开放式多体系统动力学仿真算法软件研发（II）DAEs 求解算法对比

摘要

The high efficiency,high accuracy and high performance numerical integration algorithms are hot tops in the field of multibody system dynamics.Direct numerical integration methods which solve the structural dynamics equation are applied to solve the DAEs in this paper.Based on the SiPESC platform and the open simulation algorithm software for multibody system dynamics,comparison study of Newmark method,HHT-I3 method,Generalized α method,Bathe method and Zu Chongzi Symplectic method is made.By using the compound pendulum and the rigid-flexible double pendulum examples,this paper studied the relationship between parameters and numerical dissipative of different algorithms.For solving the high-low frequency coupled and high-speed rotation of the gyro problems,the system can be accurately simulated by the non-dissipative Newmark method and Zu Chongzi Symplectic method.%研究求解微分-代数方程组(DAEs)的高效率、高精度和高稳定性数值积分方法一直是多体系统动力学领域的热点问题之一。本文将求解结构动力学方程的 Bathe 数值积分策略应用于 DAEs 的求解,并基于 SiPESC 平台开发了开放式多体系统动力学仿真算法软件,综合比较研究了 Newmark 法、HHT-I3法、Generalizedα方法、Bathe 方法和祖冲之类 Symplectic 方法。通过复摆、刚-柔耦合双摆和对称陀螺三个数值算例研究了算法参数与数值阻尼的关系。数值实验表明,Newmark 方法在特定参数下引入的数值阻尼通常不可控,HHT-I3方法、Generalizedα方法和 Bathe 方法通过选择特定步长和参数可引入可控的数值阻尼,祖冲之类 Symplectic 方法无数值阻尼。在求解真实高频和低频耦合问题以及高速旋转的陀螺问题时,采用祖冲之类 Symplectic 方法或者无耗散的 Newmar 方法能够对系统的高频成分进行准确模拟。