Two lower order nonconforming quadrilateral elements for the Reissner-Mindlin plate

Abstract

This paper generalizes two nonconforming rectangular elements of the Reissner-Mindlin plate to the quadrilateral mesh. The first quadrilateral element uses the usual conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element enriched with the intersected term on each element to approximate the displacement, whereas the second one uses the enriched modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a more complicated shear force space to overcome the shear force locking, which will be described in detail in the introduction. We prove that both methods converge at optimal rates uniformly in the plate thickness t and the mesh distortion parameter in both the H 1 -and the L 2 -norms, and consequently they are locking free.