Stability analysis of simply-supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane stress solutions

The non-classical problem of buckling of a simply-supported rectangular plate due to various types of non-uniform compressive edge loads is analysed here. For each case, the elasticity solution for the internal in-plane stress field is obtained rigorously using a superposition of Airy's stress functions and also approximately using extended Kantorovich method. Subsequently, the convergent buckling loads are obtained using Galerkin's method. Results are presented to highlight the dependence of the total buckling load and the corresponding buckled shape on the edge load distribution, as well as to illustrate the applicability of the approximate plane stress solutions.