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

Hu, Jun; Shi, Zhong-Ci

doi:10.1090/S0025-5718-07-01952-7

Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate
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by Jun Hu and Zhong-Ci Shi PDF

Math. Comp. 76 (2007), 1771-1786 Request permission

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

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