多体系统动力学微分-代数方程L-稳定方法

李博文; 丁洁玉; 李亚男

doi:10.21656/1000-0887.400038

多体系统动力学微分-代数方程L-稳定方法

doi: 10.21656/1000-0887.400038

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

基金项目: 国家自然科学基金（11472143；11772166）

详细信息

作者简介:
李博文（1995―），女，硕士生(E-mail: 1032788712@qq.com);丁洁玉(1978―)，女，教授，博士，博士生导师(通讯作者. E-mail: djy@qdu.edu.cn).

中图分类号: TP301.6;O175.1
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- 文章访问数: 1053
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- PDF下载量: 439
- 被引次数: 0
出版历程
- 收稿日期: 2019-01-17
- 修回日期: 2019-02-09
- 刊出日期: 2019-07-01

An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

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

Funds: The National Natural Science Foundation of China（11472143；11772166）

摘要

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.
- 多体系统动力学 /
- L-稳定方法 /
- 微分-代数方程 /
- Padé逼近 /
- 稳定性
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.
- multibody system dynamics /
- L-stable method /
- differential-algebraic equation /
- Padé approximation /
- stability

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参考文献(17)

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多体系统动力学微分-代数方程L-稳定方法

doi: 10.21656/1000-0887.400038

作者简介:
李博文（1995―），女，硕士生(E-mail: 1032788712@qq.com);丁洁玉(1978―)，女，教授，博士，博士生导师(通讯作者. E-mail: djy@qdu.edu.cn).

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An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

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留言板

多体系统动力学微分-代数方程L-稳定方法

doi: 10.21656/1000-0887.400038

作者简介: 李博文（1995―），女，硕士生(E-mail: 1032788712@qq.com);丁洁玉(1978―)，女，教授，博士，博士生导师(通讯作者. E-mail: djy@qdu.edu.cn).

计量

出版历程

An L-Stable Method for Differential-Algebraic Equations of Multibody System Dynamics

计量

出版历程

目录

作者简介:
李博文（1995―），女，硕士生(E-mail: 1032788712@qq.com);丁洁玉(1978―)，女，教授，博士，博士生导师(通讯作者. E-mail: djy@qdu.edu.cn).