On Various Variationai Principles in Nonlinear Theory of Elasticity

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Tai Tien-min. On Various Variationai Principles in Nonlinear Theory of Elasticity[J]. Applied Mathematics and Mechanics, 1982, 3(5): 585-596.

Citation:

Tai Tien-min. On Various Variationai Principles in Nonlinear Theory of Elasticity[J]. Applied Mathematics and Mechanics, 1982, 3(5): 585-596.

Citation:

Tai Tien-min. On Various Variationai Principles in Nonlinear Theory of Elasticity[J]. Applied Mathematics and Mechanics, 1982, 3(5): 585-596.

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].

[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).