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  

Study of open simulation algorithm software for multibody system dynamics(Ⅱ) comparison of algorithms for solving DAEs

作　　者：阚子云[1] 彭海军[1] 陈飙松[1] 钟万勰[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室工程力学系,大连116024

出　　处：《计算力学学报》2015年第6期707-715,721,共10页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11102031;11472069;11372064;11432010)资助项目

摘　　要：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。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 a method, Bathe method and Zu Chongzi Sympleetic 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.

关 键 词：多体动力学 微分-代数方程组(DAEs) 数值积分算法 算法比较 

分 类 号：O313.7[理学—一般力学与力学基础]