凑合反推法和弹性理论中的多变量广义变分原理

何吉欢

凑合反推法和弹性理论中的多变量广义变分原理

何吉欢

上海大学;上海市应用数学和力学研究所, 上海200072

基金项目: 国家重点基础研究专项经费资助项目(G1998020318)

详细信息

作者简介:
何吉欢(1965~ ),博士,纽约科学院士,乌克兰科学院名誉教授,主要研究方向:变分原理和非线性分析,已发表论文80多篇.

中图分类号: O176;O343
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- 被引次数: 0
出版历程
- 收稿日期: 1999-10-20
- 修回日期: 2000-01-30
- 刊出日期: 2000-07-15

Semi-Inverse Method and Generalized Variational Principles With Multi-Variables in Elasticity

He Jihuan

Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China

摘要

摘要: 详细介绍了如何应用凑合反推法(semi-inverse method)构造弹性理论中的两类独立变量的广义变分原理(包括熟知的Hellinger-Reissner变分原理,Hu-Washizu变分原理)及三类独立变量的广义变分原理(钱伟长广义变分原理) 。应用凑合反推法还可以清楚地看出各变量之间的约束关系,从而再一次证明了Hu-Washizu变分原理实际上是两类独立变量的广义变分原理。
- 弹性力学变分原理 /
- 钱伟长广义变分原理 /
- 胡-鹫原理 /
- 凑合反推法 /
- 试泛函 /
- 临界变分
Abstract: Semi-inverse method,which is an integration and an extension of Hu's try-and-error method,Chien's veighted residual method and Liu's systematiic method,is proposed to establish generalized variational principles with multi-variables without any variational crisis phenomenon.The method is to construct an energy trial-functional with an unknown function F,which can be readilyi-dentified by making the trial-functional stationary and using known constraint equations.As a result generalized variational principles with two kinds of independent variables(such as well-known Hellinger-Reissner variational principle and Hu-Washizu principle)and generalized variational principles with three kinds of independent variables(such as Chien's generalized variational principles)in elasticity have been deduced without using Lagrange multiplier method.By semi-inverse method,the author has also proved that Hu-Washizu principle is actually a variational principle with only two kinds of independent variables,stress-strain relations are still its constraints.
- variational principle in elasticy /
- Chien’s generalized variational principles /
- Hu-Washizu principle /
- semiinverse method /
- trial-functional /
- variational crisis

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参考文献(18)

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