Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate |
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Authors: | Jun Hu Zhong-Ci Shi |
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Institution: | No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China ; No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China |
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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 element to approximate the displacement, whereas the second one uses the modified nonconforming rotated 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 - and -norms, and consequently they are locking free. |
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Keywords: | Reissner-Mindlin plate bilinear element rotated $Q_1$ element bubble function locking-free |
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