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

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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.

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参考文献(15)

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