Structural Engineering and Mechanics

  • 제38권6호
  • /
  • Pages.767-802
  • /
  • 2011
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A proposed set of popular limit-point buckling benchmark problems

  • 투고 : 2010.10.11
  • 심사 : 2011.03.09
  • 발행 : 2011.06.25
⟨ 이전 논문 다음 논문 ⟩

초록

Developers of new finite elements or nonlinear solution techniques rely on discriminative benchmark tests drawn from the literature to assess the advantages and drawbacks of new formulations. Buckling benchmark tests provide a rigorous evaluation of finite elements applied to thin structures, and a complete and detailed set of reference results would therefore prove very useful in carrying out such evaluations. Results are usually presented in the form of load-deflection curves that developers must reconstruct by extracting the points, a procedure which is often tedious and inaccurate. Moreover the curves are usually given without accompanying information such as the calculation time or number of iterations it took for the model to converge, even though this type of data is equally important in practice. This paper presents ten different limit-point buckling benchmark tests, and provides for each one the reference load-deflection curve, all the points necessary to recreate the curve in tabulated form, analysis data such as calculation time, number of iterations and increments, and all of the inputs used to obtain these results.

키워드

참고문헌

  1. ABAQUS. (2007), Version 6.7 Documentation, Dassault Systemes Simulia Corp.
  2. Abed-Meraim, F. (1999), "Sufficient conditions for stability of viscous solids", Comptes rendus de l'Academie des sciences. Serie IIb, mecanique, physique, astronomie, 327(1), 25-31. https://doi.org/10.1016/S1287-4620(99)80006-4
  3. Abed-Meraim, F. and Combescure, A. (2002), "SHB8PS - a new adaptive, assumed-strain continuum mechanics shell element for impact analysis", Comput. Struct., 80, 791-803. https://doi.org/10.1016/S0045-7949(02)00047-0
  4. Abed-Meraim, F. and Nguyen, Q.S. (2007), "A quasi-static stability analysis for Biot's equation and standard dissipative systems", Eur. J. Mech. - A/Solids, 26, 383-393. https://doi.org/10.1016/j.euromechsol.2006.06.005
  5. Abed-Meraim, F. and Combescure, A. (2009), "An improved assumed strain solid-shell element formulation with physical stabilization for geometric non-linear applications and elastic-plastic stability analysis", Int. J. Numer. Meth. Eng., 80, 1640-1686. https://doi.org/10.1002/nme.2676
  6. Abed-Meraim, F. and Combescure, A. (2011), "New prismatic solid-shell element: assumed strain formulation and hourglass mode analysis", Struct. Eng. Mech., 37, 253-256. https://doi.org/10.12989/sem.2011.37.2.253
  7. Alves de Sousa, R.J., Cardoso, R.P., Fontes Valente, R.A., Yoon, J.W., Gracio, J.J. and Natal Jorge, R.M. (2006), "A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness-Part II: Nonlinear applications", Int. J. Numer. Meth. Eng., 67, 160-188. https://doi.org/10.1002/nme.1609
  8. Areias, P.M.A., César de Sá, J.M.A., Conceição António, C.A. and Fernandes, A.A. (2003), "Analysis of 3D problems using a new enhanced strain hexahedral element", Int. J. Numer. Meth. Eng., 58, 1637-1682. https://doi.org/10.1002/nme.835
  9. Betsch, P., Gruttmann, F. and Stein, E. (1996), "A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains", Comput. Meth. Appl. Mech. Eng., 130, 57-79. https://doi.org/10.1016/0045-7825(95)00920-5
  10. Boutyour, E.H., Zahrouni, H., Potier-Ferry, M. and Boudi, M. (2004), "Bifurcation points and bifurcated branches by an asymptotic numerical method and Padé approximants", Int. J. Numer. Meth. Eng., 60, 1987- 2012. https://doi.org/10.1002/nme.1033
  11. Budiansky, B. (1974), "Theory of buckling and post-buckling behaviour of elastic structures", Adv. Appl. Mech., 14, 1-65. https://doi.org/10.1016/S0065-2156(08)70030-9
  12. Chen, Y.I. and Wu, G.Y. (2004), "A mixed 8-node hexahedral element based on the Hu-Washizu principle and the field extrapolation technique", Struct. Eng. Mech., 17, 113-140. https://doi.org/10.12989/sem.2004.17.1.113
  13. Cho, C., Park, H.C. and Lee, S.W. (1998), "Stability analysis using a geometrically nonlinear assumed strain solid shell element model", Finite Elem. Anal. Des., 29, 121-135. https://doi.org/10.1016/S0168-874X(98)00021-3
  14. Chroscielewski, J., Makowski, J. and Stumpf, H. (1992), "Genuinely resultant shell finite elements accounting for geometric and material non-linearity", Int. J. Numer. Meth. Eng., 35, 63-94. https://doi.org/10.1002/nme.1620350105
  15. Crisfield, M.A. (1981), "A fast incremental/iterative solution procedure that handles snap-through", Comput. Struct., 13, 55-62. https://doi.org/10.1016/0045-7949(81)90108-5
  16. DaDeppo, D.A. and Schmidt, R. (1975), "Instability of clamped-hinged circular arches subjected to a point load", J. Appl. Mech. Trans. ASME, 42, 894-896. https://doi.org/10.1115/1.3423734
  17. Eriksson, A., Pacoste, C. and Zdunek, A. (1999), "Numerical analysis of complex instability behaviour using incremental-iterative strategies", Comput. Meth. Appl. Mech. Eng., 179, 265-305. https://doi.org/10.1016/S0045-7825(99)00044-4
  18. Hauptmann, R. and Schweizerhof, K. (1998), "A systematic development of solid-shell element formulations for linear and non-linear analyses employing only displacement degrees of freedom", Int. J. Numer. Meth. Eng., 42, 49-69. https://doi.org/10.1002/(SICI)1097-0207(19980515)42:1<49::AID-NME349>3.0.CO;2-2
  19. Hitchings, D., Kamoulakos, A. and Davies, G.A.O. (1987), Linear Statics Benchmarks, National Agency for Finite Element Methods and Standards, Glasgow, UK.
  20. Hutchinson, J.W. and Koiter, W.T. (1970), "Post-buckling theory", Appl. Mech. Rev., 23, 1353-1366.
  21. Ibrahimbegovic, A. and Al Mikdad, M. (2000), "Quadratically convergent direct calculation of critical points for 3D structures undergoing finite rotations", Comput. Meth. Appl. Mech. Eng., 189, 107-120. https://doi.org/10.1016/S0045-7825(99)00291-1
  22. Killpack, M. and Abed-Meraim, F. (2011), "Limit-point buckling analyses using solid, shell and solid-shell elements", J. Mech. Sci. Tech., 25, 1105-1117. https://doi.org/10.1007/s12206-011-0305-3
  23. Kim, J.H. and Kim, Y.H. (2001), "A predictor-corrector method for structural nonlinear analysis", Comput. Meth. Appl. Mech. Eng., 191, 959-974. https://doi.org/10.1016/S0045-7825(01)00296-1
  24. Kim, J.H. and Kim, Y.H. (2002), "A three-node C0 ANS element for geometrically non-linear structural analysis", Comput. Meth. Appl. Mech. Eng., 191, 4035-4059. https://doi.org/10.1016/S0045-7825(02)00338-9
  25. Kim, K.D., Liu, G.Z. and Han, S.C. (2005), "A resultant 8-node solid-shell element for geometrically nonlinear analysis", Comput. Mech., 35, 315-331. https://doi.org/10.1007/s00466-004-0606-9
  26. Klinkel, S. and Wagner, W. (1997), "A geometrical non-linear brick element based on the EAS-method", Int. J. Numer. Meth. Eng., 40, 4529-4545. https://doi.org/10.1002/(SICI)1097-0207(19971230)40:24<4529::AID-NME271>3.0.CO;2-I
  27. Koiter, W.T. (1945), "On the stability of elastic equilibrium", Ph.D. Thesis, Delft. English translation NASA Techn. Trans. F10, 1967.
  28. Kouhia, R. and Mikkola, M. (1989), "Tracing the equilibrium path beyond simple critical points", Int. J. Numer. Meth. Eng., 28, 2923-2941. https://doi.org/10.1002/nme.1620281214
  29. Lee, S.L., Manuel, F.S. and Rossow, E.C. (1968), "Large deflection and stability of elastic frames", ASCE J. Eng. Mech. Div., 94, 521-533.
  30. Legay, A. and Combescure, A. (2003), "Elastoplastic stability analysis of shells using the physically stabilized finite element SHB8PS", Int. J. Numer. Meth. Eng., 57, 1299-1322. https://doi.org/10.1002/nme.728
  31. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elem. Anal. Des., 1, 3-20. https://doi.org/10.1016/0168-874X(85)90003-4
  32. Planinc, I. and Saje, M. (1999), "A quadratically convergent algorithm for the computation of stability points: The application of the determinant of the tangent stiffness matrix", Comput. Meth. Appl. Mech. Eng., 169, 89- 105. https://doi.org/10.1016/S0045-7825(98)00178-9
  33. Prinja, N.K. and Clegg, R.A. (1993), Assembly Benchmark Tests for 3-D Beams and Shells Exhibiting Geometric Non-Linear Behaviour, NAFEMS, Glasgow, UK.
  34. Ramm, E. (1981), "Strategies for tracing the nonlinear response near limit points", Nonlinear Finite Element Analysis in Structural Mechanics (Eds. Wunderlich, W., Stein, E. and Bathe, K.J.), Springer-Verlag, New York.
  35. Reese, S. (2007), "A large deformation solid-shell concept based on reduced integration with hourglass stabilization", Int. J. Numer. Meth. Eng., 69, 1671-1716. https://doi.org/10.1002/nme.1827
  36. Riks, E. (1979), "An incremental approach to the solution of snapping and buckling problems", Int. J. Solids Struct., 15, 529-551. https://doi.org/10.1016/0020-7683(79)90081-7
  37. Schreyer, H. and Masur, E. (1966), "Buckling of shallow arches", J. Eng. Mech. Div.-ASCE, 92, 1-19.
  38. Sharifi, P. and Popov, E.P. (1971), "Nonlinear buckling analysis of sandwich arches", J. Eng. Mech. Div.-ASCE, 97, 1397-1412.
  39. Smolenski, W.M. (1999), "Statically and kinematically exact nonlinear theory of rods and its numerical verification", Comput. Meth. Appl. Mech. Eng., 178, 89-113. https://doi.org/10.1016/S0045-7825(99)00006-7
  40. Sze, K.Y., Liu, X.H. and Lo, S.H. (2004), "Popular benchmark problems for geometric nonlinear analysis of shells", Finite Elem. Anal. Des., 40, 1551-1569. https://doi.org/10.1016/j.finel.2003.11.001
  41. Sze, K.Y. and Zheng, S.J. (2002), "A stabilized hybrid-stress solid element for geometrically nonlinear homogeneous and laminated shell analyses", Comput. Meth. Appl. Mech. Eng., 191, 1945-1966. https://doi.org/10.1016/S0045-7825(01)00362-0
  42. Thompson, J.M.T. and Hunt, G.W. (1973), A General Theory of Elastic Stability, Wiley, New York.
  43. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic Stability, McGraw-Hill, New York.
  44. Voce, E. (1948), "The relation between the stress and strain for homogeneous deformation", J. Inst. Metals, 74, 537-562.
  45. Wagner, W. and Wriggers, P. (1988), "A simple method for the calculation of post-critical branches", Eng. Comput., 5, 103-109. https://doi.org/10.1108/eb023727
  46. Wardle, B.L. (2006), "The incorrect benchmark shell buckling solution", Proceedings of the 47th AIAA Structures, Dynamics, and Materials Conference, Newport RI, doc. 2028.
  47. Wardle, B.L. (2008), "Solution to the incorrect benchmark shell-buckling problem", AIAA J., 46, 381-387. https://doi.org/10.2514/1.26698
  48. Weinitshke, H.J. (1985), "On the calculation of limit and bifurcation points in stability problems of elastic shells", Int. J. Solids Struct., 21, 79-95. https://doi.org/10.1016/0020-7683(85)90106-4
  49. Wriggers, P. and Simo, J.C. (1990), "A general procedure for the direct computation of turning and bifurcation points", Int. J. Numer. Meth. Eng., 30, 155-176. https://doi.org/10.1002/nme.1620300110

피인용 문헌

  1. Application of the continuum shell finite element SHB8PS to sheet forming simulation using an extended large strain anisotropic elastic–plastic formulation vol.82, pp.9, 2012, https://doi.org/10.1007/s00419-012-0620-x
  2. Comprehensive evaluation of structural geometrical nonlinear solution techniques Part I: Formulation and characteristics of the methods vol.48, pp.6, 2013, https://doi.org/10.12989/sem.2013.48.6.849
  3. A new assumed strain solid-shell formulation “SHB6” for the six-node prismatic finite element vol.25, pp.9, 2011, https://doi.org/10.1007/s12206-011-0710-7
  4. Assumed-strain solid–shell formulation for the six-node finite element SHB6: evaluation on non-linear benchmark problems vol.21, pp.1-2, 2012, https://doi.org/10.1080/17797179.2012.702430
  5. An Optimized Approach for Tracing Pre- and Post-Buckling Equilibrium Paths of Space Trusses pp.1793-6764, 2018, https://doi.org/10.1142/S0219455419500408
  6. Limit-point buckling analyses using solid, shell and solid-shell elements vol.25, pp.5, 2011, https://doi.org/10.1007/s12206-011-0305-3