A New Approach to Reduce Transverse Shear Locking of Reissner–Mindlin Plate Based on The Cell-Centered Finite Element Method

Abstract

This study investigates a new approach to solve a shear locking free on a low-order cell-centered finite element method (FECC) of the Reissner–Mindlin plate. The proposed method pursues the Lagrange piecewise of linear polynomial functions to attain the transverse displacement and rotations on the dual sub-mesh derived from the general one. The suggested theory is employed in numerical computation to verify the effectiveness and accurate performance. Detailed studies are carried out on several mesh types to compare with the analytical solutions reported by the low-order mimetic finite difference method [Beir ao Da Veiga, L., Lovadina, C. and Mora, D. [2013] “Numerical results for mimetic discretization of Reissner–Mindlin plate problems,” Calcolo 50, 209–237] and high-order mixed finite element methods [Chinosi, C. and Lovadina, C. [1995] “Numerical analysis of some mixed finite element methods for Reissner–Mindlin plates,” Comput. Mech. 16, 36–44]. The numerical results indicated that the present scheme based on the low-order FECC approximation can effectively predict on even the distorted meshes, satisfy the optimized convergence and be uniformly stable to the thin plate thicknesses.