基于线性互补问题的多体系统接触/碰撞动力学研究

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (5) : 276-282.

论文

张欣刚1，齐朝晖2，王刚3，国树东2，吴志刚2

作者信息 +

Contact/impact dynamics of multi-body system based on LCP

ZHANG Xingang1, QI Zhaohui2, WANG Gang3, GUO Shudong2, WU Zhigang2

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文章历史 +

摘要

多体系统往往包含大量的接触/碰撞行为，这些非光滑事件的存在造成了动力学方程的不连续或分段连续，给数值求解带来了很大的困难。为综合考虑平顺接触与碰撞，采用基于线性互补问题的非光滑动力学方法，首先在当前时刻为起点的短时间内对对缝隙函数进行均匀化，然后与法向接触力建立标准线性互补方程，最后将线性互补方程改造为一组非线性代数方程，通过非线性迭代可直接求解接触力。算例结果表明，采用该方法不需在接触状态发生改变时切换模型,且严格满足互补关系，保证了接触力的非负性。研究成果可成为求解多柔体系统接触/碰撞问题的新途径。

Abstract

Multibody systems always contain plenty of contact-impact behaviors, these non-smooth events cause the discontinuity or piecewise continuous of the govern equations and make the numerical solution more difficult. To overcome this difficulty, first, the instant gap function can be replaced by its time-averaged gap to set the standard linear complementarity equation. In the following, these equations can be modified as its equivalent non-linear equations, contact force can then be solved by nonlinear iteration. Numerical results showed that impact and smoothing contact are comprehensive consideration without change contact force model when contact status changes. Moreover, the non-negativity of the contact fore is guaranteed by the strict complementarity condition. The proposed method can be a new available approach to numerical analysis of contact/impact problems of flexible multibody systems.

导出引用

张欣刚1，齐朝晖2，王刚3，国树东2，吴志刚2. 基于线性互补问题的多体系统接触/碰撞动力学研究[J]. 振动与冲击, 2021, 40(5): 276-282

ZHANG Xingang1, QI Zhaohui2, WANG Gang3, GUO Shudong2, WU Zhigang2. Contact/impact dynamics of multi-body system based on LCP[J]. Journal of Vibration and Shock, 2021, 40(5): 276-282

参考文献

[1] 刘铖, 叶子晟, 胡海岩. 基于区域分解的柔性多体系统高效并行算法[J]. 中国科学: 物理学力学天文学, 2017, 47: 104603.
Liu C, Ye Z S, Hu H Y. An efficient parallel algorithm for flexible multibody systems based on domain decomposition method[J]. Sci Sin-Phys Mech Astron, 2017, 47: 104603.
[2] 曹登庆,白坤朝,丁虎,周徐斌,潘忠文,陈立群,詹世革. 大型柔性航天器动力学与振动控制研究进展[J]. 力学学报, 2019, 51(1):1-13.
Cao Dengqing, Bai Kunchao, Ding Hu, Zhou Xubin, Pan Zhongwen, Chen Liqun, Zhan Shige. Advances in dynamics and vibration control of large-scale flexible spacecraft[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 1-13.
[3] 田强, 刘铖, 李培等. 多柔体系统动力学研究进展与挑战[J]. 动力学与控制学报, 2017, 15(5): 385-405.
Tian Qiang, Liu Cheng, Li Pei, et al. Advances and challenges in dynamics of flexible multibody systems[J]. Journal of Dynamics and Control, 2017, 15(5): 385-405.
[4] 刘才山, 陈滨. 多柔体系统碰撞动力学研究综述[J]. 力学进展，2000,30(1):7-14
Liu C S, Chen B. A global review for the impact dynamic research of flexible multibody systems[J]. Advances in Mechanics, 2000,30(1): 7-14
[5] Flores P , Leine R , Glocker C . Modeling and analysis of planar rigid multibody systems with translational clearance joints based on the non-smooth dynamics approach[J]. Multibody System Dynamics, 2010, 23(2):165-190.
[6] Glocker C, Studer C. Formulation and Preparation for Numerical Evaluation of Linear Complementarity Systems in Dynamics[J]. Multibody System Dynamics, 2005, 13(4):447-463.
[7] 王琪, 庄方方, 郭易圆, 章杰, 房杰. 非光滑多体系统动力学数值算法的研究进展[J]. 力学进展, 2013, 43(1): 101-111.
Wang Qi, Zhuang Fangfang, Guo Yiyuan, et al. Advances in the research on numerical methods for non-smooth dynamics of multibody systems[J]. Advances in Mechanics, 2013, 43(1): 101-111
[8] Flores P, Machado M, Silva M T, et al. On the continuous contact force models for soft materials in multibody dynamics[J]. Multibody System Dynamics, 2011, 25(3):357-375.
[9] Lankarani H M , Nikravesh P E . A contact force model with hysteresis damping for impact analysis of multibody systems [J]. Journal of Mechanical Design, 1990, 112(3):369-376.
[10] Hunt KH, Crossley FRE. Coefficient of restitution interpreted as damping in vibroimpact[J]. J Appl Mech T ASME 1975,7:440–445
[11] Bowling A, Flickinger D M, Harmeyer S. Energetically consistent simulation of simultaneous impacts and contacts in multibody systems with friction[J]. Multibody System Dynamics, 2009, 22(1):27-45.
[12] 白争锋,赵阳,田浩. 柔性多体系统碰撞动力学研究[J]. 振动与冲击, 2009, 28(6): 75-78.
BAI Zheng-feng, ZHAO Yang, TIAN Hao. Study on contact dynamics for flexible multi-body system [J]. Journal of vibration and shock 2009, 28(6): 75-78.
[13] Margarida M, Pedro M, Paulo F, et al. Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory [J]. Mechanism and Machine Theory, 2012, 53: 99-121
[14] Zhang Xingang, Qi Zhaohui, et al. Model smoothing method of contact-impact dynamics in flexible multibody systems[J]. Mechanism and Machine Theory, 2019, 138: 124-148
[15] 王检耀, 刘铸永, 洪嘉振. 基于两种接触模型的柔性体间多次微碰撞问题研究[J]. 振动与冲击, 2018, 37(11).
Wang Jianyao, LIU Zhuyong, et.al. Multi-micro impact among flexible bodies using two contact models[J]. Journal of vibration and shock, 2018, 37(11):202-206.
[16] 董富祥,洪嘉振.多体系统动力学碰撞问题研究综述[J].力学进展,2009,39(03):352-359.
Dong Fuxiang, Hong Jiazhen. Review of impact problem for dynamics of multibody system[J]. Advances in Mechanics, 2009, 39(3): 352-359
[17] 齐朝晖.多体系统动力学[M].北京:科学出版社,2008.
Qi Z H. Dynamics of multibody systems[M]. Beijing: Science Press, 2008
[18] Machado M , Moreira P , Flores P , et al. Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory[J]. Mechanism & Machine Theory, 2012, 53:99-121.
[19] 齐朝晖, 曹艳, 王刚. 多柔体系统数值分析的模型降噪方法[J]. 力学学报, 2018, 50(4): 863-870
Qi Zhaohui, Cao Yan, Wang Gang. Model smoothing methods in numerical analysis of flexible multibody systems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 863-870
[20] 王庚祥, 刘宏昭. 多体系统动力学中关节效应模型的研究进展[J]. 力学学报, 2015, 47(1): 31-50.
Wang Gengxiang, Liu Hongzhao. Research progress of joint effects model in multibody system dynamics [J]. Chinese Journal of Theoretical and Applied Mechani, 2015, 47(1): 31-50.
[21] Leine, R.I., van de Wouw, N.: Stability and Convergence of Mechanical Systems with Unilateral Constraints [J]. Lecture Notes in Applied and Computational Mechanics, vol. 36. Springer, Berlin
[22] Pfeiffer, F., Foerg, M., Ulbrich, H.: Numerical aspects of non-smooth multibody dynamics [J]. Comput. Methods Appl. Mech. Eng.2006, 195(50–51), 6891–6908
[23] Glocker, C.: Set-Valued Force Laws: Dynamics of Non-Smooth System. Lecture Notes in Applied Mechanics [J], 2001,vol. 1. Springer, Berlin
[24] 王刚, 齐朝晖, 汪菁. 含铰接杆系结构几何非线性分析子结构方法[J]. 力学学报, 2013, 46(2).
Wang Gang, Qi Zhaohui, Wang Jing. Substructure methods of geometric nonlinear analysis for member structures with hinged supports [J]. Chinese Journal of Theoretical and Applied Mechani, 2014, 46(2): 273-283.