冗余约束多刚体系统摩擦碰撞问题的数值求解方法

针对冗余约束多刚体系统的摩擦碰撞问题,以牛顿恢复系数作为碰撞终止条件,以离散化的系统动力学方程和线性规划理论为基础,建立了相应的混合互补模型。为有效求解该模型,利用最小二乘法和线性化方法,将混合互补模型转化为标准的线性互补模型,用线性互补模型的求解算法进行数值求解。接着,提出一种直接投影修正算法对碰撞计算过程进行修正,有效防止了碰撞加剧约束违约的现象。最后,通过一个算例,验证了数值求解方法和修正算法的有效性。

Numerical resolution method for frictional collision problems of multi-rigid-body with redundant constraints

Aiming at frictional collision problems of multi-rigid-body with redundant constraints, a corresponding mixed complementary model with Newton restitution coefficients as termination conditions of collision was established based on linear programming theories and discretized dynamic equations. In order to solve the problem effectively, the mixed complementary model was changed into a linear complementary model by using the least square method and the linearization method and then a resolution algorithm for the linear complementary model was applied. Furthermore, a direct projection algorithm was proposed for stabilizing the resolution process of the collision in advance, which effectively prevented aggravation of constraint violation due to the collision. At last, the validity of the numerical resolution method and the constraint stabilization algorithm was verified through a numerical example.