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Analysis of some low order quadrilateral Reissner-Mindlin plate elements


Authors: Pingbing Ming and Zhong-ci Shi
Journal: Math. Comp. 75 (2006), 1043-1065
MSC (2000): Primary 65N30, 74K20
DOI: https://doi.org/10.1090/S0025-5718-06-01833-3
Published electronically: May 1, 2006
MathSciNet review: 2219018
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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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Additional Information

Pingbing Ming
Affiliation: LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55, Zhong-Guan-Cun East Road, Beijing, 100080, People’s Republic of China
Email: mpb@lsec.cc.ac.cn

Zhong-ci Shi
Affiliation: LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences, No. 55, Zhong-Guan-Cun East Road, Beijing, 100080, People’s Republic of China
Email: shi@lsec.cc.ac.cn

DOI: https://doi.org/10.1090/S0025-5718-06-01833-3
Keywords: Reissner-Mindlin plate, stabilized methods, locking-free
Received by editor(s): October 6, 2002
Received by editor(s) in revised form: February 5, 2005
Published electronically: May 1, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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