Plastic Buckling Analysis of Mindlin Plates using the Ritz Method

Abstract

This paper is concerned with the application of the Ritz method for the plastic buckling analysis of thick plates under uniform compressive stress. The plate may take any shape defined by polynomial functions. In order to capture the plastic behaviour, the most commonly used plasticity theories, namely the incremental (flow) theory of plasticity (IT) and the deformation theory of plasticity (DT), are adopted. The material properties of the plates are assumed to obey the Ramberg-Osgood stress strain relation. The effect of transverse shear deformation, which is significant in thick plates, is taken into account by using the Mindlin theory to model the plates. The convergence, validity and accuracy of the method are checked against existing analytical solutions for rectangular and triangular plates. It is found that the Ritz method is able to furnish accurate plastic buckling results for various plate shapes. The results obtained by the DT are found to be consistently lower than their IT counterparts.