Error analysis of quadrilateral Wilson element for Reissner–Mindlin plate Original Research Article

In this paper, we generalize the rectangular nonconforming Wilson element method proposed in [Z. Zhang, S. Zhang, Wilson element for the Reissner–Mindlin plate,Comput. Methods Appl. Mech. Engrg. 113 (1994) 55–65] for the Reissner–Mindlin plate problem to the general quadrilateral mesh and analyze the error. It is proved that this method converges at uniformly optimal rates with respect to both the energy and image norms. These estimates improve those of [Z. Zhang, S. Zhang, Wilson element for the Reissner–Mindlin plate, Comput. Methods Appl. Mech. Engrg. 113 (1994) 55–65] in the sense that the requirement of image regularity on the solution is dropped, and that the image error estimate of this scheme is analyzed. The numerical examples at the end of this paper demonstrate the superiority of this method over the MITC4 [K.J. Bathe, E. Dvorkin, A four-node plate bending element based on Mindlin–Reissner plate theory and a mixed interpolation, Int. J. Numer. Methods Engrg. 21 (1985) 367–383].