论非线性弹性理论的各种变分原理
On Various Variationai Principles in Nonlinear Theory of Elasticity
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摘要: 本文从“全能量原理”出发推导出非线性弹性理论中各种可能的主要的变分原理的泛函,其中有几个是在我们所能见到的文献中还没有的.通过本文的推导过程,我们提出了胡海昌的专著[1]中表6.1的第11类和第6类变分原理不存在的猜想.Abstract: In the present paper functionals for the various possible main variational principles in the nonlinear theory of e-lasticity are derived from the "full energy principle" and several of them are not found yet in the literatures available. Through the derivation of this paper we suggest a conjecture on the nonexistence of the eleventh and the sixth classes for the variational principles in Table 6.1 of H.C. Hu's monograph [1].
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[1] 胡海昌著,《弹性力学的变分原理及其应用》,科学出版社(1981). [2] 郭仲衡著,《非线性弹性理论》,科学出版社(1980). [3] 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). [4] 钱伟长著,《变分法及有限元》,上册,科学出版社(1980). [5] Washizu,K.,Variational Methods in Elasticity and Plasticity,Pergamon Press,(1968). -
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