A locking-free Reissner-Mindlin quadrilateral element
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Abstract:
On arbitrary regular quadrilaterals, a new finite element method for the Reissner-Mindlin plate is proposed, where both transverse displacement and rotation are approximated by isoparametric bilinear elements, with local bubbles enriching rotation, and a local reduction operator is applied to the shear energy term. This new method gives optimal error bounds, uniform in the thickness of the plate, for both transverse displacement and rotation with respect to $H^1$ and $L^2$ norms.References
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Additional Information
- Huo-Yuan Duan
- Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China
- Email: dhymath@yahoo.com.cn, hyduan@lsec.cc.ac.cn
- Guo-Ping Liang
- Affiliation: Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China
- Email: guoping@math03.math.ac.cn, ling@fegensoft.com
- Received by editor(s): July 19, 2002
- Received by editor(s) in revised form: March 17, 2003
- Published electronically: November 24, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Math. Comp. 73 (2004), 1655-1671
- MSC (2000): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-03-01619-3
- MathSciNet review: 2059730