数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (3): 815-825.doi: 10.1016/S0252-9602(11)60278-6

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NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

陈绍春, 郑艳君, 毛士鹏   

  1. Department of Mathematics, Zhengzhou University, Zhengzhou 450052, China|LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2009-09-11 出版日期:2011-05-20 发布日期:2011-05-20
  • 基金资助:

    September 11, 2009.  Supported by NSFC (11071226).

NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

 CHEN Shao-Chun, ZHENG Yan-Jun, MAO Shi-Peng   

  • Received:2009-09-11 Online:2011-05-20 Published:2011-05-20
  • Supported by:

    September 11, 2009.  Supported by NSFC (11071226).

摘要:

In the use of  finite element methods to the planar elasticity problems, one difficulty is to overcome locking when elasticity constant λ→∞. In the case of traction boundary condition, another difficulty is to make the discrete Korn's second inequality valid. In this paper, a triangular element is presented. We prove that this element is locking-free, the discrete Korn's second inequality holds and the convergence order is two.

关键词: planar elasticity problems, pure displacement and traction boundary conditions, nonconforming finite element, discrete Korn’s second inequality

Abstract:

In the use of  finite element methods to the planar elasticity problems, one difficulty is to overcome locking when elasticity constant λ→∞. In the case of traction boundary condition, another difficulty is to make the discrete Korn's second inequality valid. In this paper, a triangular element is presented. We prove that this element is locking-free, the discrete Korn's second inequality holds and the convergence order is two.

Key words: planar elasticity problems, pure displacement and traction boundary conditions, nonconforming finite element, discrete Korn’s second inequality

中图分类号: 

  • 65N30