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 引用本文: 郭仲衡. 非线性弹性理论变分原理的统一理论[J]. 应用数学和力学, 1980, 1(1): 5-23.
Guo Zhong-heng. Unified Theory of Variational Principles in Non-linear Theory of Elasticity[J]. Applied Mathematics and Mechanics, 1980, 1(1): 5-23.
 Citation: Guo Zhong-heng. Unified Theory of Variational Principles in Non-linear Theory of Elasticity[J]. Applied Mathematics and Mechanics, 1980, 1(1): 5-23.

Unified Theory of Variational Principles in Non-linear Theory of Elasticity

• 摘要: 本文旨在介绍和讨论非线性弹性理论的几个主要变分原理——古典的势能原理,余能原理以及目前争论甚多的另两个余能原理(Levinson原理和Fraeijs de Veubeke原理),同时给出了和这些原理相对应的广义变分原理.本文单一地从虚功原理出发,系统推导并严格论证了这些原理,并且指出了各原理间的内在联系.出发点是一个,采取不同的变量和Legendre变换就导致不同的原理.这样,各变分原理在统一的框架里构成一个有机的整体.文中未涉及的其它原理也同样可以纳入这框架.给出的关系图使读者更能看清各原理间的纵横关系.
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出版历程
• 收稿日期:  1979-07-30
• 刊出日期:  1980-02-15

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