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

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.