Post-Buckling Finite Element Analysis of Flat Plates

A finite element analysis procedure that is capable of yielding the initial and secondary critical buckling loads and corresponding buckling modes for thin elastic plates is presented. The solution procedure is based on an iterative solution of the geometrically nonlinear equilibrium equations. It is shown that this procedure will converge to the absolute minimum potential energy state possible for a symmetrical buckled mode if the plate is initially disturbed in a symmetrical mode. A method of determining the minimum potential energy state corresponding to an initially unsymmetrical mode is also included. Simple equations representing the basic uncoupled plate deflection forms and the relation between these forms and the final converged forms are also given. Numerical examples for square and rectangular plates subjected to several magnitudes of in-plane loading are presented and compared to available data.