Buckling and Post-buckling of Plates

Synonyms

Analysis of non-linear equilibria; Expansions methods near a bifurcation point; Linear bifurcation and weakly non-linear analyses in thin elastic bodies

Definition

An elastic plate is a thin, quasi two-dimensional elastic body, whose dimension in one direction (thickness) is much smaller than its dimensions in the perpendicular directions. By definition, and contrary to elastic shells, elastic plates are naturally planar i.e., do not bend out of their midplane. When subject to in-plane loading, plates can give rise to non-planar solutions by a symmetry-breaking bifurcation called buckling. Buckling and post-buckling analyses are concerned with the derivation of buckled solutions to plate theories in the neighborhood of a bifurcation point, using expansion methods.

Overview

Owing to their geometry, thin elastic plates can easily bend and are prone to rotations of moderate to large amplitude, even when subjected to relatively small loads. Linear elasticity theory is unable to...