多刚体系统动力学方向矢量模型及多步块数值方法  

A Multibody System Dynamics Vector Model and the Multistep Block Numerical Method

作　　者：王桢 丁洁玉 WANG Zhen;DING Jieyu(School of Mathematics and Statistics,Qingdao University,Qingdao,Shandong 266071,P.R.China;Center for Computational Mechanics and Engineering Simulation,Qingdao University,Qingdao,Shandong 266071,P.R.China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071 [2]青岛大学计算力学与工程仿真研究中心,山东青岛266071

出　　处：《应用数学和力学》2020年第12期1323-1335,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11772166;11472143)。

摘　　要：使用方向矢量法描述了多刚体系统动力学模型,将指标3的微分-代数方程降至指标1,构造多步块数值求解格式,对一个多刚体系统进行了长时间仿真计算.仿真实验表明:在相同时间步长下,多步块方法解决指标1的方程在能量误差、位移约束、速度约束、加速度约束以及方向矢量约束的保持上比经典Runge-Kutta方法效果好;Chebyshev多项式零点和Legendre多项式零点构造的多步块格式,在最大能量误差以及方向矢量约束误差方面的控制上要比等距节点构造的多步块方法所得的结果更好;在长时间仿真下,多步块格式依然能够保持较好的计算精度,能够克服Runge-Kutta方法不适应长时间仿真的缺点.A multi-body system dynamics model was described with the direction vector method,and the index 3 differential-algebraic equation was reduced to index 1.The multistep block numerical solution scheme was built for the long-time simulation of multi-body systems.The simulation results show that,under the same time step,the multistep block method is better than the classical Runge-Kutta method in terms of the energy error,the position constraint,the speed constraint,the acceleration constraint and the direction vector constraint.The multistep block schemes constructed with the Chebyshev nodes and the Legendre nodes are better than that with the equidistant nodes in terms of the maximum energy error and the direction vector constraint error.The Runge-Kutta method is not suitable for long-time simulation,but the multistep block method can maintain good computational accuracy for long-time simulation.

关 键 词：多体系统动力学 方向矢量法 微分-代数方程 多步块格式 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O175.1[自动化与计算机技术—计算机科学与技术]