International Journal of Pressure Vessels and Piping 79 (2002) 1±26www.elsevier.com/locate/ijpvp Review Finite elements in the analysis of pressure vessels and piping, an addendum: a bibliography (1998±2001) Jaroslav Mackerle* Department of Mechanical Engineering, LinkoÈping Institute of Technology, S-581 83 LinkoÈping, Sweden Received 28 September 2001; revised 8 October 2001; accepted 8 October 2001 Abstract The paper gives a bibliographical review of ®nite element methods (FEMs) applied for the analysis of pressure vessel structures/ components and piping from the theoretical as well as practical points of view. This bibliography is an addendum to the Finite elements in the analysis of pressure vessels and pipingÐa bibliography (1976±1996) published [Int J Press Vess Piping 69 (1996) 279] and Finite elements in the analysis of pressure vessels and piping, an addendum (1996±1998) published [Int J Press Vess Piping 76 (1999) 461]. The new bibliography at the end of the paper contains approximately 670 references to papers and conference proceedings on the subject that were published in 1998±2001. These are classi®ed in the following categories: linear and nonlinear, static and dynamic, stress and de¯ection analyses; stability problems; thermal problems; fracture mechanics problems; contact problems; ¯uid±structure interaction problems; manufacturing of pipes and tubes; welded pipes and pressure vessel components; development of special ®nite elements for pressure vessels and pipes; ®nite element software; and other topics. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Finite element; Bibliography; Pressure vessels; Pipes; Linear and nonlinear static and dynamic analysis; Fracture mechanics; Contact problems; Thermal problems; Fluid±structure interaction; Welding Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Finite elements in the analysis of pressure vessels and piping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Linear and nonlinear, static and dynamic, stress and de¯ection analyses (STR) . . . . . . . . . . . . . . . . . . . . . . . 2.2. Stability problems (STA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Thermal problems (THE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Fracture mechanics problems (FRA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Contact problems (CON) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Fluid±structure interaction problems (FLU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7. Manufacturing of pipes and tubes (MAN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8. Welded pipes and pressure vessel components (WEL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.9. Development of special ®nite elements for pressure vessels and pipes (ELE) . . . . . . . . . . . . . . . . . . . . . . . . 2.10. Finite element software (SOF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.11. Other topics (OTH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A. A bibliography (1998±2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1. Linear and nonlinear, static and dynamic, stress and de¯ection analyses (STR) . . . . . . . . . . . . . . . . . . . . . . . A.2. Stability problems (STA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.3. Thermal problems (THE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.4. Fracture mechanics problems (FRA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.5. Contact problems (CON) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.6. Fluid±structure interaction problems (FLU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.7. Manufacturing of pipes and tubes (MAN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . * Tel.: 146-13-28-1111; fax: 146-13-28-2717. E-mail address:
[email protected] (J. Mackerle). 0308-0161/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0308-016 1(01) 00128-4 1 2 2 3 3 3 3 3 3 4 4 4 4 4 4 4 9 10 11 19 21 21 2 J. Mackerle / International Journal of Pressure Vessels and Piping 79 (2002) 1±26 A.8. Welded pipes and pressure vessel components (WEL) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.9. Development of special ®nite elements for pressure vessels and pipes (ELE) . . . . . . . . . . . . . . . . . . . . . . . . A.10. Finite element software (SOF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.11. Other topics (OTH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Introduction Pressure vessels and piping are widely used in reactor technology, the chemical industry, marine and space engineering. They often operate under extremes of high and low temperatures and high pressures, are becoming highly sophisticated and therefore also need advanced methods for their analyses. Advances are also made with materials applied for their fabrication. Concrete and composite materials are used in pressure vessels and their components more frequently to replace, in some cases, conventional steels. During the last three decades considerable advances have been made in the applications of numerical techniques to analyze pressure vessels and piping problems. Among the numerical procedures, ®nite element methods are the most frequently used. Pressure vessel and piping analyses may have a variety of phases such as: elastic stress and deformation analysis where both mechanical and thermal loads may be applied; heat transfer analysis; dynamic analysis; plastic and creep analysis; etc. There is in existence a large number of general purpose and special purpose ®nite element programs available to cope with each phase of the analysis. This review on the subject is divided into the following parts and it concerns: ² linear and nonlinear, static and dynamic, stress and de¯ection analyses (STR); ² stability problems (STA); ² thermal problems (THE); ² fracture mechanics problems (FRA); ² contact problems (CON); ² ¯uid±structure interaction problems (FLU); ² manufacturing of pipes and tubes (MAN); ² welded pipes and pressure vessel components (WEL); ² development of special ®nite elements for pressure vessels and pipes (ELE); ² ®nite element software (SOF); ² other topics (OTH). The status of ®nite element literature published between 1976 and 2001, and divided into the categories described earlier, is illustrated in Fig. 1. Data presented in this ®gure include published technical papers in the primary literature; this means papers appearing in the various general and specialized journals, conference proceedings as well as theses and dissertations. If we take the number of published 22 24 24 24 26 papers as a measure of research activity in these various subjects, we can see the priority trend in research in the past. This paper is organized into two parts. In the ®rst, each subject listed above is brie¯y described by keywords where current trends in application of ®nite element techniques are mentioned. The second part, Appendix A, is a listing of references on papers published in the open literature for the period 1998±2001, retrieved from the author's database MAKEBASE [1,2]. Readers interested in the ®nite element literature in general are referred to Ref. [3] or to the author's Internet Finite Element Book Bibliography (http://www.solid.ikp.liu.se/fe/index.html). The presented bibliography is an addendum to the author's earlier bibliographies [4,5] where approximately 1900 and 630 references, respectively, have been listed. 2. Finite elements in the analysis of pressure vessels and piping 2.1. Linear and nonlinear, static and dynamic, stress and de¯ection analyses (STR) The main topics included deal with the static and dynamic ®nite element analyses of pressure vessels, their components and piping, namely: stress and deformation analysis; 2D and 3D linear elastic static and dynamic analysis; material and geometrical nonlinear static and dynamic analysis; shakedown analysis; stress concentration factor studies; local stresses and deformations; free vibration analysis; response to shock loading; cyclic loading; seismic response analysis; random excitation; vibro-impact dynamics; estimation of residual stresses; study of mechanical properties; creep relaxation; whipping analysis; constraint effects; prestressing effects; boundary conditions identi®cation; stiffness properties identi®cation; structural integrity. Applications to: pipes; tubes; pipelines; pressure vessels; Fig. 1. Finite elements and various topics in pressure vessels and piping (1976±2001). J. Mackerle / International Journal of Pressure Vessels and Piping 79 (2002) 1±26 reactor pressure vessels; curved pipes; cantilevered pipes; dented pipelines; multi-supported pipelines; saddlesupported pipelines and pressure vessels; sling-supported pressure vessels; pressure vessel heads; pressure vessel components; ¯anges; piping elbows; pipe bends; nozzles; bellows; perforated tubesheets; framed-tube systems; vertical pumps; conical reducers; burst discs; PWR cores; boilers; corroded pipes; submarine pipelines; pipeline crossings; in¯atable tubes; coaxial ¯exible tubes; tubes with coating; shell intersections. Materials under consideration: steels; stainless steels; aluminium; composites; polymers; ®lament wound composites; ®bre-reinforced composites; concrete-®lled steel tubes. 2.2. Stability problems (STA) Stability problems are the main subject of this section. Other topics included are: stability and instability; buckling; postbuckling; local buckling; lateral buckling; torsional buckling; lateral thermal buckling; high-temperature buckling; buckle propagation; collapse; plastic collapse. Applications to: pipes; tubes; pipelines; pressure vessels; ellipsoids and toroids; corroded pipes; braced tubes; elbows; liners; bellows; cone±cylinder intersections; buckle arrestors. Materials: steels; low-alloy steels. 2.3. Thermal problems (THE) Heat transfer problems and thermomechanical ®nite element analyses are the main subjects of this section. The following topics are included: heat transfer analysisÐ natural convection, forced convection, mixed convection, radiation, turbulent problems; thermomechanical 2D and 3D analysis; thermoviscoplastic analysis; thermal deformation analysis; thermal shock; thermal ratchetting; transient and residual thermal stresses. Applications to: pipes; tubes; pressure vessels; reactor pressure vessels; PWR vessels; tube bundles; tubesheets; ®ns; pipe-cooling systems; liquid metal target container; boiler drums. Materials: steels; zircaloy; composites; glass reinforced plastics. 2.4. Fracture mechanics problems (FRA) In this section fracture mechanics and fatigue problems are handled. The listing of references in Section A.4 includes: linear and nonlinear 2D and 3D static and dynamic fracture mechanics problems; mechanical and thermal loading; macromechanical and micromechanical studies; cracks; multiple cracks; crack growth; crack opening; crack path bifurcation; crack arrest; crack shape development; circumferential cracks; longitudinal cracks; transverse cracks; axial cracks; surface cracks; through-wall cracks; part-through cracks; tight cracks; ductile fracture; brittle fracture; residual strength; ultimate strength; fracture 3 toughness; fatigue studies; thermal fatigue; multi-axial fatigue; damage; local damage; damage identi®cation; creep-damage analysis; creep failure; failure behaviour; cleavage failure; damage tolerance; creep crack growth; ¯aws; ¯aw detection; cladding effects; leak-before-break; load bearing capacity; limit load analysis; wave scattering; ring test; squash test; wide-plate test; failure probability; stochastic analysis; autofrettage; parametric studies. Applications to: pipes; tubes; pipelines; pressure vessels; reactor pressure vessels; bellows; elbows; nozzles; pump casing; threaded pressure vessels; pressure vessel closures; ring joint groove; tube-gusset plate connections; adhesively bonded connections; reinforced branch connections; ¯ange joints; welded pipes; pipe couplers; pipe piers; crushed tubes; corroded pipes; shell intersections; concrete containments. Materials: steels; stainless steels; low-alloy steels; aluminium; zircaloy; zirconium; concrete; composites; ®brereinforced composites; polymers; PVC; graphite±epoxy; refractory; functionally graded materials. 2.5. Contact problems (CON) 2D and 3D ®nite element studies of static and dynamic contact problems dealing with pipes and pressure vessels are included in this section. Other subjects under consideration are: mechanical behaviour of joints; structures under impact loading; blast loading effects; stress concentration factors; expansion and residual contact pressure. Applications to: pipes; tubes; pressure vessels; reactor pressure vessels; tube-to-tubesheet joints; reinforced nozzle connections; gasket seal rings; cylindrical shell connections; casing-tubing connections; threaded connections; bolted joints; bonded connections; adhesive butt joints; pipe ¯ange connections; press ®t joining; piping branch junctions; multi-connected systems. Materials: steels; stainless steels; aluminium; composites. 2.6. Fluid±structure interaction problems (FLU) The main topics include: coupled ¯uid±structure response analyses; pipe/tube conveying ¯uids; cross-¯owinduced vibrations; modal analysis and damping; active modal control; dynamic analysis of ¯uid-®lled pipes; ¯uid±structure interaction under cavitation; large displacement ¯uid±structure interaction; Stokes ¯ow problems; internal unsteady ¯ow; gas±solid ¯ow; instability analysis. Applications to: pipes; tubes; pressure vessels; tube bundles; submerged perforated tubes; cylindrical shells. Materials: steels; composites; elastomers; ¯uids; hot liquid sodium; high temperature ¯uids. 2.7. Manufacturing of pipes and tubes (MAN) The ®nite element simulation of manufacturing processes is the subject of this section. The main topics listed are: material characteristics and formability; spring-back analysis; drawing; bulge forming; hot extrusion process; isostatic 4 J. Mackerle / International Journal of Pressure Vessels and Piping 79 (2002) 1±26 pressing; hydro-bulge forming; roll bending; rolling; extruding±bulging process; cold upsetting±extruding; dieless forming; hydroforming; backward tube spinning; local induction heating; pressure ®ltrating process; hydraulic bulge testing. Applications to manufacturing of: pipes; tubes; pressure vessels and closures; non-circular tubes; tube ¯anges; pipe bends; toroidal shells; elbows. Materials: steels; stainless steels; metals; copper; tungsten; composites; silicon carbide; ferromagnetic materials. 2.8. Welded pipes and pressure vessel components (WEL) The subjects in the simulation of welding processes included here are: 2D and 3D thermomechanical analysis; heat transfer analysis; shrinkage analysis; assessment of creep behaviour; residual stresses; effect of welding conditions on residual stresses; measurement of residual stresses; burn-through prediction; effects of repair; friction welding; seam welds; butt welds; multi-pass butt welds; multi-pass girth welds; circular patch welds; spiral weld cladding; bimetallic welds; wet repair welding. Welding of: pipes; tubes; pressure vessels; reactor pressure vessels; pipe-to-pipe; nozzles on spheres; pipe±¯ange. Materials: steels; stainless steels; austenitic steels; bimetallic materials. 2.9. Development of special ®nite elements for pressure vessels and pipes (ELE) In this section, references dealing with development as well as applications of special ®nite elements used for analyses of pressure vessels and piping systems are given. The element types included are: experiences with various types of elements; 3D special shell element; axisymmetric thin shell element; axisymmetric hybrid-stress±displacement element; enhanced pipe elbow element; interface beam element. 2.10. Finite element software (SOF) At present, thousands of ®nite element software packages exist and new programs are under development. The existing software can vary from large, sophisticated, general purpose, integrated systems to small, special purpose programs for PCs. Most of these programs have been mentioned and described in Ref. [4]. In Section A.10 some new references dealing with development/applications of FE software are listed. They are concerned with: code developments for pressure vessels and piping, code evaluations, users' experiences, etc. 2.11. Other topics (OTH) In this section, subjects not treated earlier are included. They deal with: static and dynamic geomechanical analyses of pressure vessels and pipes in 2D and 3D; buried structures; soil±structure interaction; seismic studies; inspection and maintenance; nondestructive testingÐeddy current, neutron diffraction; health monitoring; design sensitivity analysis; structural integrity assessment; pipeline bundles on seabed; reliability analysis; optimization problems. Applications to: crossbores; high-curvature well bores; steam generator tubes; evacuation pipes; offshore pipelines; pile-supported buried pipelines; metal beverage containers; pressure vessels with embedded sensors. Materials: steels; composites; braided composites; ®lament wound composites. Acknowledgements The bibliography presented in Appendix A is by no means complete, but it gives a comprehensive representation of different ®nite element applications on the subject. The author wishes to apologize for the unintentional exclusions of missing references and would appreciate receiving comments and pointers to other relevant literature for a future update. Appendix A. A bibliography (1998±2001) This bibliography provides a list of literature references on ®nite element analysis of pressure vessel structures/ components and pipes/tubes. The listings presented contain papers published in scienti®c journals and conference proceedings retrospectively to 1998. References have been retrieved from the author's database, MAKEBASE. They are grouped into the same sections described in the ®rst part of this paper, and are sorted alphabetically according to the ®rst author's name. In some cases, if a speci®c paper is relevant to several subject categories, the same reference is listed under the respective section headings. A.1. Linear and nonlinear, static and dynamic, stress and de¯ection analyses (STR) 1. STR Abdel-Hamid AN, Farahat WA. Evaluation of stresses in piping systems subjected to unspeci®ed random excitation. 17th Int Modal Anal Conf. Kissimmee: IMAC, 1999. p. 463±9. 2. STR Abdel-Haq M, et al. Constraint effects on energy absorption in unidirectional PMC tubes. J Compos Mater 1999;33(9):774±93. 3. STR Abhary K, et al. Exact analytical method for stress analysis of pipelines. Int J Press Vess Piping 1999; 76(8):561±5. 4. STR Afshari P, Widera GEO. Free vibration analysis of composite plates. J Press Vess Technol, ASME 2000; 122(3):390±8. 5. STR Al-Hassani STS, Vartdal B. Investigation into the effect of circumferential through-wall slits on a cantilevered pipe subjected to a transverse end load. Proc Inst Mech Engng, Part E 1998;212(3):163±70. 6. STR Alexander CR. Analysis of dented pipelines J. Mackerle / International Journal of Pressure Vessels and Piping 79 (2002) 1±26 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. considering constrained and unconstrained dent con®gurations. 1999 ASME Energy Sources Technology Conference, Houston. New York: ASME, 1999. p. 1±13. STR Alleyne DN, et al. The re¯ection of guided waves from circumferential notches in pipes. J Appl Mech, ASME 1998;65(3):635±41. STR Averbuch D, et al. Implementation of elastoplastic material laws in dynamic riser analysis with applications to reeled pipes. 9th International Offshore Polar Engineering Conference, ISOPE, vol. 2. 1999. p. 272±7. STR Babu S, Iyer PK. Inelastic analysis of components using a modulus adjustment scheme. J Press Vess Technol, ASME 1998;120(1):1±5. STR Babu S, Iyer PK. A robust method for inelastic analysis of components made of anisotropic material. J Press Vess Technol, ASME 1999;121(2):154±9. STR Badr EA, et al. An analytical procedure for estimating residual stresses in blocks containing crossbores. Int J Press Vess Piping 2000;77(12):737±49. STR Baniotopoulos CC, Preftitsi F. In¯uence of the design parameters on the stress state of saddlesupported pipelines: an arti®cial neural network approach. Int J Press Vess Piping 1999;76(7):401±9. STR Beltman WM, et al. The structural response of cylindrical shells to internal shock loading. J Press Vess Technol, ASME 1999;121(3):315±22. STR Betten J, Krieger J. Bestimmung des Aushartungsein¯usses bei FVK-Bauteilen mittels FEA. ZAMM 1999;79(S3):855±6. STR Binienda WK, Wang Y. Residual stress reduction in ®lament wound composite tubes. J Reinf Plast Compos 1999;18(8):684±701. STR Blachut J, Jaiswal OR. On the choice of initial geometric imperfections in externally pressurized shells. J Press Vess Technol, ASME 1999;121(1):71±6. STR Burdekin FM, Lidbury DPG. Views of TAGSI on the current position with regard to bene®ts of warm prestressing. Int J Press Vess Piping 1999;76(13):885± 90. STR Carter P. Stress analysis and design for cyclic loading. J Press Vess Technol, ASME 2000;122(4); 427±30. STR Chan WS, Demirhan KC. A simple closed-form solution of bending stiffness for laminated composite tubes. J Reinf Plast Compos 2000;19(4):278±91. STR Chawla DS, et al. Assessment of operability and structural integrity of a vertical pump for extreme loads. Int J Press Vess Piping 1998;75(4):297±306. STR Cohn MJ, Yee RK. Creep relaxation behavior of high energy piping. ASME/JSME Joint Pressure Vessel Piping Conference PVP 380, New York: ASME, 1998. p. 135±50. STR Cunha J, Piranda J. Identi®cation of stiffness pro- 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 5 perties of composite tubes from dynamic tests. Exp Mech 2000;40(2):211±8. STR Da Dilveira JLL, et al. Shakedown and limit analysis in a pressure vessel. Fourth World Cong Comput Mech, Buenos Aires, 1998. p. 198. STR Datta TK. Seismic response of buried pipelines: a state-of-the-art review. Nucl Engng Des 1999; 192(2/3):271±84. STR Desikan V, Sethuraman R. Analysis of material nonlinear problems using pseudo-elastic ®nite element method. J Press Vess Technol, ASME 2000;122(4):457±61. STR El-Abbasi N, et al. Three-dimensional ®nite element analysis of saddle supported pressure vessels. Int J Mech Sci 2001;43(5):1229±42. STR Filippov SB, et al. Free vibrations of square elastic tubes with a free end. Mech Res Commun 2000; 27(4):457±64. STR Franco JRQ, Barros FB. Advances in ®nite element modelling of plastic behaviour of pressure vessels. 4th World Cong Comput Mech, Buenos Aires. 1998. p. 185. STR Frikha S, et al. Boundary condition identi®cation using condensation and inversionÐapplication to operating piping network. J Sound Vib 2000;233(3):495±514. STR Fyrileiv O, et al. Free span assessment of the Zeepipe IIA pipeline. 17th Int Conf Offshore Mech Arctic Engng. Lisbon: OMAE, 1998. p. 1±8. STR Goncalves JPM, De Castro PMST. Application of the line spring model to some complex geometries, and comparison with three-dimensional results. Int J Press Vess Piping 1999;76(8):551±60. STR Hajjar JF, et al. Distributed plasticity model for concrete-®lled steel tube beam-columns with interlayer slip. Engng Struct 1998;20(8):663±76. STR Halldorsson B. On modeling of earthquake wave motion and its effects on multi-support pipelines. Acta Polytech Scand, Civ Engng Build Cons 1999;(115):1± 29. STR Hamilton R, et al. A simple upper-bound method for calculating approximate shakedown loads. J Press Vess Technol, ASME 1998;120(2):195±9. STR Hari Y, Williams DK. Analysis of transition radii in conical reducers. ASME/JSME Joint Press Vess Piping Conf PVP 360. New York: ASME, 1998. p. 335±42. STR Hauch S, Bai Y. Bending moment capacity of groove corroded pipes. 10th Int Offshore Polar Engng Conf, Seattle. 2000. p. 253±62. STR Hersh CL, Herakovich CT. Local effects in stiffened composite tubes under generalized plane deformation. J Compos Mater 1999;33(5):420±42. STR Hsieh CS, et al. Investigation of ¯anges subjected to operating conditions of pressure, temperature and bending moments. ASME/JSME Joint Press Vess Piping Conf PVP 368. New York: ASME, 1998. p. 245±57. 6 J. Mackerle / International Journal of Pressure Vessels and Piping 79 (2002) 1±26 39. STR Hsu PW. Stresses in a uniformly paralelepiped solid with a pressurized cylindrical cavity. 42nd Str, Str Dyn Mater Conf, Seattle. 2001. p. 2947±50. 40. STR Hu G, et al. Mechanical behaviour of ®lamentwound glass-®bre/epoxy-resin tubes. III. Macromechanical model of the macroscopic behaviour of tubular structures. Compos Sci Technol 1998;58(1): 19±29. 41. STR Hyer MW, Riddick JC. Internal pressure loading of segmented-stiffness composite cylinders. Compos Struct 1999;45(4):311±20. 42. STR Jacquelin E, et al. Modelling the behaviour of a PWR core by a homogenization technique. Comp Meth Appl Mech Engng 1999;155(1/2):1±13. 43. STR Jones DP, Holliday JE. Elastic±plastic analysis of the PVRC burst disk tests with comparison to the ASME code primary stress limits. J Press Vess Technol, ASME 2000;122(2):146±51. 44. STR Jones DP, et al. Application of equivalent elastic methods in three-dimensional ®nite element structural analysis. J Press Vess Technol, ASME 1999;121(3): 283±90. 45. STR Kabir MZ. Computer analysis of ®lament overwrapped metallic pressure vessels with an optimum head shape. 6th Int Conf Comput Meth Compos Mater, Montreal. Southampton: CMP, 1998. p. 483±92. 46. STR Kabir MZ. Finite element analysis of composite pressure vessels with a load sharing metallic liner. Compos Struct 2000;49(3):247±55. 47. STR Kalliontzis C. Non-linear ®nite element simulations of highly curved submarine pipelines. Commun Numer Meth Engng 1998;14(11):1067±88. 48. STR Kalliontzis C. Geometric nonlinear modelling of submarine pipeline crossings. Int J Offshore Polar Engng 1998;8(4):292±302. 49. STR Kardaras C, Lu G. Finite element analysis of thin walled tubes under point loads subjected to large plastic deformation. Key Engng Mater 2000;177±180: 733±8. 50. STR Knudsen J, Massih AR. Vibro-impact dynamics of a periodically forced beam. J Press Vess Technol, ASME 2000;122(2):210±21. 51. STR Koerner JP, Hiller W. Elastic±plastic ®nite element analysis of high pressure components in low density polyethylene plants. ASME/JSME Joint Press Vess Piping Conf PVP 371. New York: ASME, 1998. p. 17±22. 52. STR Koh BK, Park GJ. Analysis and optimization of bellows with general shape. J Press Vess Technol, ASME 1998;120(4):325±33. 53. STR Konno K, et al. Study on mechanical property of prestressed concrete encased by double steel tubes subjected to axial forces. Proc Jpn Soc Civil Engng 1999;613(V):1±18. 54. STR Kosasayama H, et al. New stress analysis procedure for piping with refractory lining. ASME/JSME Joint 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. Press Vess Piping Conf PVP 368. New York: ASME, 1998. p. 201±10. STR Kristiansen NO, et al. Structural modelling of multispan pipe con®gurations subjected to vortex induced vibrations. 8th Int Offshore Polar Engng Conf, Montreal, vol. 2. 1998. p. 127±33. STR Kumar R, Saleem MA. Bend angle effect on B2 and C2 stress indices for piping elbows. J Press Vess Technol, ASME 2001;123(2):226±31. STR Kussmaul K, Mayinger W. Numerical and experimental analyses of the behaviour of a nozzle with thermal sleeve under strati®ed ¯ow. Nuclear Engng Des 1999; 190(1/2):127±40. STR Lengsfeld M, et al. Spring rates for low type tank nozzles. ASME/JSME Joint Press Vess Piping Conf PVP 368. New York: ASME, 1998. p. 275±80. STR Lengsfeld M, et al. Alternate method to determine ®xed tube sheet thickness. ASME/JSME Joint Press Vess Piping Conf PVP 368. New York: ASME, 1998. p. 41±6. STR Liang CC, et al. 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Finite element analysis of pipeline bundles on uneven seabed. 8th Int Offshore Polar Engng Conf, Montreal, vol. 2. 1998. p. 46±52. OTH Guo R, Li G. Study of mechanical law of omega type section of buried heating pipe. J Tsinghua Univ 1998;38(1):23±7. OTH Hofstetter G, et al. Design of pile-supported buried pipelines by a synthesis of FE ultimate load analyses and experimental investigations. Finite Elem Anal Des 1999;32(2):97±111. OTH Igland RT, Moan T. Reliability analysis of pipelines during laying, considering ultimate strength under combined loads. 17th Int Conf Offshore Mech Arctic Engng. Lisbon: OMAE, 1998. p. 1±8. OTH Igland RT, Moan T. Reliability analysis of pipelines during laying, considering ultimate strength under combined loads. J Offshore Mech Arctic Engng, ASME 2000;122(1):40±6. OTH Inoue K, et al. Neutron diffraction measurement and ®nite element method calculation of residual stress of a heat treated steel pipe. Jpn J Appl Phys I 2000;39(12A):6652±7. 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