中文摘要：

针对双柔性杆碰撞问题，考虑杆的弹塑性波传播，推导动力学控制方程，建立动态子结构模型，提出双柔性杆轴向碰撞的动态子结构方法。通过与三维弹塑性动力有限方法的对比表明，该方法的数值计算结果合理、精确，不仅能够计算复杂多变的碰撞力响应和变形响应，而且能够准确计算碰撞弹塑性波的传播，清晰刻画弹塑性波的传播、反射、相互作用等波传播规律。因此，可以作为一种研究多柔性杆弹塑性碰撞响应的有效的数值分析手段。

英文摘要：

A dynamic substructure technique is presented for elastic-plastic impacts between two flexible bars. By the considerations of the elastic-plastic deformation and the propagations of elastic-plastic waves induced by impacts, the dynamic controlling equations are derived and the substructure model is built. The comparisons with the three-dimensional elastic-plastic dynamical finite element method showed that the present dynamic substructure technique can calculate correctly the complicated impact force and deformation responses. In addition, the numerical results of displacement waves, velocity waves and stress waves illustrated that the present technique can depict the elastic-plastic wave propagation, wave reflections and wave interactions as well.