THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (2): 127-137.

THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR

何东升, 唐立民

Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, P R China

收稿日期:2000-12-25 修回日期:2001-10-09 出版日期:2002-02-18 发布日期:2002-02-18

THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR

HE Dong-sheng, TANG Li-min

Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, P R China

Received:2000-12-25 Revised:2001-10-09 Online:2002-02-18 Published:2002-02-18

摘要/Abstract

摘要： Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacement items, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.

Abstract: Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacement items, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.

中图分类号:

O302

何东升;唐立民. THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(2): 127-137.

HE Dong-sheng;TANG Li-min. THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(2): 127-137.

参考文献

[1] Argris J H,Fried I,Scharpf D W.The TUBA family of plate elements for the matrix displacement method[J].The Aeronautical J R Ae S,1968,72:701-709.
[2] Pian T H H.Deriation of element stiffness matrices by assumed stress distribution[J].J AIAA,1964,2(7):1333-1335.
[3] TANG Li-min,CHEN Wan-ji,LIU Ying-xi.The quasi-conforming element in finite element analysis[J].Journal of Dalian Institute of Technology,1980,19(2):19-35.(in Chinese).
[4] CHENG Wan-ji,TANG Li-min,LIU Ying-xi.The formulae of the the quasi-conforming element[J].Journal of Dalian Institute of Technology,1980,19(2):37-49.(in Chinese).
[5] ZHANG Hong-qing,WANG M ing.Finite element approximations with multiple sets of functions and quasi-conforming plate element[J].AppliedMathematics and Mechanics(English Edition),1985,6(1):41-52.
[6] WANG Ming.Approximations with multiple sets of functions and quasi-conforming element method[D].Master thesis.Dalian:Dalian University of Technology,1984.(in Chinese).
[7] SHI Zhong-ci.On the nine parameter quasi-conf orming plate element[J].Mathematic Numerica Sinica,1988,8(1):100-106.(in Chinese).
[8] Bazeley G P,Cheung Y K,Irons B M,et al.Triangular elements in bending-conforming and non-conforming solutions[A].In:Proc 1st Conf on Matrix Methods in Struct Mech[C].Ohio:Air Force Inst of Tech,Wright Patterson A F Base,1965,547-576.
[9] SHI Zhong-ci,CHEN Shao-chun.A direct analysis of the 9-parameter quasi-conforming plate element[J].Mathematic Numerica Sinica,1990,12(1):76-84.(in Chinese).
[10] CHIEN Wei-zang.Variation Method and Finite Element[M].Beijing:Science Press,1981.(in Chinese).
[11] Stummel F.The limitations of the patch test[J].Int J Num Meth Eng,1980,15(1):177-188.
[12] Taylor R L,Simo J C,Zienkiewicz O C,et al.The patch test,a condition for assessing FEM convergence[J].Int J Num Meth Eng,1986,22(1):39-62.
[13] Razzaque A.The patch test for elements[J].Int J Num Meth Eng,1986,22(1):63-72.
[14] Zienkiewicz O C,Qu S,Taylor R L,et al.The patch test for mixed formulations[J].Int J Num Meth Eng,1986,23(10):1873-1884.
[15] Belytschk T,Lasry D.A fractal patch test[J].Int J Num Meth Eng,1988,26(10):2199-2210.
[16] Zhang W,Chen D P.The patch test conditions and some multivariable finite element formulations[J].Int J Num Meth Eng,1997,40(16):3015-3032.
[17] Stummel F.The generalized patch test[J].SIAM J Numer Anal,1979,16(3):449-471.
[18] SHI Zhong-ci.The F-E-M-test for convergence of nonconforming finite elements[J].Math Comput,1987,49(3):391-405.

THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR

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