中文摘要：

在柔性多体的接触碰撞动力学问题中，多变量方法基于附加约束的接触模型，将柔性体的变形用不同变量来描述：接触局部区域的变形用有限元节点坐标描述，非接触局部区域的变形用模态坐标描述，兼顾了计算精度和效率．将该方法推广到三维空间碰撞问题，对两柔性杆纵向碰撞过程进行动力学仿真，数值结果与实验结果吻合良好，验证了该方法的有效性．针对柔性体各自区域的变量如何选取的问题，研究了节点取法、模态阶数以及材料参数对计算结果精度的影响，寻找到合理的多变量选取方法，保证精度的同时使自由度得到最大程度的缩减．

英文摘要：

In flexible multi-body dynamics with contact/impact, multi-variable method （MVM） which is based on appended contact constraint model is proposed. With this method, two types of variables are used to describe the flexible body deformation： small superposed deformation is depicted with finite element nodal coordinates in contact region and modal coordinates in non-contact region respectively, thus this method takes account of both accuracy and efficiency. This method is extended to three-dimensional spatial contact issue which is more complicated than the planar one, and the numerical simulation of a longitudinal impact between two rods agrees well with the experiment result. To solve the variable selection problem, the influences on result accuracy of node position, modal orders and material parameter are studied. Based on this, the optimal multi-variable selection is realized which reduces the DOFs to the maximum extent and also achieves accuracy in the same time.