HE Dong-sheng, TANG Li-min. The Displacement Function of Quasi-Conforming Element and Its Node Error[J]. Applied Mathematics and Mechanics, 2002, 23(2): 119-127.
Citation: HE Dong-sheng, TANG Li-min. The Displacement Function of Quasi-Conforming Element and Its Node Error[J]. Applied Mathematics and Mechanics, 2002, 23(2): 119-127.

The Displacement Function of Quasi-Conforming Element and Its Node Error

  • Received Date: 2001-02-25
  • Rev Recd Date: 2001-10-09
  • Publish Date: 2002-02-15
  • 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 displacementitems, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.
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  • [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]
    唐立民、陈万吉、刘迎曦.有限元分析中的拟协调元[J].大连工学院学报,1980,19(2):19-35.
    [4]
    陈万吉、唐立民、刘迎曦.拟协调元列式[J].大连工学院学报,1980,19(2):37-49.
    [5]
    张鸿庆、王鸣.多套函数有限元逼近与拟协调板元[J].应用数学和力学,1985,6(1):41-52.
    [6]
    王鸣.多套函数逼近与拟协调元方法[D].硕士论文.大连:大连理工大学,1984.
    [7]
    石钟慈.关于九参拟协调板元[J].计算数学,1988,8(1):100-106.
    [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]
    石钟慈、陈绍春.九参拟协调元的直接分析[J].计算数学,1990,12(1):76-84.
    [10]
    钱伟长.变分法及有限元[M].北京:科学出版社,1981.
    [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.
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