An exact solution for stability analysis of orthotropic rectangular thin plate under biaxial nonlinear in-plane loading resting on Pasternak foundation

Abstract

In this research, the buckling analysis of orthotropic rectangular plate resting on Pasternak elastic foundation was studied, using Frobenius exact solution method. The plate is subjected to biaxial in-plane loading with non-uniform distribution. It is assumed that it is simply supported by two opposite sides, and the remaining two edges can have any arbitrary conditions. To extract the governing equations on the buckling of the plate, the classical plate theory based on Kirchhoff hypothesis is employed. According to Levy solution, the buckling equation is reduced to an ordinary differential equation. Frobenius method is exploited in the governing equation, and the eigenvalue equation is obtained, imposing the boundary conditions on the other two sides. By solving the eigenvalue equation, the dimensionless critical buckling loads are determined. The accuracy of presented results is validated by comparing with available results in previous studies and also finite element method. Furthermore, the influences of some parameters such as aspect ratio, the ratio of elasticity modulus of the plate in two in-plane directions, the type of non-uniform loading in two states of uniaxial and biaxial loadings, various combinations of boundary conditions, lateral and shear stiffness coefficients of elastic foundation are examined on critical buckling.