非光滑多体系统动力学数值算法的研究进展

非光滑多体系统动力学数值计算方法是多体系统动力学研究的重要内容之一. 本文介绍了近年来含摩擦与碰撞的非光滑多体系统动力学数值算法方面的研究进展. 首先, 讨论了库仑摩擦模型和修正的库仑摩擦模型, 以及具有单边和双边约束的多体系统中法向约束力的特点. 其次, 回顾了基于连续模型和非连续模型的多体系统动力学方程的数值计算方法, 详细介绍了基于互补概念的非光滑多体系统动力学的事件驱动法和时间步进法, 分析比较了相关的数值算法. 最后, 指出了一些需要进一步研究的问题.

ADVANCES IN THE RESEARCH ON NUMERICAL METHODS FOR NON-SMOOTH DYNAMICS OF MULTIBODY SYSTEMS

The numerical method for the non-smooth dynamics of multibody systems is one of the hot topics of researches on the dynamics of multibody systems. In this paper, recent advances in the research on numerical methods are presented for the non-smooth dynamics of multibody systems with impact and friction. First, the Coulomb friction model, modified Coulomb friction model and the characteristics of the normal forces of multibody systems with unilateral and bilateral constraints are discussed. Second, recently developed numerical methods for the non-smooth dynamics of multibody systems based on continuous and discontinuous models are reviewed. The Event-driven scheme and time-stepping method for the non-smooth dynamics of multibody systems are described in detail based on the complementarity concept. These numerical methods are then analysed and compared. Finally, the problems in need of further studies are pointed out.