Analysis of some low order quadrilateral Reissner-Mindlin plate elements

Ming, Pingbing; Shi, Zhong-ci

doi:10.1090/S0025-5718-06-01833-3

Analysis of some low order quadrilateral Reissner-Mindlin plate elements
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by Pingbing Ming and Zhong-ci Shi PDF

Math. Comp. 75 (2006), 1043-1065 Request permission

Abstract:

Four quadrilateral elements for the Reissner-Mindlin plate model are considered. The elements are the stabilized MITC4 element of Lyly, Stenberg and Vihinen (1933), the MIN4 element of Tessler and Hughes (1983), the Q4BL element of Zienkiewicz et al. (1993) and the FMIN4 element of Kikuchi and Ishii (1999). For all elements except the Q4BL element, a unifying variational formulation is introduced, and optimal H$^1$ and L$^2$ error bounds uniform in the plate thickness are proven. Moreover, we propose a modified Q4BL element and show that it admits the optimal H$^1$ and L$^2$ error bounds uniform in the plate thickness. In particular, we study the convergence behavior of all elements regarding the mesh distortion.

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