多柔体系统刚柔耦合动力学有限单元法

摘要

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。%The traditional dynamic theory for flexible multi-body systems is base d on the small deformation assumption, which describing the linear strain-displ acement relations by Cauchy strain theory. But for the displacement field with t he rigid rotating motions, the Cauchy strain theory is not suitable. By adopting the Green-lagrangin strain theory which describing the non-linear strain-dis placement relations of the beam element with large displacement, analyzing and linearizing the strain energy, the finite element equations can be founded for t he flexible multi-body system with consistent linearization and first order acc u rate ralativne deformation coordinate. The simulation result shows the effectivi ty of the presented method and the importance of geometrical nonlinearization in the structure for the flexible multi-body system dynamics.