Finite Element Formulations for Buckling Analysis of Isotropic and Orthotropic Plates using Two-Variable Refined Plate Theory

In this paper, a finite element formulation based on two-variable refined plate theory is developed for buckling analysis of isotropic and orthotropic plates. The two-variable refined plate theory, which can be used for both thin and thick plates, predicts parabolic variation of transverse shear stresses across the plate thickness, satisfies the zero traction condition on the plate surfaces and does not need the shear correction factor. After constructing weak form equations using principle of minimum potential energy, a new four-node rectangular plate element with six degrees of freedom at each node is introduced for discretization of the domains. The uniaxial and biaxial buckling loads are obtained for simply supported isotropic plates. Also, the uniaxial buckling loads in two principal directions and the biaxial buckling loads are obtained for Levy-type orthotropic plates. Comparison of results with exact solutions and other common plate theories shows that besides the simplicity of presented finite element formulations, it presents accurate and efficient results. Also, the effects of orthotropy ratio, side-to-thickness ratio and types of boundary conditions on the buckling loads are studied.