Elastoplastic buckling of circular annular plates under uniform in-plane loading

This paper deals with the elastoplastic buckling of a circular annular plate, with various axially symmetric boundary conditions and uniform axially symmetric in-plane radial loads on the inner and outer edge. The analysis is based on the standard linear buckling equations and the material behaviour is modelled by the small strain J₂ flow and deformation theories of plasticity where an elastic linear hardening rheological model of the material is considered. The solutions are obtained using the equilibrium approach where the governing differential equation is solved by the finite difference method which leads to the determination of eigenvalues of a homogeneous system of linear equations. Elastoplastic buckling loads for axially symmetric and asymmetric buckling shape modes with m waves in the circumferential direction are calculated and compared for both theories of plasticity. For one case, an experiment was performed and the results were compared with theoretical predictions.