Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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

Author(s): Jun Hu; Zhong-Ci Shi.
Journal: Math. Comp. 76 (2007), 1771-1786.
MSC (2000): Primary 65N30
Posted: May 24, 2007
MathSciNet review: 2336267
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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 in both the $H^{1}$ - and -norms, and consequently they are locking free.

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