A Locking-Free and Reduction-Free Conforming Finite Element Method for the Reissner-Mindlin Plate on Rectangular Meshes

Abstract

A family of conforming finite elements are designed on rectangular grids for solving the Reissner-Mindlin plate equation. The rotation is approximated by $C^1-Q_{k+1}$ in one direction and $C^0-Q_k$ in the other direction finite elements. The displacement is approximated by $C^1-Q_{k+1,k+1}$. The method is locking-free without using any projection/reduction operator. Theoretical proof and numerical confirmation are presented.

Funding

National Natural Science Foundation of China(12131005)