包含初值或终值条件为驻值条件的非线性弹性动力学的变分原理

历史上为使初始条件为驻值条件的哈氏型原理曾在文献1～2]中研究过。但文献1]中仍要求末时刻位移变分为零;而文献2]中的形式实为虚功原理。对于线性情形,文献3]中给出了包括初始条件为驻值条件的哈氏型原理。本文给出非线性情形的结果,并推广其可用于终值问题。

VARIATIONAL PRINCIPLES WITH INITIAL OR FINAL VALUE CONDITIONS INCLUDED IN STATIONARY CONDITIONS FOR NONLINEAR ELASTODYNAMICS

The momentum conditions at the time tp are explained as the impulse body forces by means of Delta function △(t-tp). Based on this point, the definitions of the action of momentum potential at the time terminal tp -gp (ui) and its complementary one-gp(pi)are formulated, respectively. The two parameters q and q' ,q + q* = 1, are introduced. Furthermore, some variational principles for nonlinear elastodynamics are developed. They are the variational principles of potential energy action, the one of complementary energy action, the two forms of generalized potential energy action and the two forms of generalized complementary energy action. It may be attractive that initial value conditions or the final value ones are remained in the stationary conditions of these variational principles.