A Method for Establishing Generalized Variational Principle

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1985 > 6(6): 481-488

Hsueh Dah-wei. A Method for Establishing Generalized Variational Principle[J]. Applied Mathematics and Mechanics, 1985, 6(6): 481-488.

Citation:

Hsueh Dah-wei. A Method for Establishing Generalized Variational Principle[J]. Applied Mathematics and Mechanics, 1985, 6(6): 481-488.

Citation:

Hsueh Dah-wei. A Method for Establishing Generalized Variational Principle[J]. Applied Mathematics and Mechanics, 1985, 6(6): 481-488.

Abstract

A method for establishing generalized variational principle is proposed in this paper. It is based on the analysis of mechanical meaning and it can be applied to problems in which the variational principles are needed but no corresponding variational principle is available. In this paper, the Hu-Washizu's generalized variational principle and the Hu's generalized principle of complementary energy are derived from the mechanical meaning instead of from the generalization of the principle of minimum potenlial energy and the correct proofs of these two generaleed variational principles are given. It is also proved that this is wrong if one beleives that σ_ij, e_ij and ui are independent variables each other based on the reason that these three kinds of variables are all contained in these two generalized variational principles. The condition of using these two variational principles in a correct manner is also explained.

[1]	胡海昌,论弹性体力学与受范性体力学中的一般变分原理.物理学报,10, 3 (1954),259.
[2]	钱伟长,再论弹性力学中的广义变分原理—就等价定理问题和胡海昌先生商榷,力学学报,4 (1983),325.
[3]	钱伟长,关于弹性力学中的广义变分原理及其在板壳问题上的应用,未发表,见力学学报编辑部64-057号来信,1964年10月6日.
[4]	钱伟长,弹性理论中广义变分原理的研究及其在有限元计算中的应用,机械工程学报,15,2 (1979),1-23,
[5]	钱伟长,《变分法和有限元》,科学出版社,北京(1980).
[6]	钱伟长,高阶拉氏乘子法和弹性理论中更一般的广义变分原理,应用数学和力学,4, 2(1983),137-150.
[7]	胡海昌,《弹性力学的变分原理及其应用》,科学出版社,北京(1981), 387.
[8]	胡海昌,略论Hellinger-Reissner和胡海昌一鹜津久一郎两种广义变分原理的联系,力学学报,3 (1983),301.