多柔体系统刚柔耦合动力学有限单元法

传统的多柔体系统动力学建模理论 ,往往基于小变形线性动力学的基本假定 ,采用线性的Cauchy应变理论描述应变—位移关系。但是 ,对于具有刚性旋转的位移场来说 ,Cauchy应变理论并不适用。本文采用Green Lagrange应变理论 ,描述有大位移运动的梁单元的非线性位移—应变关系 ,通过对应变能的分析和线性化处理 ,建立起相对变形坐标一阶精确的一致线性化的多柔体系统有限元模型 ,仿真算例的结果验证了该方法的有效性和结构中的几何非线性对系统动力学响应的重要作用。

A finite element method of the rigid-flexible coupling dynamics for a flexible multi-body system

The traditional dynamic theory for flexible multi body systems is based on the small deformation assumption, which describing the linear strain displacement relations by Cauchy strain theory. But for the displacement field with the rigid rotating motions, the Cauchy strain theory is not suitable. By adopting the Green lagrangin strain theory which describing the non linear strain displacement relations of the beam element with large displacement, analyzing and linearizing the strain energy, the finite element equations can be founded for the flexible multi body system with consistent linearization and first order accurate ralativne deformation coordinate. The simulation result shows the effectivity of the presented method and the importance of geometrical nonlinearization in the structure for the flexible multi body system dynamics.