精确有限元法

叶开沅; 纪振义

精确有限元法

叶开沅¹,
纪振义²

1.
兰州大学力学系;
2.
安徽建筑工业学院

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- 被引次数: 0
出版历程
- 收稿日期: 1990-02-22
- 刊出日期: 1990-11-15

Exact Finite Element Method

Yeh Kai-yuan¹,
Ji Zhen-yi²

1.
Lanzhou University, Lanzhou;
2.
Anhui Architectural Industry College, Hefei

摘要

摘要: 本文提出构造有限单元的新方法——精确有限元法.它可以求解在任意边界条件下任意变系数正定或非正定偏微分方程。文中给出它的收敛性证明和计算偏微分方程的一般格式。用精确元法所得到的单元是一个非协调元,单元之间的相容条件容易处理.与相同自由度普通有限元相比,由精确元法所得到的解的高阶导数具有较高的收敛精度.文末给出数值算例,所得到的结果均收敛于精确解,并有较好的数值精度.
- 精确有限元 /
- 偏微分方程 /
- 热传导 /
- 薄板
Abstract: In this paper, a new method, exact element method for constructing finite element, is presented.It can be applied to solve nonpositive definite or positive definite partial differential equation with arbitrary variable coefficient under arbitrary boundary condition.Its convergence is proved and its united formula for solving partial differential equation is given.By the present method, a noncompatible element can be obtained and the compatibility conditions between elements can be treated very easily.Comparing the exact element method with the general finite element method with the same degrees of freedom, the high convergence rate of the high order derivatives of solution can be obtained.Three numerical examples are given at the end of this paper, which indicate all results can converge to exact solution and have higher numerical precision.
- exact finite element /
- partial differential equation /
- heat conduction /
- thin plate

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参考文献(6)

[1]	Zienkiewicz,O.C.,The Finite Element Method,McGraw-Hill.Third Edition(1977).
[2]	叶开沅,非均匀变厚度弹性力学的若干问题的一般解,Ⅳ.非均匀变厚度梁的弯曲,稳定性和自由振动,兰州大学学报力学专号,1 (1979), 133-157.
[3]	纪振义,矩阵迁移法收敛性的条件及其证明,工程力学,5, 3 (1988), 20-29.
[4]	纪振义、叶开沅,任意变系数微分方程的精确解析法,应用数学和力学,10, 10 (1989), 841-851.
[5]	Hood,P.,Frontal solution program for unsymmetric matrices,Int.J Num.Meth.Engng.,10,(1976),377-379.
[6]	Timoshenko,S.,and S.Woinowsky-krieger,Theory of Plate and Shell.McGraw-Hill Book Company.Second Edition(1959)