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

Source abstract

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 Q 1 Q_{1} element to approximate the displacement, whereas the second one uses the modified nonconforming rotated Q 1 Q_{1} 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 t in both the H 1 H^{1} - and L 2 L^2 -norms, and consequently they are locking free.