A nonlinear finite element computer program for thin-walled members

Abstract

A nonlinear finite element computer program has been developed to analyse thin-walled metal structural members. The program has the ability to handle both geometrical and material nonlinearities so that the post-buckling behaviour and ultimate strength of members can be predicted. A bending-membrane rectangular element with six degrees of freedom at each node forms the basic type of element used in the program. Marguerre's shallow shell theory is adopted for the strain-displacement relationships and hence the bifurcation point at buckling can be bypassed by providing an initial inperfection. The finite element formulation is based on the total Lagrange coordinate system and the flow theory of plasticity. Explicitly shown in the paper is the formation of the tangent stiffness matrix and the tridiagonal block form of solution procedure. Two problems of a square tube and a channel section beam subjected to pure bending were tested and found to be in close agreement with previous theoretical work.