NONCONFORMING ROTATED ${\mathcal Q}_1$ ELEMENT FOR REISSNER–MINDLIN PLATE

Abstract

A new locking-free low order nonconforming rectangular finite element for the Reissner–Mindlin plate is presented. It consists of the nonconforming rotated [Formula: see text] element for one of the rotation components and the conforming [Formula: see text] element for the other component together with the conforming [Formula: see text] for the deflection. This element gives optimal error bounds for all variables uniform in the plate thickness t with respect to the energy norm as well as the L 2 -norm. Moreover, we have derived another nonconforming rectangular element with optimal error bounds uniform in t provided [Formula: see text].