摘要
本文集中研究弹性力学广义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Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ亚广义变分原理（简记作“Ｈ－Ｒ原理”）广而得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 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.
出处
《上海大学学报（自然科学版）》
CAS
CSCD
1998年第6期591-599,共9页
Journal of Shanghai University:Natural Science Edition
关键词
弹性力学
变分原理
有限元法
广义
临界变分状态
variational principles
elasticity
Lagrange multiplier
finite element method
