吉磊，钱林方，陈光宋，尹强 . 基于Bathe积分算法的机械系统多体动力学方程求解方法[J]. 上海交通大学学报, 2020 , 54(11) : 1218 -1226 . DOI: 10.16183/j.cnki.jsjtu.2019.018

［1］刘延柱, 潘振宽, 戈新生. 多体系统动力学［M］. 北京: 高等教育出版社, 2014. LIU Yanzhu, PAN Zhenkuan, GE Xinsheng. Dynamics of multibody systems［M］. Beijing: Higher Education Press, 2014. ［2］洪嘉振. 计算多体系统动力学［M］. 北京: 高等教育出版社, 1999. HONG Jiazhen. Computational dynamics of multibody systems［M］. Beijing: Higher Education Press, 1999. ［3］洪嘉振, 刘铸永. 刚柔耦合动力学的建模方法［J］. 上海交通大学学报, 2008, 42(11): 1922-1926. HONG Jiazhen, LIU Zhuyong. Modeling methods of rigid-flexible coupling dynamics［J］. Journal of Shanghai Jiao Tong University, 2008, 42(11): 1922-1926. ［4］王铁成, 陈国平, 孙东阳. 基于绝对节点坐标法的柔性多体系统灵敏度分析［J］. 振动与冲击, 2015, 34(24): 89-92. WANG Tiecheng, CHEN Guoping, SUN Dongyang. Sensitivity analysis of flexible multibody systems based on absolute nodal coordinate formulation［J］. Journal of Vibration and Shock, 2015, 34(24): 89-92. ［5］CHO H J, BAE D S, CHOI J H, et al. An efficient general purpose contact search algorithm using the relative coordinate system for multibody system dynamics［J］. Solid State Phenomena, 2007, 120: 129-134. ［6］杜晓旭, 崔航, 向祯晖. 基于Kane方法的波浪驱动水下航行器动力学模型建立［J］. 兵工学报, 2016, 37(7): 1236-1244. DU Xiaoxu, CUI Hang, XIANG Zhenhui. The multi-body system dynamics modeling of wave-driven underwater vehicle based on Kane method［J］. Acta Armamentarii, 2016, 37(7): 1236-1244. ［7］SUZUKI T, CHO H J, RYU H S. A recursive implementation method with implicit integrator for multibody dynamics［J］. The Proceedings of the Asian Conference on Multibody Dynamics, 2002, 2002: 600-601. ［8］盛立伟, 刘锦阳, 余征跃. 柔性多体系统弹性碰撞动力学建模［J］. 上海交通大学学报, 2006, 40(10): 1790-1793. SHENG Liwei, LIU Jinyang, YU Zhengyue. Dynamic modeling of a flexible multibody system with elastic impact［J］. Journal of Shanghai Jiao Tong University, 2006, 40(10): 1790-1793. ［9］OMAR M. Multibody dynamics formulation for modeling and simulation of roller chain using spatial operator［J］. MATEC Web of Conferences, 2016, 51: 01003. ［10］GONZLEZ F, DOPICO D, PASTORINO R, et al. Behaviour of augmented Lagrangian and Hamiltonian methods for multibody dynamics in the proximity of singular configurations［J］. Nonlinear Dynamics, 2016, 85(3): 1491-1508. ［11］NEGRUT D, RAMPALLI R, OTTARSSON G, et al. On an implementation of the Hilber-Hughes-Taylor method in the context of index 3 differential-algebraic equations of multibody dynamics (DETC2005-85096)［J］. Journal of Computational and Nonlinear Dynamics, 2007, 2(1): 73-85. ［12］NEGRUT D, JAY L O, KHUDE N. A discussion of low-order numerical integration formulas for rigid and flexible multibody dynamics［J］. Journal of Computational and Nonlinear Dynamics, 2007, 4(2): 021008. ［13］JAY O L, NEGRUT D. A second order extension of the generalized-α method for constrained systems in mechanics［M］. Multibody dynamics. Dordrecht: Springer Netherlands, 2009: 143-158. ［14］LUNK C, SIMEON B. Solving constrained mechanical systems by the family of Newmark and α-methods［J］. ZAMM-Journal of Applied Mathematics and Mechanics, 2006, 86(10): 772-784. ［15］SHABANA A A, HUSSEIN B A. A two-loop sparse matrix numerical integration procedure for the solution of differential/algebraic equations: Application to multibody systems［J］. Journal of Sound and Vibration, 2009, 327(3/4/5): 557-563. ［16］马秀腾, 翟彦博, 罗书强. 基于θ1方法的多体动力学数值算法研究［J］. 力学学报, 2011, 43(5): 931-938. MA Xiuteng, ZHAI Yanbo, LUO Shuqiang. Numerical method of multibody dynamics based on θ1 method［J］. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(5): 931-938. ［17］马秀腾, 翟彦博, 谢守勇. 多体系统动力学指标-2超定运动方程HHT积分改进方法［J］. 中国科学: 技术科学, 2018, 48(2): 229-236. MA Xiuteng, ZHAI Yanbo, XIE Shouyong. Improved HHT integration method for index-2 over-determined equations of motion in multibody system dynamics［J］. Scientia Sinica (Technologica), 2018, 48(2): 229-236. ［18］郭晛, 章定国, 陈思佳. Hilber-Hughes-Taylor-α法在接触约束多体系统动力学中的应用［J］. 物理学报, 2017, 66(16): 147-157. GUO Xian, ZHANG Dingguo, CHEN Sijia. Application of Hilber-Hughes-Taylor-α method to dynamics of flexible multibody system with contact and constraint［J］. Acta Physica Sinica, 2017, 66(16): 147-157. ［19］姚廷强, 黄亚宇, 王立华. 圆柱滚子轴承多体接触动力学研究［J］. 振动与冲击, 2015, 34(7): 15-23. YAO Tingqiang, HUANG Yayu, WANG Lihua. Multibody contact dynamics for cylindrical roller bearing［J］. Journal of Vibration and Shock, 2015, 34(7): 15-23. ［20］丁洁玉, 潘振宽. 多体系统动力学微分-代数方程广义-α投影法［J］. 工程力学, 2013, 30(4): 380-384. DING Jieyu, PAN Zhenkuan. Generalized-α projection method for differentialalgebraic equations of multibody dynamics［J］. Engineering Mechanics, 2013, 30(4): 380-384. ［21］刘颖, 马建敏. 多体系统动力学方程的基于离散零空间理论的Newmark积分算法［J］. 机械工程学报, 2012, 48(5): 87-91. LIU Ying, MA Jianmin. Discrete null space method for the newmark integration of multibody dynamic systems［J］. Journal of Mechanical Engineering, 2012, 48(5): 87-91. ［22］BATHE K J, BAIG M M I. On a composite implicit time integration procedure for nonlinear dynamics［J］. Computers & Structures, 2005, 83(31/32): 2513-2524. ［23］BATHE K J. Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme［J］. Computers & Structures, 2007, 85(7/8): 437-445. ［24］陈光宋. 弹炮耦合系统动力学及关键参数识别研究［D］. 南京: 南京理工大学, 2016. CHEN Guangsong. The study on the dynamic of the projectile-barrel coupled system and the corresponding key parameters［D］. Nanjing: Nanjing University of Science and Technology, 2016. ［25］BAUMGARTE J. Stabilization of constraints and integrals of motion in dynamical systems［J］. Computer Methods in Applied Mechanics and Engineering, 1972, 1(1): 1-16. ［26］KIM J K, CHUNG I S, LEE B H. Determination of the feedback coefficients for the constraint violation stabilization method［J］. Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science, 1990, 204(4): 233-242. ［27］HERTZ H. On the contact of rigid elastic solids and on hardness ［M］. London: Macmillan, 1896: 146-183.