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多刚体系统动力学方向矢量模型及多步块数值方法

王桢 丁洁玉

王桢, 丁洁玉. 多刚体系统动力学方向矢量模型及多步块数值方法[J]. 应用数学和力学, 2020, 41(12): 1323-1335. doi: 10.21656/1000-0887.400340
引用本文: 王桢, 丁洁玉. 多刚体系统动力学方向矢量模型及多步块数值方法[J]. 应用数学和力学, 2020, 41(12): 1323-1335. doi: 10.21656/1000-0887.400340
WANG Zhen, DING Jieyu. A Multibody System Dynamics Vector Model and the Multistep Block Numerical Method[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1323-1335. doi: 10.21656/1000-0887.400340
Citation: WANG Zhen, DING Jieyu. A Multibody System Dynamics Vector Model and the Multistep Block Numerical Method[J]. Applied Mathematics and Mechanics, 2020, 41(12): 1323-1335. doi: 10.21656/1000-0887.400340

多刚体系统动力学方向矢量模型及多步块数值方法

doi: 10.21656/1000-0887.400340
基金项目: 国家自然科学基金(11772166;11472143)
详细信息
    作者简介:

    王桢(1995—),女,硕士生(E-mail: 1339934464@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

A Multibody System Dynamics Vector Model and the Multistep Block Numerical Method

Funds: The National Natural Science Foundation of China(11772166;11472143)
  • 摘要: 使用方向矢量法描述了多刚体系统动力学模型,将指标3的微分-代数方程降至指标1,构造多步块数值求解格式,对一个多刚体系统进行了长时间仿真计算.仿真实验表明:在相同时间步长下,多步块方法解决指标1的方程在能量误差、位移约束、速度约束、加速度约束以及方向矢量约束的保持上比经典Runge-Kutta方法效果好;Chebyshev多项式零点和Legendre多项式零点构造的多步块格式,在最大能量误差以及方向矢量约束误差方面的控制上要比等距节点构造的多步块方法所得的结果更好;在长时间仿真下,多步块格式依然能够保持较好的计算精度,能够克服Runge-Kutta方法不适应长时间仿真的缺点.
  • [1] DE JALN J G, BAYO E. Kinematic and Dynamic Simulation of Multibody Systems the Real-Time Challenge [M]. Berlin: Springer, 1994.
    [2] DE JALN J G. Twenty-five years of natural coordinates[J]. Multibody System Dynamics,2007,18(1): 15-33.
    [3] VON SCHWERIN R. Multibody System Simulation, Numerical Methods, Algorithms and Software [M]. Berlin: Springer, 1999.
    [4] KRAUS C, BOCK H G, MUTSCHLER H. Parameter estimation for biomechanical models based on a special form of natural coordinates[J]. Multibody System Dynamics,2005,13(1): 101-111.
    [5] UHLAR S, BETSCH P. Arotationless formulation of multibody dynamics: modeling of screw joints and incorporation of control constraints[J]. Multibody System Dynamics,2009,22(1): 69-95.
    [6] BUTCHER J C. On the convergence of numerical solutions to ordinary differential equations[J]. Mathematics of Computation,1966,20(93): 1-10.
    [7] CHOLLOM J P, NDAM J N, KUMLENG G M. On some properties of the block linear multi-step methods[J]. Science World Journal,2007,2(3): 11-17.
    [8] OLABODE B T. An accurate scheme by block method for third order ordinary differential equations[J]. Pacific Journal of Science and Technology,2009,10(1): 136-142.
    [9] MEHRKANOON S, MAJID Z A, SULEIMAN M. A variable step implicit block multistep method for solving first-orderODEs[J]. Journal of Computational and Applied Mathematics,2010,233(9): 2387-2394.
    [10] MEHRKANOON S. A direct variable step block multistep method for solving general third-order ODEs[J]. Numerical Algorithms,2011,57(1): 53-66.
    [11] AWOYEMI D O, ADEBILE E A, ADESANYA A O, et al. Modified block method for the direct solution of second order ordinary differential equations[J]. International Journal of Applied Mathematics and Computation,2011,3(3): 181-188.
    [12] MAJID A Z, MOKHTAR N Z, SULEIMAN M. Direct two-point block one-step method for solving general second-order ordinary differential equations[J]. Mathematical Problems in Engineering,2012: 184253. DOI: 10.1155/2012/184253.
    [13] OLABODE B T. Block multistep method for the direct solution of third order of ordinary differential equations[J]. FUTA Journal of Research in Sciences,2013,9(2): 194-200.
    [14] MOHAMED N A, MAJID Z A. Multistep block method for solvingvolterra integro-differential equations[J]. Malaysian Journal of Mathematical Sciences,2016,10: 33-48.
    [15] 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.(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.(in Chinese))
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出版历程
  • 收稿日期:  2019-11-11
  • 修回日期:  2020-05-09
  • 刊出日期:  2020-12-01

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