Exact solution for linear buckling of rectangular Mindlin plates

In the present paper, the Mindlin plate theory is used to study buckling of in-plane loaded isotropic rectangular plates with different boundary conditions. The novelty of the paper is that the analytical closed-form solution is developed without any use of approximation for a combination of six different boundary conditions; specifically, two opposite edges are simply supported and any of the other two edges can be simply supported, clamped or free. Monoaxial in-plane compressive loads on both directions are considered, as well as equal biaxial loads. The present analytical solution can be obtained with any required accuracy and can be used as benchmark. Dimensionless critical buckling loads and mode shapes are given for the six cases analyzed. The effect of boundary conditions, loading conditions, variations of aspect ratios and thickness ratios are examined and discussed in detail. Finally, based on comparison with previously published results, the accuracy of the results is shown.