A finite element solution of Bergan-Wang plate model

Abstract

Bergan-Wang approach has led to a formulation of the strain energy of a plate bending deflection as function of only the transversal deflection of the plate. In this paper, two rectangular plate bending finite elements are introduced, using new degrees of freedom based on Bergan-Wang approach for analysis of thin, moderately thick plates, in terms of this unique variable. The first element has four nodes with 24 DOF while the second has 36 DOF. These two elements are conforming in case of thin plates. Adopting the usual 3 boundary conditions of Reissner-Mindlin theory, variety of examples have been analysed for thin and moderately thick plate bending problems with plurality of finite element meshes and a variety of thickness to plate length ratios with different boundary conditions on sides. As typical characteristics of Bergan-Wang approach, there is no locking as the thickness decreases and convergence to the classical thin plate solution is achieved. Comparison with Reissner-Mindlin and 3D solutions supports the study.