大变形对称弹性理论的广义变分原理
Generalized Variational Principles of Symmetrical Elasticity Problem of Large Deformation
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摘要: 本文以陈至达提出的变形几何非线性理论[1]为基础,应用Lagrange乘子法,对大变形对称弹性力学问题进行了研究,给出了相应的位能广义变分原理、余能广义变分原理,以及动力学问题的广义变分原理;同时,文中还证明了位能广义变分原理和余能广义变分原理的等价性.Abstract: This paper is based on the geometrical nonlinear theories of deformation presented by Chen Zhi-da[1],Lagrange's multiplier mothod is used to study the symmetry elasticity problems of large deformation.The general rariational priieiplesof potential energy and complemenlary energy,and the general variation principle of dynamic problem have been proved.In the meantme it is also proved that the general vatiaton principles of potential energy and complementary energy are equivalent.
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Key words:
- dynamics /
- large deformation /
- independent function /
- generalized variational principle
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[1] 陈至达,《有理力学》,中国矿业研究生部(1980). [2] 钱伟长.弹性理论中广义变分原理的研究其在有限元计算中的应用.力学与实践.1(1979). [3] 钱伟长.《变分法及是限元》,科学出版社(1980). [4] 郭仲衡,非线性弹性理论变分原理的统一理论,应用数学和力学,1(1)(1980).5-24. [5] 陈至达.钱氏定理在有限变形极矩弹性力学广义变分原理的应用.应用数学和力学.2(2)(1981),181-196. [6] 戴天民.论非线性弹理理论的各种变分原理,应用数学和力学,5(5)(1982).585-506. -
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