Analysis of some low order quadrilateral Reissner-Mindlin plate elements

Four quadrilateral elements for the Reissner-Mindlin plate model are considered. The elements are the stabilized MITC4 element of Lyly, Stenberg and Vihinen [27], the MIN4 element of Tessler and Hughes [35], the Q4BL element of Zienkiewicz et al [39] and the FMIN4 element of Kikuchi and Ishii [21]. For all elements except the Q4BL element, a unifying variational formulation is introduced, and optimal H1 and L2 error bounds uniform in the plate thickness are proven. Moreover, we propose a modified Q4BL element and show that it admits the optimal H1 and L2 error bounds uniform in the plate thickness. In particular, we study the convergence behavior of all elements regarding the mesh distortion.