Finite Element Analysis for Combined Material and Geometric Nonlinearities
For a number of years, the author has used the finite element method to investigate the collapse strength of thin plated steel structures [1–3]. The work has been directed primarily towards steel bridges which are usually fabricated from engineering steel for which the stress-strain curve exhibits a significant plateau. The collapse behaviour usually involves an interaction between material and geometric non-linearities and is influenced by initial geometric imperfections and residual welding stresses. The present communication describes a number of numerical techniques that the author has developed in order to analyse such structures. The topics covered include approximate yield criteria, accelerated iterative methods and incremental solutions using a ‘length constraint’.
KeywordsYield Surface Residual Welding Stress Length Constraint Steel Bridge BFGS Method
Unable to display preview. Download preview PDF.
- 1.Crisfield, M.A.: Large deflection elasto-plastic buckling analysis of plates using finite elements. TRRL Report LR 598, Crowthorne, England, (1973).Google Scholar
- 2.Crisfield, M.A. and Puthli, R.S.: Approximations in the non-linear analysis of thin plated structures. Finite elements in non-linear mechanics, Vol. 1, Tapir Press, Trondheim, (1978) 373–392.Google Scholar
- 3.Crisfield, M.A.: The automatic nonlinear analysis of stiffened plates and shallow shells using finite elements. Proc. Instn. Civ. Engrs., Part 2, Paper 8335, to be published (Sept. 1980).Google Scholar
- 7.Ilyushin, A.: Plasticité. Editions Eyrolles, Paris, (1965).Google Scholar
- 9.Crisfield, M.A.: On an approximate yield criterion for thin shells. TRRL Report LR 658, Crowthorne, England (1974).Google Scholar
- 10.Ivanov, E.V.: Inzhenernyi Zhurnal Mekhanika Tverdogo Tela. 6 (1967) 74–75.Google Scholar
- 11.Crisfield, M.A.: Ivanov’s yield criterion for thin and shells using finite elements. TRRL Report LR 919, Crowthorne, England (1979).Google Scholar
- 13.Crisfield, M.A.: Incremental/iterative solution procedures for nonlinear structural analysis. Int. Conf. Num. Meth. for Nonlinear Problems, Swansea (Sept. 1980).Google Scholar
- 14.Crisfield, M.A.: A fast incremental/iterative solution procedure that handles ‘snap through’. Symp. on Comp. Meth. in Nonlinear Struct. and Solid Mech., Washington, ( Oct. 1980 ).Google Scholar
- 19.Bergan, P.G.: Solution algorithms for nonlinear structural problems. Engineering Appls. of the Finite Element Method, Computas, Hovik, Norway, (1979) 13. 113. 39.Google Scholar