Elastoplastic buckling analysis of thick rectangular plates by using the differential quadrature method

The paper investigates the elastoplastic buckling behavior of thick rectangular plates by using the Differential Quadrature (DQ) method. Mindlin plate theory is adopted to take the transverse shear effect into considerations. Both incremental theory and deformation theory are employed. Due to the material non-linearity, iteration processes are involved for obtaining solutions. Detailed methodology and procedures are derived. The elastoplastic buckling behavior of thick rectangular plates with ten combinations of boundary conditions and under various loadings is studied. To verify the DQ solution procedures, DQ results are compared with existing analytical solutions for plates with two boundaries simply supported and the others simply supported, clamped, or free. Then the DQ method is used to obtain solutions of rectangular thick plates with other combinations of boundary conditions. Since no analytical solutions for such cases are available, the buckling loads obtained by the DQ method could serve as a reference. The phenomenon reported in the literature, namely, the deformation theory generally gives consistently lower buckling loads than the incremental theory and large discrepancy in predictions between the two theories exists with increasing of plate thickness. E/σ0E/σ0, and cc in the Ramberg–Osgood relations, is also observed for the cases studied herein. Apart from the phenomenon reported earlier by Durban that deformation theory predicted a progressively lower in-plane shear modulus as the level of plasticity increased, thus predicted lower buckling loads, another reason is given herein to explain the large discrepancy in predictions for thicker plates with the deformation theory and incremental theory.