## 留言板

 引用本文: 何东升, 唐立民. 拟协调元的位移函数及节点误差[J]. 应用数学和力学, 2002, 23(2): 119-127.
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.

• 中图分类号: O302

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

• 摘要: 直接从拟协调元的应变关系式出发,构造具有明确物理意义的幂级数形式的位移函数,从而得出拟协调元的常应变和线性应变系数是唯一确定的,它只能收敛到常应变的结论;刚性位移项可采用多种构造方法,不同的方法得出的节点参数与单元的本身的节点参数存在不同阶次的误差,这与常规位移法有限元不同。
•  [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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##### 出版历程
• 收稿日期:  2001-02-25
• 修回日期:  2001-10-09
• 刊出日期:  2002-02-15

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