Natural element approximation of Reissner–Mindlin plate for locking-free numerical analysis of plate-like thin elastic structures

A rotation-free mixed natural element approximation of Reissner–Mindlin plate for the locking-free numerical analysis of plate-like thin elastic structures is presented, motivated by the rotation-free approximation for plate- and shell-like elastic structures and the high smoothness of Laplace interpolation functions used in natural element method. The mid-surface deflection and the rotation of shear are directly approximated using Laplace interpolation functions, while the Voronoi polygon-wise constant curvatures and bending moments are indirectly computed by area-averaging the boundary integrals of deflection derivatives and rotation of shear. The present approximation of the deflection and rotation of shear of discretized Reissner–Mindlin plate bending problem is formulated according to the modified mixed Hu-Washizu principle. Through the numerical results, it is verified that the rotation-free mixed natural element approximation of only the deflection and rotation of shear successfully prevents shear locking in the numerical analysis of plate-like thin elastic structures.