Prediction of the elasto-plastic post-buckling strength of uniformly compressed plates from the fictitious elastic strain at failure

This paper discusses the use of the theory of elasticity to determine the post-buckling strength of uniformly loaded square simply supported thin (steel) plates with sinusoidal-shaped initial imperfections and longitudinal edges free to wave in plane. Based on the findings from a FEM parameter study two main types of failure are distinguished: edge failure and center failure. The parameters determining which failure mode occurs are explained using a simple two-strip model. To determine the elastic post-buckling behavior of plates a modified far post-buckling solution is proposed, which is simpler to use than the existing far post-buckling solutions reported in the literature, giving results with engineering accuracy for loads up to about three times the buckling load. It is shown that determining the post-buckling strength as the elastic load corresponding to first membrane yield (as is done in the effective width method) paradoxically gives reasonable results for plates failing by center failure, but very conservative results for plates failing by edge failure. For plates failing by edge failure a more accurate strength prediction is obtained by deriving empirical expressions for a fictitious elastic strain at failure.