Buckling of shear deformable plates subjected to nonuniform in-plane forces

This chapter is concerned with the elastic buckling of thick plates under nonuniform in-plane loads. The effect of transverse shear deformation on the buckling load is allowed for by using the first- and third-order shear deformation plate theories. The effects of higher order nonlinear strain terms (curvature terms) are considered as well. The governing equations and the boundary conditions are derived by using the principle of minimum potential energy. The solution is obtained by the extended Kantorovich method in combination with the exact element method for stability analysis of compressed members. By considering several numerical examples, the buckling results from the two shear deformation theories are compared with those obtained by the classical thin plate theory and with published results. Several loading combinations of constant compressive load and in-plane moments applied in both directions are considered. The inclusion of the higher order curvature terms in the formulation is seen to reduce the buckling loads for square plates by up to 8% depending on the loading combination, the boundary conditions, and the thickness-to-plane dimensions ratio.