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

In this paper, we propose two lower order nonconforming rectangular elements for the Reissner-Mindlin plate. The first one uses the conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element to approximate the displacement, whereas the second one uses the modified nonconforming rotated Q1 element to approximate both the rotation and the displacement. Both elements employ a projection operator to overcome the shear force locking. We prove that both methods converge at optimal rates uniformly in the plate thickness t in both the H1and L2-norms, and consequently they are locking free.