消除临界变分的一种新方法  

A New Method to Eliminate Variational Crisis

作　　者：何吉欢[1] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《上海大学学报（自然科学版）》1999年第5期453-455,共3页Journal of Shanghai University:Natural Science Edition

基　　金：上海市高等学校青年基金

摘　　要：在应用拉氏乘子法消除泛函的约束时，往往会出现临界变分现象（拉氏乘子为零）．本文认为拉氏乘子为零隐含着一个消失的欧拉方程，因此如果把拉氏乘子为零这个方程看作是一个欧拉方程，则可以非常方便识别拉氏乘子。In using the Lagrange multiplier method to eliminate the constraints imposed on conditional variational principles, the multipliers might vanish during the process of variation ( λ =0, where λ is a Lagange multiplier). The phenomenon is called variational crisis. It is pointed out in this paper that the equation λ =0 must be an inexplicit field equation, which is lost during the variation. The multiplier, therefore, can be readily identified, and various generalized variational principles can be established.

关 键 词：变分原理 拉氏乘子法 弹性力学 临界变分 

分 类 号：O343[理学—固体力学]