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

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