基于线性互补问题的多体系统接触/碰撞动力学研究

Contact/impact dynamics of multi-body system based on LCP

多体系统往往包含大量的接触/碰撞行为,这些非光滑事件的存在造成了动力学方程的不连续或分段连续,给数值求解带来了很大的困难。为综合考虑平顺接触与碰撞,采用基于线性互补问题的非光滑动力学方法,首先在当前时刻为起点的短时间内对对缝隙函数进行均匀化,然后与法向接触力建立标准线性互补方程,最后将线性互补方程改造为一组非线性代数方程,通过非线性迭代可直接求解接触力。算例结果表明,采用该方法不需在接触状态发生改变时切换模型,且严格满足互补关系,保证了接触力的非负性。研究成果可成为求解多柔体系统接触/碰撞问题的新途径。

Multibody systems may contain a large number of contact/impact behaviors,these non-smooth events cause discontinuity or piecewise continuous of dynamic equations of multi-body system and make these equations’numerical solving be more difficult.Here,in order to comprehensively consider smooth contact and collision,a non-smooth dynamic method based on linear complementarity problem(LCP)was proposed.Firstly,the gap function was homogenized within a short time duration starting from the current moment,and then a standard linear complementary equation was established for the gap function and the normal contact force.Finally,the linear complementarity equation was converted into a set of nonlinear algebraic equations to directly solve the contact force with nonlinear iteration.Example results showed that the proposed method does not need to switch the model when the contact state changes,it strictly satisfies the complementary relationship to ensure the non-negativity of contact force;the research results can be a new way to solve contact/collision problems of flexible multi-body systems.