Buckling of rectangular plates subjected to nonlinearly distributed in-plane loading

The problem of buckling of a rectangular plate subjected to uniformly distributed in-plane compressive loading at each end goes back to the work of Bryan in 1890– 91. The same problem, for the case of linearly varying in-plane compressive loading at each end, was first treated by several European investigators about 90 years ago. The case of loading that is nonlinearly distributed along two opposite plate edges is considerably more complicated in that it requires that first the plane elasticity problem be solved to obtain the distribution of in-plane stresses. Then the buckling problem must be solved. This problem was claimed to have been solved by van der Neut in 1958 for a half-sine load distribution and later by Benoy for a parabolic distribution. However, their work was based on an incorrect in-plane stress distribution. Here is presented a solution for the half-sine load distribution on two opposite sides, based on a more realistic in-plane stress distribution. This distribution shows a decrease (diffusion) in axial stress as the distance from the loaded edges is increased. The buckling loads are calculated using Galerkin method and the results are compared with the inaccurate results in the literature.