Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis

This paper introduces exact solutions for the buckling analysis of rectangular Mindlin plates subjected to uniformly and linearly distributed in-plane loading on two opposite edges simply supported resting on elastic foundation. The other two edges may be given any combination of free, simply supported, and clamped boundary conditions. In order to extract characteristic equations of the rectangular plate under in-plane load, and resting on elastic foundation, the analysis procedure is based on the Mindlin plate theory considering the first-order shear deformation effect, including plate-foundation interaction. The elastic foundation is considered as a Pasternak model with adding a shear layer to the Winkler model. Comparisons are first made with a few existing data to reveal the excellent accuracy of the present closed-form exact solution. Then, the influence of foundation stiffness coefficients and boundary conditions together with other plate parameters, such as aspect ratios, thickness to length ratios as well as loading factors, on the buckling in-plane load is comprehensively tabulated. In addition, the effect of the above-mentioned parameters on dimensionless critical buckling loads is graphically presented for a large range of aspect ratios. Finally, some 3-D plots of the mode shapes and their corresponding contour plots are depicted for the rectangular Mindlin plate.