| 弹性力学广义变分原理中的一个悖论 |
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| 引用本文： | 程兆雄. 弹性力学广义变分原理中的一个悖论[J]. 北京理工大学学报, 1990, 10(4): 57-61 |
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| 作者姓名： | 程兆雄 |
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| 作者单位： | 北京理工大学应用力学系 |
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| 摘 要： | 先从一个数学例题说明任意地应用变分法基本引理可能导致一个悖论,进而论述在弹性力学三类变量的广义变分原理中也出现了类似的悖论,最后指出:弹性本构关系不可能充任变分学中的Euler-Lagrangn方程。
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| 关 键 词： | 弹性力学 广义 变分原理 悖论 变分 |
Paradoxes of Existence in Generalized Variational Principles in Theory of Elasticity |
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| Cheng Zhaoxiong. Paradoxes of Existence in Generalized Variational Principles in Theory of Elasticity[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 1990, 10(4): 57-61 |
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| Authors: | Cheng Zhaoxiong |
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| Affiliation: | Department of Applied Mechanics |
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| Abstract: | Paradoxes can arise when the basic lemma of calculus of variation is applied too arbitrarily in mathematics . Similar cases could also arise on generalized variational principles with three kinds of variables in elasticity . Constitutive relations of elasticity cannot serve the purpose of Euler- Lagrange equations on calculus of variation . |
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| Keywords: | variation Euler - Lagrange equations .constitutive relations paradoxes / independent variation . |
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