NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

doi:10.1016/S0252-9602(11)60278-6

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

NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

陈绍春, 郑艳君, 毛士鹏

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/Abstract

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:

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

陈绍春, 郑艳君, 毛士鹏. NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS[J]. 数学物理学报(英文版), 2011, 31(3): 815-825.

CHEN Shao-Chun, ZHENG Yan-Jun, MAO Shi-Peng. NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS[J]. Acta mathematica scientia,Series B, 2011, 31(3): 815-825.

参考文献

[1] Arnold D N, Brezzi F, Douglas Jr J. PEERS: A new mixed finite element for planar elasticity. Japan J Appl Math, 1984, 1: 347--367

[2] Arnold D N, Winther R. Mixed finite elements for elasticity. Numer Math, 2002, 92: 401--419

[3] Brenner S C, Scott L R. The Mathematical Theory of Finite Element Methods. New York: Springer-Verlag, 1994

[4] Brenner S C, Sung L Y. Linear finite element methods for planar linear elasticity. Math Comp, 1992, 59: 321--338

[5] Clement P. Approximation by finite element functions using local regularization. RAIRO Anal Numer, 1975, 9: 77--84

[6] Ciarlet P G. The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland, 1978

[7] Crouzeix M, Raviart D A. Conforming and nonconforming finite element methods for solving the stationary Stokes equations. RAIRO, 1973, R-3: 33--75

[8] Falk R S. Nonconforming finite element methods for the equations of linear elasticity. Math Comp, 1991, 57: 529--550

[9] Lee L O, Lee J, Sheen D. A lacking-free nonconforming finite element method for planar linear elasticity. Adv Comp Math, 2003, 19: 277--291

[10] Qi H. Locking-free finite element methods for linear elasticity with pure displacement boundary condition [D]. Beijing: Academy of Mathematics and Systems Science, CAS, 2002(in Chinese)

[11] Stenberg R. A family of mixed finite elements for the elasticity problem. Numer Math, 1988, 53: 513--538

[12] Wang L H, Qi H. A locking-free finite element scheme for the planar elasticity problem. Math Numer Sinica, 2002, 24: 243--256 (in Chinese)

[13] Zhang Z. Analysis of some quadrilateral nonconforming elements for incompressible elasticity. SIAM J Numer Anal, 1997, 34: 640--663

[14] Chen S C, Shi D Y. Accuracy analysis for quasi-wilson element. Acta Math Sci, 2000, 20B(1): 44--48

NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

NEW SECOND ORDER NONCONFORMING TRIANGULAR ELEMENT FOR PLANAR ELASTICITY PROBLEMS

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