Static analysis of thick plates using a mixed parametried theory

A finite element model has been introduced for static bending analysis of thick plates based on a mixed plate variational formulation. A refined Reissner's mixed variational theoy is employed to derive the governing equations, in terms of the introduced transverse normal stress and displacement variables. The in-plane displacement components of the plate are described by a combination of polynomial and exponential terms. Concerning the transverse displacement component, a first-order polynomial is adopted. A second-order expansion is considered for the variations of the transverse normal component of the stress tensor along the thickness direction of the plate. The boundary conditions of shear and normal tractions on the top and bottom surfaces of the plate are exactly satisfied. Based on the proposed mixed plate theory, a four nodded compatible Hermitian rectangular element which ensures C1-type continuity of all unknown parameters of the plate along in-plane directions is employed. An arbitrary free parameter, called the splitting factor, appears in the functional of the proposed variational formulation. In the numerical part of the present paper, a simple formulation has been proposed for selecting the splitting factor which leads to the results of higher precision. Comparison of present bending results for thin and thick plates with results of the three-dimensional theory of elasticity and other plate theories available in literature reveals efficiency of the proposed parametrized mixed plate theory. Moreover, the proposed model has a high convergence rate and is computationally low cost.