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


Authors: Jun Hu and Zhong-Ci Shi
Journal: Math. Comp. 76 (2007), 1771-1786
MSC (2000): Primary 65N30
Published electronically: 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 $ t$ in both the $ H^{1}$- and $ L^2$-norms, and consequently they are locking free.


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Additional Information

Jun Hu
Affiliation: No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China
Address at time of publication: LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
Email: hujun@lsec.cc.ac.cn, hujun@math.pku.edu.cn

Zhong-Ci Shi
Affiliation: No 55, Zhong-Guan-Cun Dong Lu, Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing 100080, China
Email: shi@lsec.cc.ac.cn

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01952-7
Keywords: Reissner-Mindlin plate, bilinear element, rotated $Q_1$ element, bubble function, locking-free
Received by editor(s): July 5, 2005
Received by editor(s) in revised form: May 18, 2006
Published electronically: May 24, 2007
Additional Notes: This research was supported by the Special Funds for Major State Basic Research Project.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.