非线性弹性体的弹性力学变分原理

钱伟长

非线性弹性体的弹性力学变分原理

钱伟长

上海工业大学; 上海应用数学和力学研究所

计量
- 文章访问数: 1771
- HTML全文浏览量: 87
- PDF下载量: 1550
- 被引次数: 0
出版历程
- 收稿日期: 1986-12-25
- 刊出日期: 1987-07-15

Variational Principles in Elasticity with Nonlinear Stress-Strain Relation

Chien Wei-zang

Shanghai University of Technology; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai

摘要

摘要: 作者自1978年以后,曾发表了一系列有关弹性力学的变分原理和广义变分原理的文章如[1](1978),[6](1980),[2]、[3](1983),[4]、[5](1984),都是指线性应力应变关系的线性弹性体的.在1985年出版的广义变分原理中,初步推广至非线性弹性体,但并未进行较全面的探讨.本文特别讨论非线性应力应变关系的弹性体的变分原理和广义变分原理,这里有不少问题是值得注意的,有时,它对线性弹性体的变分原理,有指导意义.当应变很小,其高次项可以略去时,本文所得结论,都能近似地化简为通常线性理论的结果.

Abstract: Since 1979, a series of papers have been published concerning the variational principles and generalized variational principles in elasticity such as [1](1979), [6](1980), [2,3](1983) and[4,5](1984). All these papers deal with the elastic body with linear stress-strain relations. In 1985, a book was published on generalized variational principles dealing with some nonlinear elastic body, but never going into detailed discussion. This paper discusses particularly variational principles and generalized variational principles for elastic body with nonlinear stress-strain relations. In these discussions, we find many interesting problems worth while to pay some attention. At the same time, these discussions are also instructive for linear elastic problems. When the strain is small, the high order terms may be neglected, the results of this paper may be simplified to the well-known principles in ordinary elasticity problems.

HTML全文

参考文献(15)

[1]	钱伟长,弹性理论中广义变分原理的研究及其在有限元计算中的应用,清华大学科学报告TH78011 (1978);力学与实践,1,1 (1979),16-24,1,2 (1979),18-27;机械工程学报,15,(1979),1-23.
[2]	钱伟长,高阶拉氏乘子法和弹性理论中更一般的广义变分原理,应用数学和力学,4,2 (1983),137-150.
[3]	钱伟长,再论弹性力学中的广义变分原理—就等价定理问题和胡海昌先生商榷,力学学报,4(1983),325-340.
[4]	钱伟长,亦论广义变分原理和无条件变分原理—就本题答胡海昌先生,固体力学学报,3(1984),461-468.
[5]	钱伟长,弹性理论中各种变分原理的分类,应用数学和力学,5,6(1984),765-770.
[6]	钱伟长,《变分法及有限元》,科学出版社(上册)(1980年8月).
[7]	钱伟长,《广义变分原理》,多学科学术讲座丛书,知识出版社,上海(1985).
[8]	朱以文,关于胡海昌-鹫津变分原理中三类变量的独立性的研究,武汉水利电力学院弹性力宇教研室印(1984年11月).
[9]	王润富,线弹性、小位移情形下,弹性力学中三类、两类、一类变量的有约束条件变分原理和无约束条件变分原理,华东水利学院(1985年),私人通讯(未发表).
[10]	Courant and Hilbert,Methods of Mathematical Physics,German Edition(1924),Springer Verlag,First English Edition(1952),Interscience Publisher New York,Vol.I,164-274.
[11]	Zienkeiwicz,O.C.,The Finite Element Method,3rd Edition,McGraw Hill,(U.K.)(1977),68,77,80,304,309,333.
[12]	Washizu,K.,On the variational principles of elasticity and plasticity,Technical Report,Aeroelastic and Structural Research Laboratory,M.I.T.25-18,March(1955).
[13]	胡海昌,论弹性力学与受范体力学中的一般变分原理,物理学报,10,3 (1954),259.
[14]	胡海昌,《弹性力学的变分原理及其应用》,科学出版社(1982).
[15]	胡海昌,关于拉氏乘子法及其它,力学学报,5 (1985),426-434.