) TYPE Designation SPRI Maximum values for spring elements (not usable for superposition) P Spring force in main direction PT Resultant spring force in transverse direction PT = p PTX 2 + PTY 2 + PTZ 2 PTX Spring component in global X direction PTY Spring component in global Y direction PTZ Spring component in global Z direction M Spring moment SP Sum of spring forces SPX Sum of spring force components in X direction SPY Sum of spring force components in Y direction SPZ Sum of spring force components in Z direction SPRX Sum of rotational spring forces about X direction SPRY Sum of rotational spring forces about Y direction SPRZ Sum of rotational spring forces about Z direction SOFiSTiK 2016 3-41 .26: For cables (CABL) TYPE Designation CABL Forces in cable elements Table 3.Input Description | DYNA Table 3. 28: For plates/shells (QUAD) TYPE Designation QUAD Maximum values for QUAD elements (not usable for superposition) MXX Bending moment m-xx MYY Bending moment m-yy MXY Torisonal moment m-xy VXX Shear force v-x VYY Shear force v-y NXX Membrane force n-xx NYY Membrane force n-yy NXY Membrane shear force n-xy NZZ Membrane force n-zz Table 3.DYNA | Input Description Table 3.29: For volume elements (BRIC) TYPE Designation BRIC Maximum values for BRIC elements (not usable for superposition) TXX Stress in global X direction TYY Stress in global Y direction TZZ Stress in global Z direction TXY Shear stress in global XY plane TXZ Shear stress in global XZ plane TYZ Shear stress in global YZ plane 3-42 SOFiSTiK 2016 . CQC usually gives the most reasonable results.. The versions SRS1 and CQC1 will scale the results according to the sign of the first eigenform.V. so that one can employ the complete set of the internal forces and moments. For nodal values (U. Displacements and velocities however are always relative to the free field SOFiSTiK 2016 3-43 . SRSS may overestimate or underestimate the probable magnitude. SRSS and CQC. For the global maximum values of the first row the extremas will be calculated for every force independently..30: For result sets (RSET) TYPE Designation RSET RS1 Maximum values for RSET elements (not usable for superposition) the first entry of each RSET RS2 the second entry of each RSET . The real response may be any positive or negative combination of these individual values. Special remarks on the extreme values of response spectra The maximum forces will become positive for SUM. RS31 the 31th entry of each RSET The maximum values are stored in the database. The extremas will be collected and stored within a single record.Input Description | DYNA Table 3. The algorithm used for that has been invented by SOFiSTiK and is therefore hardly to be found in other programs. Use ECHO DISP. VELO or ACCE to see all nodal results. At superposition of a single internal force on the other hand the corresponding internal forces are formed in the same ratio with a linear combination. The base accelerations are also included within the resulting nodal accelerations. SUM offers an upper limit. and it is definitely not suited for a display with the program ANIMATOR. if a load case number is input for MAX and/or MIN. (SRS2 to CQC9 analogue to the second to the 9th eigenform) In any case the results have to be inserted in other tasks with a positive or a negative sign multiplier.A) only the maximum values are output as default. This might be unconvenient for design purpose. Types PTX to PTZ have only the tangential components. The types SP and SPX. The output is done group-wise. 3-44 SOFiSTiK 2016 . SPY. All actions preset in program SOFiLOAD record ACT are possible here. Action names of the results At ACT the results can be assigned to a specific action for a later superposition. SPZ address the total sum of all components of support spring forces in the global coordinate directions.DYNA | Input Description movements of the soil. EXTR ECHO Item Description Unit Default OPT A literal from the following list: LT FULL LT FULL NODE Nodal values SECT Cross section values ELEM Elements MASS Masses in nodes EIGE Natural frequencies LOAD Loads DISP Displacements FORC Internal forces and moments VAL VELO Velocities ACCE Accelerations STAT Warning for convergence check FULL All the above options The extent of the output OFF Option complete deactivate NO No output YES Regular output FULL Extensive output EXTR Extreme output The name ECHO must be repeated in each record to avoid confusion with similar record names (e. and ELEM. HIST. GRP. MASS. LC. 10918 (No convergence of the iterative equation solver in load vector) for convergence checks can be switched off with ECHO STAT NO.Input Description | DYNA 3. CROS. EIGE. STEP. CONT. MODD.g. for all others it is YES. The default value is NO for NODE. CROS).17 ECHO – Extent of Output See also: CTRL. The warning no. SOFiSTiK 2016 3-45 . DYNA | Input Description 3-46 SOFiSTiK 2016 . Output Description | DYNA 4 Output Description 4. and by ECHO NODE FULL the equation numbers of the freedom degrees as well.3 General Parameters At the beginning of a dynamic analyses appears a table CONTROL INFORMATIONS with the general parameters.1 Nodes The nodes are output by use of ECHO NODE YES only. The table includes the coordinates and constraints. These are: • Number of unknowns and profile size of the equation system • Number of used eigenvalues SOFiSTiK 2016 4-1 . 4.2 Cross Sections The table of the cross sections appears after request by ECHO SECT and contains the following value: CROSS SECTIONS A Cross sectional area Ay Shear cross sectional area Az Shear cross sectional area It Torsional moment of inertia Iy Geometric moment of inertia about principal axis Iz Geometric moment of inertia about secondary axis E Elastic modulus G Shear modulus Da Factor of external (mass proportional) damping Di Factor of internal (stiffness proportional) damping Rho Mass density 4. In the table of the total masses.6 Load Cases. 4. The eigenvectors are normalised with respect to the masses (equation 2. i. Functions and Loads The table of functions and loads is always introduced before the description of the function. The internal forces and moments of the eigenvectors are usually to be understood as an indication of the stressing type. followed by the loads of this load case. 4. Taken as percentage of the total mass this gives a criteria for a sufficient number of eigenvalues.e.8 of the theoretical principles). the rotational masses are only the rotational inertias of the nodes. the length. 4-2 SOFiSTiK 2016 . the first line has the sum of the nodal masses.4 Elements The tables of beam elements and spring or truss elements as well as lumped masses and damping elements appear upon request by ECHO ELEM. the local axis directions and the mass components.5 Natural Frequencies After the first computation of the natural frequencies the program outputs the error in the eigenvalues along with the number of the required iterations.DYNA | Output Description • Number and size of time steps • Rayleigh’s damping by direct integration • Parameters of the integration method 4. f-YY and f-ZZ). The rest of the output is controlled by ECHO EIGE as follows: ECHO EIGE YES frequencies and modal damping only ECHO EIGE FULL node displacements as well ECHO EIGE EXTR element internal forces and moments as well For a uniform ground acceleration in the three coordinate directions the modal contributions may be evaluated (columns f-XX. The generalised loads of the individual modes and the sum of their squares are output in the case of a modal loading. They contain for each element the participating nodes. However the following rows contain the ordinates of the global centre of gravity and the total rotational inertia of all translatoric masses measured to this centre as a 3x3 matrix. The absolute value depends on the normalisation and it can take considerably large values. the spring stiffnesses. There result two lines per node with the minimum and maximum values as well as the corresponding time values if a time analysis was carried out.9 Time Variations The time variation of the structural magnitudes specified with HIST is presented lastly. 4. while the various magnitudes are plotted in the transverse direction. This can take the form of a table. The given time value holds for the whole line. The maximum values are calculated for all internal forces and moments specified by EXTR along with the other corresponding values.Output Description | DYNA There is a second value printed. Time is plotted in the longitudinal direction of the paper. The curves are marked by numbers or letters. A common scale for all involved magnitudes is selected for each plot. SOFiSTiK 2016 4-3 . a printer graph and/or a curve in the database for further processing with DYNR. 4. In case of stochastic or steady-state excitation the extreme values were computed by statistical methods. The nodes or elements addressed by each HIST record are output in a general graph.7 Displacements The displacements of the individual load cases are output by static analysis. which may be used to integrate the square of Eigenvalues for only parts of the structure via special load patterns.8 Internal Forces and Moments The internal forces of the individual load cases are output by static analysis. In case of dynamic analysis the maximum displacements. 4. velocities and accelerations can be output for all nodes. In case of stochastic or steady-state excitation the extreme values were computed by statistical methods or by analysis of one period of the steady-state excitation.
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