A Finite Element Formulation for bending analysis of isotropic and orthotropic plates based on Two-Variable Refined Plate Theory

A finite element formulation based on two-variable refined plate theory has been developed in this paper and has been implemented for bending analysis of isotropic and orthotropic plates. The two-variable refined plate theory can be used for thin and thick plates and predicts parabolic variation of transverse shear stresses across the plate thickness. In this theory the zero traction condition on the plate surfaces is satisfied without using shear correction factor. The governing equations have been derived using the principle of minimum potential energy. After constructing weak form equations، a new 4-node rectangular plate element with six degrees of freedom at each node has been used for discretization of the domain. The finite element code is written in MATLAB and some benchmark problems have been solved. Comparison of results with exact solution and other common plate theories shows the accuracy and efficiency of presented finite element formulation.