多体系统动力学子系统求解算法

Efficient numerical solution for multi-body system dynamics based on subsystem algorithm

为了降低系统求解规模,提高复杂多体系统动力学求解效率,研究了多体动力学子系统求解算法。通过分析系统拓扑构型,基于雅克比矩阵分块特性,提出子系统综合算法。算法采用半递归法建立含开环、闭环的子系统运动方程,将子系统质量和外力等效作用在内接基体上,解耦系统运动方程组装和加速度求解。此外,针对松散耦合子系统,提出了子系统分治算法。算法针对子系统间的耦合特点,分解复杂多体系统模型,实现子系统的独立求解。最后以机构动力学数值求解实例,验证上述算法的正确性和求解效率。

To improve the computational efficiency and reduce the scale of dynamic analysis of complicated multibody system, the solution based on subsystem algorithm is studied. By analyzing the topological relationship of the system and the traits of the Jacobian matrix, a subsystem synthesis algorithm is developed. The algorithm uses the semi-recursive method to construct the motion equations of open-and closed-loop subsystem, and then synthesizes the effective masses and forces to the inner base body to decompose the assembly of the motion equation of the whole system. Furthermore, for the subsystems coupled weakly with the others, in terms of the coupling characteristics among subsystems, a divide-and-conquer algorithm is also proposed to divide the system into the smaller subsystems. This algorithm adopts a gluing method to coordinate the displacement constraints connecting the subsystems and analyze each subsystem using their own independent solvers to improve the integration efficiency of subsystem models. Finally, the proposed algorithms are demonstrated and validated through two examples of dynamic analysis for the six-link mechanisms.