| 多体系统动力学微分-代数方程L-稳定方法 |
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| 引用本文： | 李博文,丁洁玉,李亚男. 多体系统动力学微分-代数方程L-稳定方法[J]. 应用数学和力学, 2019, 40(7): 768-779. DOI: 10.21656/1000-0887.400038 |
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| 作者姓名： | 李博文 丁洁玉 李亚男 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金（11472143；11772166） |
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| 摘 要： | 针对多体系统动力学微分-代数方程形式,在时间区间上构造L-稳定方法,分别基于等距节点、Chebyshev节点和Legendre节点等非等距节点建立求解格式,依据Ehle定理及猜想,与Padé逼近式对比得到待定矩阵和向量,从而获得L-稳定求解公式,循环求解过程采用Newton迭代法计算.以平面双连杆机械臂系统为例,使用L-稳定方法进行数值仿真,通过改变时间区间节点数和步长对各个指标结果进行比较,并与经典Runge-Kutta法对比.结果表明,该方法具有稳定性好、精度高等优点,适用于长时间情况下的多体系统动力学仿真.
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| 关 键 词： | 多体系统动力学 L-稳定方法 微分-代数方程 PADÉ逼近 稳定性 |
| 收稿时间： | 2019-01-17 |
An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics |
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| LI Bowen,DING Jieyu,LI Yanan. An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics[J]. Applied Mathematics and Mechanics, 2019, 40(7): 768-779. DOI: 10.21656/1000-0887.400038 |
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| Authors: | LI Bowen DING Jieyu LI Yanan |
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| Affiliation: | 1School of Mathematics and Statistics, Qingdao University, Qingdao, Shandong 266071, P.R.China;2Center for Computational Mechanics and Engineering Simulation, Qingdao University, Qingdao, Shandong 266071, P.R.China |
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| Abstract: | An L-stable method over time intervals for differential-algebraic equations of multibody system dynamics was presented. The solution scheme was established based on equidistant nodes and non-equidistant nodes such as Chebyshev and Legendre nodes. According to Ehle’s theorem and conjecture, the unknown matrix and vector in the L-stable solution formula were obtained through comparison with the Padé approximation. The Newtonian iteration method was used during the solution process. The planar 2-link manipulator system was taken as an example, and the results from the L-stable method were compared for different node numbers in the time interval and different steps in the simulation, with those from the classic Runge-Kutta method. The comparison shows that, the proposed method has the advantages of good stability and high precision, and is suitable for multibody system dynamics simulation under long-term conditions. |
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| Keywords: | multibody system dynamics L-stable method differential-algebraic equation Padé approximation stability |
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