带参数拉氏乘子法与胡海昌-鹫津变分原理中三类变量都独立的推证及其它

Parametrized Lagrange Multiplier Method and Proof ofFull Independence of the Three Field Variablesin Hu Washizu Variational Principle and Others

本文将笔者在１９８１年提出的分裂因子（任意参数）的概念引入拉氏乘子，称为带参数拉氏乘子法。本文将用它推证胡海昌－鹫津变分原理中的三类变量都独立。带参数拉氏乘子法是建立新变分原理的普遍方法，为近代兴起的广义混合变分原理提供一个理论基础。本文还对它们的理论和实用价值予以扼要阐述，而这个新方法在很多重要方面的开拓。

A concept of splitting factor (an arbitrary parameter) is introduced into Lagrange multiplier,enabling it to do what the traditional Lagrange multiplier could not do.Therefore,the method of derivation being discussed in this paper is called the parametrized Lagrange multiplier method. As an application of the parametrized Lagrange multiplier method,the authors try show full independence of the three field variables contained in Hu Washizu Variational Principle Π HW . During this procedure,the parametrized Lagrange multiplier is employed to remove the stress strain relation constraints, and therefore, the variational principles with three field independent variables, including Π HW , will be established from Reissner′s functional Π HR . The theoretical and practical significance of the generalized mixed variational principles (GMVP) involved in this paper is also discussed.The parametrized Lagrange multiplier is a general method for establishing new variational principles,having a great potential in both the theoretical and the practical areas,which will be discussed in other papers.