非线性弹性薄壳动力学的各类非传统Hamilton型变分原理

Unconventional Hamilton-type variational principles for nonlinear dynamics of thin elastic shells

根据对偶互补的基本思想,通过一条简单而统一的新途径,系统地建立了非线性弹性薄壳动力学的各类非传统Hamilton型变分原理.这种新的变分原理能反映这种动力学初值—边值问题的全部特征.首先给出非线性薄壳动力学的广义虚功原理的表达式,然后从该式出发,不仅能得到非线性薄壳动力学的虚功原理,而且通过所给出的一系列广义Legendre变换,还能系统地成对导出非线性弹性薄壳动力学的5类变量和3类变量非传统.Hamilton型变分原理的互补泛函、以及相空间非传统Hamilton型变分原理的泛函与1类变量非传统Hamilton型变分原理势能形式的泛函.同时,通过这条新途径还能清楚地阐明这些原理的内在联系.

According to the basic ideas on dual-complementarity, the unconventional Hamilton-type variation- al principles for the nonlinear dynamics of thin elastic shells were established systematically in a simple and unified way, which could fully characterize the initial-value problem of this type of dynamics. In this paper, an important integral relation was given, which can be considered as a generalized principle of virtual work for nonlinear dynamics of thin shells. Based on this relation, it was not only possible to obtain the principle of virtual work and the reciprocal theorem, but also to systematically derive the complementary functionals for the five-field and three-field unconventional Hamilton-type variational principles. The functionals for the uncon- ventional Hamilton-type variational principle in phase space and the potential energy functionals for one-field unconventional Hamilton-type variational principle for nonlinear dynamics of thin elastic shells by the generalized Legendre transformation were given in this paper. Furthermore, with this approach, the intrinsic relationships among various principles can be clearly explained.