基于基面力的有限变形广义拟Hamilton原理

Generalized Hamilton-type quasi-variational principles of finite deformation based on base forces

传统的有限变形变分原理采用二阶张量的描述方法,因此在模型的推导和建立上都较为复杂。基面力作为一种描述应力状态的新方法,较传统的应力张量表示方法简单。基于基面力理论框架,定义了有限变形时域边值问题的基本方程。考虑到体力与面力为伴生力,采用变积法建立了有限变形广义拟Hamilton原理。按照基本变量之间的对应关系,将基于基面力的有限变形广义拟Hamilton原理转化为以第二类P-K应力张量和Green应变张量为基本变量的有限变形广义拟Hamilton原理。进而证明本文建立的基于基面力的有限变形广义拟Hamilton原理的正确性。

The traditional variational principle of finite deformation is described by the second-order tensor, so the deduction and establishment of a model are more complicated. As a new description of the stress state at a point, the base force method is simpler than the traditional stress tensor expression method. Based on the theory framework of a base force, a basic equation of the time-domain boundary value at finite deformation was defined. Considering that both the body force and the surface force are follower forces, the generalized Hamilton-type quasi-variational principles of finite deformation were established through the use of the variational integral method. According to the corresponding relations of basic variables, the generalized Hamilton-type quasi-variational principles of finite de-formation based on base forces were transformed into the generalized Hamilton-type quasi-variational principles of fi-nite deformation with the second category of the Piola-Kirchhoff stress tensor and Green finite strain tensor as basic variables. The purpose of this was to further verify the accuracy of the generalized Hamilton-type quasi-variational principles of finite deformation based on base forces which were established in this paper.