3-D elasticity buckling solution for simply supported thick rectangular plates using displacement potential functions

• Exact solution of buckling of simply supported thick rectangular plats is presented.
• There isn't any simplifying assumption in regard to shear strain in thickness of plat.
• Increasing of plates thickness increases the buckling load and critical buckling mode.
• Increasing of plates thickness decreases buckling factor mode.
• Compression load in second direction decreases the critical buckling load and mode.

This paper concentrates on the elastic buckling of thick plates. The shear strains in thick structures such as thick plates are important and thus, cannot be neglected. On the other hand, shear strains in the analysis of thick plates leads to complicity of governing equations. In this paper, with the use of displacement potential functions, the governing equations are simplified to two partial differential equations for the potential functions, one of which is second order and the other is forth order. These PDEs are established for a rectangular isotropic body, so that they are applicable to any arbitrary thickness of plate with no limitation on its thickness ratio. By solving the governing differential equations using separation of variables method and satisfying the exact boundary conditions, an analytical solution is obtained for linear elastic buckling of simply supported rectangular thick plates, subjected to in-plane either uniaxial or biaxial static loads, one of which could also be tensile force. Then critical buckling load is expressed in terms of non-dimensional buckling factor. The results of this paper are compared with other analytical and numerical works for thin and moderately thick plates, and also with numerical works for thick plates, which proves an excellent agreement between the results of this paper and others.