On the buckling of an isotropic rectangular plate uniformly compressed on two simply supported edges and with two free unloaded edges

This expository brief note elaborates on the solution to the buckling problem of a uniformly compressed rectangular plate for which the two opposite loaded edges and the unloaded edges are considered simply supported and free, respectively. While Reissner originally discussed briefly this problem in 1909, it was not until 1954 when Ishlinskii presented its rigorous mathematical solution in the form of a transcendental equation, the solution of which requires the use of an iterative numerical technique. Despite remaining almost unreferenced and unnoticed in the literature, the works of Reissner and Ishlinskii in connection with this specific stability problem are educationally instructive and practically relevant. Ishlinskii's solution forms the basis upon which a simple approximate closed-form solution, presented in this note, yields results that do not differ significantly from those computed iteratively using the transcendental equation. Results presented in this brief note can be used as benchmark solutions for validating structural engineering software packages.