Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate

FENG Min-fu; YANG Yan; ZHOU Tian-xiao

Volume 30 Issue 2

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Abstract

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Article Navigation > Applied Mathematics and Mechanics > 2009 > 30(2): 192-202

FENG Min-fu, YANG Yan, ZHOU Tian-xiao. Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate[J]. Applied Mathematics and Mechanics, 2009, 30(2): 192-202.

Citation:

FENG Min-fu, YANG Yan, ZHOU Tian-xiao. Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate[J]. Applied Mathematics and Mechanics, 2009, 30(2): 192-202.

Citation:

FENG Min-fu, YANG Yan, ZHOU Tian-xiao. Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate[J]. Applied Mathematics and Mechanics, 2009, 30(2): 192-202.

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Nonconforming Stabilized Combined Finite Element Method for the Reissner-Mindlin Plate

1.
College of Mathematics, Sichuan University, Chengdu 610064, P. R. China;

Received Date: 2007-12-24
Rev Recd Date: 2008-12-09
Publish Date: 2009-02-15

Abstract

Abstract

Based on the combination of two variational principles, a nonoonfornung stabilized futile element method was presented for the Reissner-Mindlin plates.
- Reissner-Mindlin plate,
- energy-compatibility,
- combined FFM,
- nonconfoming finite element

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References(22)

References

[1]	Brezzi F.Numerical approximation of Mindlin-Reissner plates[J].Math Comput,1986,47(175):151-158. doi: 10.1090/S0025-5718-1986-0842127-7
[2]	Duran R,Lieberman E.On mixed finite element methods for the Reissner-Mindlin plate model[J].Math Comput,1992,58(198):561-573.
[3]	ZHOU Tian-xiao. The partial projection method in the finite element discretization of the Reissner-Mindlin plate model[J].J Comput Math,1995,13(2):172-191.
[4]	Chinosi C. Remarks on some mixed finite element schemes for Reissner-Mindlin plate model[J].Calcolo,2002,39(2):87-108. doi: 10.1007/s100920200006
[5]	Lovadina C. A low-order nonconforming finite element for Reissner-Mindlin plates[J].SIAM J Numer Anal,2005,42(6):2688-2705. doi: 10.1137/040603474
[6]	Chinosi C,Lovadina C,Marini L D.Nonconforming locking-free finite elements for Reissner-Mindlin plates[J].Comput Methods Appl Mech Engng,2006,195(25/28):3448-3460. doi: 10.1016/j.cma.2005.06.025
[7]	MING Ping-bing,SHI Zhong-ci. Two nonconforming quadrilateral elements for the Reissner-Mindlin plate[J].Mathematical Models and Methods in Applied Science,2005,15(10):1503-1517. doi: 10.1142/S0218202505000868
[8]	LUO Kun,ZHOU Tian-xiao.An accurate quadrilateral plate element based on energy optimization[J].Commum Numer Meth Engng,2005,21(9):487-498. doi: 10.1002/cnm.761
[9]	CHEN Shao-chun,SHI Dong-yang. General error estimates of nonconforming plate elements[J].Mathematica Numerica Sinica,2000,22(1):295-300.
[10]	HU Jun,SHI Zhong-ci. Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate[J].Math Comput,2007,76(260):1771-1786. doi: 10.1090/S0025-5718-07-01952-7
[11]	龙驭球,赵俊卿.厚板薄板通用的广义协调元[J].工程力学,1988,5(1):1-8.
[12]	龙志飞,岑松.有限元法新论[M].北京：中国水利水电出版社,2001.
[13]	CEN Song,LONG Yu-qiu,YAO Zhen-han,et al.Application of the quadrilateral area co-ordinate method: a new element for Mindlin-Reissner plate[J].Interernat J Numer Methods Engrg,2006,66(1):1-45. doi: 10.1002/nme.1533
[14]	FENG Min-fu,YANG Rong-kui,XIONG Hua-xin. Stabilized finite element methods for the Reissner-Mindlin plate[J].J Numer Math,1999,8(2):125-132.
[15]	Taylor R L,Simo J C,Zienkiewicz O C,et al. The patch test—a condition for assessing FEM convergence[J].Internat J Numer Methods Engrg,1986,22(1):39-62. doi: 10.1002/nme.1620220105
[16]	WU Chang-chun,BIAN Xue-huang.Nonconforming Numerical Analysis and Combined Hybird Finite Element Methods[M].Beijing:Science Press,1997.
[17]	SHI Zhong-ci. A convergence condition for the quadrilateral Wilson element[J].Numer Math,1984,44(3):349-361. doi: 10.1007/BF01405567
[18]	ZHANG Zhi-min,ZHANG Shang-you. Derivative superconvergence of rectangular finite elements for the reissner--mindlin plate[J].Comput Methods Appl Mech Eng,1995,134(1):1-16 .
[19]	Bathe K J,Dvorkin E. A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation[J].Internat J Numer Methods Engrg,1985,21(2):367-383. doi: 10.1002/nme.1620210213
[20]	Batoz J L,Bentahar M. Evaluation of a new quadrilateral thin plate bending element[J].Internat J Numer Methods Engrg,1982,18(11):1655-1677. doi: 10.1002/nme.1620181106
[21]	Brezzi F,Fortin M. Mixed and Hybrid Finite Method[M].New York:Springer-Verlag,1991.
[22]	ZHOU Tian-xiao. Stabilized hybrid finite element methods based on the combination of saddle point principles of elasticity problems[J].Math Comput,2003,72(244):1655-1673. doi: 10.1090/S0025-5718-03-01473-X

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