中文摘要：

效率和精确性是在建模和包含接触和影响的多身体系统的模拟的二个大多数担心的问题。这份报纸为灵活多身体系统的平面接触问题基于部件模式合成方法建议了明确的表达。灵活身体被划分成二部分：一个接触地区和一个未联系地区。为未联系地区，由把改正接口基础方法用作参考，一些低顺序的形式的坐标被用来代替节点的节的坐标，并且同时，本地影响区域的节的坐标被使未改变，因此，自由( DOF )的全部的度极大地被砍倒，模拟的计算费用显著地被减少。由使用另外的限制方法，影响限制方程和运动学的限制方程被导出，并且第一种灵活多身体系统的 Lagrange 方程被获得。有固定一半的一根有弹性的横梁的影响磁盘被模仿验证这个方法的效率和精确性。

英文摘要：

The efficiency and accuracy are two most concerned issues in the modeling and simulation of multi-body systems involving contact and impact. This paper proposed a formulation based on the component mode synthesis method for planar contact problems of flexible multi-body systems. A flexible body is divided into two parts： a contact zone and an un-contact zone. For the un-contact zone, by using the fixed-interface substructure method as reference, a few low-order modal coordinates are used to replace the nodal coordinates of the nodes, and meanwhile, the nodal coordinates of the local impact region are kept unchanged, therefore the total degrees of freedom （DOFs） are greatly cut down and the computational cost of the simulation is significantly reduced. By using additional constraint method, the impact constraint equations and kinematic constraint equations are derived, and the Lagrange equations of the first kind of flexible multi-body system are obtained. The impact of an elastic beam with a fixed half disk is simulated to verify the efficiency and accuracy of this method.