在材料非线性问题中的摄动有限元法

谢志成; 王瑞五; 杨学忠; 钱振东

在材料非线性问题中的摄动有限元法

清华大学

计量
- 文章访问数: 1776
- HTML全文浏览量: 107
- PDF下载量: 703
- 被引次数: 0
出版历程
- 收稿日期: 1982-01-10
- 刊出日期: 1983-02-15

The Perturbation Finite Element Method for Solving Problems with Nonlinear Materials

Qinghua University, Beijing

摘要

摘要: 摄动法是解决非线性连续介质力学问题的一种有效方法.这种方法是建立在该问题的线性解析解的基础上的,因此,若得不到一个简单的解析解,应用这种方法去解决一些复杂的非线性问题将遇到困难.有限元法对解非线性问题也是一种十分有用的工具,然而一般来说,它需要相当长的计算时间. 本文介绍摄动有限元法.这种方法吸取上述两种方法的优点,能够解决更复杂的非线性问题,而且也能大量节省计算机的计算时间. 本文讨论了比例加载下的弹塑性力学问题,并提出一个带孔拉板的数值解.

Abstract: The perturbation method is one of the effective methods for solving problems in nonlinear continuum mechanics. It has been developed on the basis of the linear analytical solutions for the o-riginal problems. If a simple analytical solution cannot be obtained,we would encounter difficulties in applying this method to solving certain complicated nonlinear problems. The finite element method appears to be in its turn a very useful means for solving nonlinear problems,but generally it takes too much time in computation. In. the present paper a mixed approach,namely,the perturbation finite element method,is introduced,which incorporates the advantages of the two above-mentioned methods and enables us to solve more complicated nonlinear problems with great saving in computing time.Problems in the elastoplastic region have been discussed and a numerical solution for a plate with a central hole under tension is given in this paper.

HTML全文

参考文献(12)

[1]	Thomson,J.M.T.and A.C.Walker,The nonlinear perturbation analysis of discrete structural systems,International Journal of Solids and Structures,4,8,(1966).
[2]	Gallagher, R.H,非线性有限元结构分析中的摄动法,有限元素法及其在力学中的应用,译文集.译自Computational Mechanics, (1974)
[3]	Yokoo,Y.,T.Nakamura and K.Uetani,The incremental perturbation method for large displacement analysis of elastic-plastic structures,Int.J.Numerical Methods in Engineering,Vol.10,No.3,(1976).
[4]	Trifan,D.,On the plastic bending of circular plates,Quart,of Applied Mathematics,16,(1948).
[5]	古国纪,顾求林,弹塑性圆板大挠度问题,力学学报,2,3,(1958).
[6]	顾求林,有强化弹塑性平面问题的一段渐近解,清华大学基础部科研报告(未发表),(1980).
[7]	李大潜等,《有限元素法续讲》,科学出版社.
[8]	周春田,带有缺陷板在单向拉伸时弹性应力应变场的测定,清华大学基础部科研报告(未发表),(1981).
[9]	钱伟长,《变分法及有限元》,科学出版社,(1980).
[10]	钱伟长.林鸿荪.胡海昌.叶开沅.《弹性圆薄板大挠度问题》,中国科学院.(1954).
[11]	Washizu,K.,Variational Methods in Elasticity and Plasticity,(1968).
[12]	Zienkiewicz,O.C.,The Finite Element Method,(1977).