关于弹性力学广义变分原理的等价性定理的研究

基金项目: 教育部博士点基金资助项目

Study of the Equivalent Theorem of Generalized Variational Principles in Elasticity

摘要: 利用场论中的不变性原理研究弹性力学广义变分原理的等价性定理，主要目的是研究弹性力学广义变分原理之间的关系；根据弹性力学广义变分原理的泛函在无穷小标度变换下的不变性，证明了这些泛函之间的等价性定理．如果这些泛函具有无穷小标度变换下的不变性，那么只有两类变量是独立的, 应力应变关系是这些泛函必须满足的变分约束条件．所得到的结果再一次证明了钱伟长教授关于所有的弹性力学广义变分原理都是等价的结论．
- 弹性力学 /
- 广义变分原理 /
- 等价性定理 /
- 标度变换 /
- 不变性
Abstract: The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functionals and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.
- elasticity /
- generalized vatiational principle /
- equivalent theorem /
- scale transformation /
- invariance

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