平面柔性多体系统正碰撞动力学建模理论研究

针对目前柔性多体系统碰撞动力学建模方法存在的不足,对影响碰撞动力学仿真的主要因素如柔性体建模和碰撞初始条件进行分析,建立起基于变约束的柔性体碰撞动力学方程。首先,为了解决子结构法在处理碰撞界面搜索时面临的难题,引入多体系统柔性体有限元描述方法,推导出凸形柔性体接触点间法向位移约束的二阶导数形式。其次,从碰撞引起的接触界面速度不连续机理出发,结合连续介质力学间断面理论,给出碰撞瞬时由物体本身物理性质决定的接触位置处速度跳跃公式。最后对两弹性圆盘低速碰撞问题进行数值仿真。结果表明本文提出的改进方法符合力学基本原理,仿真结果满足收敛性要求。

Study on the modeling theory of the normal impact dynamics for the planar flexible multibody system

According to the disadvantages of the existing modeling methods on the flexible multibody system the main factors such as the modeling method and the initial conditions are analyzed , and based on the varying the constraints technique the dynamic equations of the flexible multibody system during impact process is derived. Firstly, the finite element formulation for the deformable bodies in multibody system is introduced to solve the difficult problems in the algorithms for contact interface search in the substructure technique, then the second-order differential equations of the normal displacement constraints between the two contact points are derived in the convex flexible body. Secondly, from the mechanism of the velocity discontinuity caused by the impact the velocity jump formulation at the impact moment is presented, which is derived by the discontinuity surface theory of continuum mechanics. The derived velocity jump formulation is determined by its physical properties. Finally, the numerical example of the low velocity impact between two elastic disks is simulated. The numerical simulation results show that the improved method in this paper is accord with mechanics principle, and the convergence of the simulation results is satisfied.