CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM

doi:10.1016/S0252-9602(18)30760-4

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 450-470.doi: 10.1016/S0252-9602(18)30760-4

CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM

段火元¹, 马俊华²

1. School of Mathematics and Statistics, Collaborative Innovation Centre of Mathematics, Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

收稿日期:2016-06-17 修回日期:2017-01-02 出版日期:2018-04-25 发布日期:2018-04-25
作者简介:Huoyuan DUAN,E-mail:hyduan.math@whu.edu.cn;Junhua MA,E-mail:2015202010036@whu.edu.cn
基金资助:
The first author is supported by NSFC (11571266, 91430106, 11171168, 11071132), NSFC-RGC (China-Hong Kong) (11661161017).

CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM

Huoyuan DUAN¹, Junhua MA²

1. School of Mathematics and Statistics, Collaborative Innovation Centre of Mathematics, Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received:2016-06-17 Revised:2017-01-02 Online:2018-04-25 Published:2018-04-25
Supported by:
The first author is supported by NSFC (11571266, 91430106, 11171168, 11071132), NSFC-RGC (China-Hong Kong) (11661161017).

摘要/Abstract

摘要：

On triangle or quadrilateral meshes, two finite element methods are proposed for solving the Reissner-Mindlin plate problem either by augmenting the Galerkin formulation or modifying the plate-thickness. In these methods, the transverse displacement is approximated by conforming (bi)linear macroelements or (bi)quadratic elements, and the rotation by conforming (bi)linear elements. The shear stress can be locally computed from transverse displacement and rotation. Uniform in plate thickness, optimal error bounds are obtained for the transverse displacement, rotation, and shear stress in their natural norms. Numerical results are presented to illustrate the theoretical results.

关键词: Reissner-Mindlin plate, continuous element, triangle element, quadrilateral element, finite element method, uniform convergence

Abstract:

Key words: Reissner-Mindlin plate, continuous element, triangle element, quadrilateral element, finite element method, uniform convergence

段火元, 马俊华. CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM[J]. 数学物理学报(英文版), 2018, 38(2): 450-470.

Huoyuan DUAN, Junhua MA. CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM[J]. Acta mathematica scientia,Series B, 2018, 38(2): 450-470.

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CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM

CONTINUOUS FINITE ELEMENT METHODS FOR REISSNER-MINDLIN PLATE PROBLEM

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