Differential quadrature buckling analyses of rectangular plates subjected to non-uniform distributed in-plane loadings

The new version of differential quadrature method (DQM), proposed by the senior author recently, is used to obtain buckling loads of thin rectangular plates under non-uniform distributed in-plane loadings for the first time. Two steps are involved: (1) solve a problem in plane-stress elasticity to obtain the in-plane stress distributions and (2) solve the buckling problem under the loads obtained in step (1). The methodology and procedures are worked out in detail and buckling problems with loadings of non-uniform distributions are studied. Numerical studies are performed and the DQ results are compared well with analytical solutions and finite element results. This fact indicates that the DQ method can be employed for obtaining buckling loads of plates with other combinations of boundary conditions subjected to non-uniform distributed loadings.