Elastoplastic buckling analyses of rectangular plates under biaxial loadings by the differential qudrature method

The paper investigates the elastoplastic buckling behavior of thin rectangular plates under biaxial loadings by using the differential quadrature (DQ) method for the first time. Both J2′ flow and deformation plasticity theories are adopted and iteration processes are involved due to the material non-linearity. The methodology and procedures are worked out in detail. The buckling behavior of thin rectangular plates with various combinations of boundary conditions and under various loadings is studied. It is found that the DQ results are compared well with existing analytical solutions for plates with two boundaries simply supported and the others either simply supported or clamped. Buckling loads for plates with other combinations of boundary conditions, no analytical solutions are available in such cases, are also presented. The existence of an optimal loading path for the deformation theory model, firstly reported by Durban and Zuckerman, is also observed in such cases. The possible reason is given to explain the large discrepancy in predictions for thicker plates by the J2′ flow theory and deformation plasticity theory.