论弹性力学广义变分原理的临界变分状态

本文集中研究弹性力学变分原理中的临界变分状态，指出它的三种表现，并提出一个带预处理的修正拉氏乘子法来排除之。文中用它成功地导出了胡海昌－鹫津广义变分原理（简记作“Ｈ－Ｗ原理”）和由Ｈｅｌｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ亚广义变分原理（简记作“Ｈ－Ｒ”原理）广而得到的另二条广义变分原理，于是，拉氏乘子法的潜力得以更充分发挥，适用范围得以拓广。

The Variational Crisis and Generalized Variational Principles in Elasticity

The present paper concentrates on the investigation of variational crisis occurring during the derivation of generalized variational principles(VP) via Lagrange multipliers, demonstrating three types of the crisis and suggesting a preconditioned Lagrange multiplier method for its removal. By means of this preconditioned method the Hu Washizu's generalized VP has been rigorously and successfully derived and two other generalized VP have also been obtained from the Hellinger Reissner principle. In this way the potential of the Lagrange multiplier method can be fully utilized and its applicability range, extended.