Buckling of rectangular plate with nonlinearly distributed compressive loading on two opposite sides: Comparative analysis and results

Buckling analysis of isotropic plates subjected to nonlinearly varying in-plane load in the x direction received lesser attention than the corresponding problem involving uniform or linearly varying in-plane load distributions. This problem was attempted by van der Neut and by Benoy. However, in their analyses, they considered an oversimplified in-plane solution by assuming the x-direction in-plane normal stress distribution to be the same at every plate section and the y-direction normal stress to be zero; that is, they completely ignored the "stress diffusion" phenomenon, which can be considerable in the case of moderate and high aspect ratios. In the present work, buckling analyses using the in-plane solutions as developed by Timoshenko and by Pickett, as well as a superposition method using a four-stress-function solution, and a numerical method were carried out and the results were compared.