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构造单元刚度矩阵的双参数法

陈绍春,石钟慈   

  1. 中国科技大学 ,中国科学院计算中心
  • 出版日期:1991-03-14 发布日期:1991-03-14

陈绍春,石钟慈. 构造单元刚度矩阵的双参数法[J]. 计算数学, 1991, 13(3): 286-296.

DOUBLE SET PARAMETER METHOD OF CONSTRUCTING STIFFNESS MATRICES

  1. Chen Shao-chun;Shi Zhong-ci China University of Science and Technology Computing Center,Academia Sinica
  • Online:1991-03-14 Published:1991-03-14
§1.引言 用位移法构造有限元单元刚度矩阵的常规方法如下:设单元为K,位移形函数空间是 ?(K)=Span{N_1,…,N_m}, (1.1)其中N_1,…,N_?是线性无关的多项式.
A new method of constructing stiffness matrices is presented. The method uses two setsof parameters, one of which consists of usual nodal parameters, like function values and theirderivatives at nodes of elements. The second set may be chosen some special type of linear func-tionals on the given finite element spece, such as integrals of functions and their derivativesalong edges of elements in order to meet certain convergence requirements. The method is very effective and easy to implement under the general framework offinite element analysis. Several unconventional plate elements, recently appeared in engineeringapplications, have been tested successfully using this new method and their convergence proper-ties are established in a unified mathematical way.
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[1] P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, 1978.
[2] F.Stummel, The generalized parch-test, SIAM. J. Numer. Anal., 16(1979) ,449-471.
[3] Shi Zhong-ci, The generalized patch-test for Zienkiewicz's triangles. J. Comput. Math., 2(1984) ,279-286.
[4] F.D.Veubeke. Variational principles and the patch-test, Int. J. Numer. Meth. Eng., 8 (1974) ,783-801.
[5] 石钟慈,两种不协调板元的统一型函数形式,计算数学,8:4(1986) ,428-434.
[6] Shi Zhong-ci, The F-E-M-Test for convergence of nonconforming finite elements, Math. Comput., 49(1987) ,391-405.
[7] H. Argyris, H. Haase, H.P.Mlejnex, On an unconventional but natural formation of a stiffness matrix, Comput. Meth. Appl. Mech. Eng., 22(1980) , 1-22.
[8] 唐立民,陈万吉,刘迎曦,有限元分析中的报协调元,大连工学院学报,2(1980) ,37-49.
[9] Long Yu-qiu, Xiu Ke-qai, Generalized conforming element,土木工程学报,1(1987) ,1-14.
[10] B. Specht, Modified shape functions for the three node plate bending element passing the patchtest, Int. J. Numer. Meths. Eng., 26(1988) .705-715.
[11] C.A. Fillipa, P,G, Bergan, A triangular bending element based on an energy-othogonal free for.mulation, Comp. Meth. Appl. Mech. Eng., 61(1987) ,129-160.
[12] 石钟慈,陈绍春,九参拟协调板元的直接分析,计算数学,12:1(1990) ,76-84.
[13] 石钟慈,陈绍春,九参数广义协调元的收敛性,计算数学,13:2(1991) ,193-203.
[14] 陈绍春,有限元的双参数法分析,博士论文,中国科技大学,1988.
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