多体动力学超定运动方程广义-<em>α</em>求解新算法

马秀腾; 翟彦博; 罗书强

doi:10.6052/0459-1879-12-028

多体动力学超定运动方程广义-α求解新算法

doi: 10.6052/0459-1879-12-028

西南大学工程技术学院, 重庆 400715

基金项目: 中央高校基本科研业务费专项资金(XDJK2009C009)和西南大学博士基金(SWU109048)资助项目.

详细信息

通讯作者:
马秀腾

中图分类号: O313.7
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出版历程
- 收稿日期: 2012-01-19
- 修回日期: 2012-02-21
- 刊出日期: 2012-09-18

NEW GENERALIZED-α METHOD FOR OVER-DETERMINED MOTION EQUATIONS IN MULTIBODY DYNAMICS

College of Engineering & Technology, Southwest University, Chongqing 400715, China

Funds: The project was supported by the Fundamental Research Funds for the Central Universities (XDJK2009C009) and Funds for Doctors of Southwest University(SWU109048).

摘要

摘要: 完整约束多体系统第一类Lagrange方程建模得到的运动方程是指标-3形式的微分-代数方程(differental-algebraic equations,DAEs).如果同时考虑速度约束,将得到超定运动方程,该方程是指标-2的超定微分-代数方程(over-determined differential-algebraic equations,ODAEs).基于结构动力学中常用的广义-α方法,将其拓展,求解包含速度约束的超定运动方程,相对于其他求解指标-2 ODAEs的算法,新的算法没有增加离散得到的非线性方程组方程的数目.通过数值实验验证算法,并说明其求解ODAEs不存在精度降阶的现象,仍然具有二阶精度,同时算法的数值耗散也是可以控制的.最后新方法与其他求解多体系统ODAEs形式运动方程算法的CPU时间进行了比较分析.
- 多体动力学 /
- 超定微分-代数方程(ODAEs) /
- 广义-α方法 /
- 二阶精度 /
- 数值耗散
Abstract: Motion equations of multibody systems with holonomic constraints via the first kind of Lagrange's equations are index-3 differential-algebraic equations (DAEs).As for the velocity-constrained equations are considered,over-determined motion equations can be obtained and named as index-2 over-determined differential-algebraic equations (ODAEs).Generalized-α method,which is used in the structural dynamics simulation,is extended to the numerical integration of motion equations in the form of index-2 ODAEs.For the new generalized-α method,the number of nonlinear equations from discretization is not increased compared with other integration methods for the index-2 ODAEs.The new method is validated by numerical experiments.There are no accuracy reductions for the new method in the integration of index-2 ODAEs and it is second-order accuracy.In addition,the numerical dissipation is controllable.In the end,new generalized-α method for motion equations in the form of ODAEs is compared with other methods from the point view of the CPU time.
- multibody dynamics /
- over-determined differential-algebraic equations(ODAEs) /
- generalized-α method /
- second-order accuracy /
- numerical dissipation

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