A high-performance parametrized mixed finite element model for bending and vibration analyses of thick plates

Abstract

Based on the parametrized mixed variational principle, a high-performance finite element model has been developed for bending and vibration analysis of thick plates. The proposed mixed variational formulation combines the concept of Reissner’s mixed variational theorem and Rong’s generalized mixed variational theorem. In addition to unknown parameters of the displacement fields, the transverse normal component of the stress tensor is also assumed as the independent field variable in the present variational formulation. The latter allows the fulfillment of the boundary conditions of the transverse normal stress at the top and bottom surfaces of the plate in a natural way. The variational constraint of the transverse normal strain–displacement relations is relaxed via the parametrized Lagrange multipliers method. The functional of the proposed variational formulation contains an arbitrary free parameter, called the splitting factor. Simple formulations have been proposed for selecting the splitting factor which leads to the results of higher precision. The numerical results obtained from the proposed mixed formulation have been compared with the results of three-dimensional (3D) theory of elasticity and other plate theories available in the literature. The comparison study shows that the proposed parametrized mixed plate theory is capable of achieving the accuracy of nearly exact 3D solutions.