Postbuckling response and ultimate strength of a compressed rectangular elastic plate using a 3-D Cosserat brick element

The objective of this paper is to obtain a fairly exact solution of the problem of the large deformation postbuckling response of a simply supported, compressed, initially rectangular elastic plate. Here, a numerical solution is obtained using a 3-D Cosserat brick element which has eight nodes. This element admits full material and geometric nonlinearity so that the deformed postbuckled configuration is treated as a general shell. The results of this analysis suggest a new physical description of the postbuckling process leading to the ultimate strength of a compressed plate. Specifically, the numerical solutions predict that as the load is increased, plate bulging causes lateral tension whose magnitude is limited by mode shape transitions which cause the plate to subdivide into smaller cells. These cells can be short and wide as opposed to square, as predicted by the small deformation bifurcation equations for a long plate. The ultimate strength occurs when yielding precedes further subdivision. Also, the lateral tension that develops at the plate's edges in the calculations indicates a potential mechanism for added flexibility at simply supported edges in experiments on plates.