Error analysis of quadrilateral Wilson element for Reissner-Mindlin plate

摘要

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 L~2 norms. These estimates improve those of [Z. Zhang, S. Zhang, Wilson element for the Reissner-Mindlin plate, Cornput. Methods Appl. Mech. Engrg. 113 (1994) 55-65] in the sense that the requirement of H~3(Ω) regularity on the solution is dropped, and that the L~2 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].