Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides

The buckling of thin rectangular plates with non-linearly distributed compressive loading on two opposite sides received lesser attention than the one with uniformly or linearly distributed loads. The problem is considerably more complicated since it requires that first the plane elasticity problem be solved to obtain the distribution of in-plane stresses, and then the buckling problem is solved. Since it is difficult to obtain the analytical solutions accurately with a few series terms for the in-plane problem, very few analytical solutions have been available in the literature thus far. Therefore, the problem is analyzed by using differential quadrature (DQ) method. Detailed formulations and solution procedures are given herein. Nine combinations of boundary conditions and various aspect ratios are considered. Comparisons are made with finite element data obtained by NASTRAN with very fine meshes and existing analytical or numerical solutions. It is found that fast convergent rate can be achieved by the DQ method with non-uniform grids. And the first known accurate results are given herein.