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

WANG Zhen; DING Jieyu

doi:10.21656/1000-0887.400340

Volume 41 Issue 12

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2020 > 41(12): 1323-1335

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

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

PDF( 3056 KB)

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

doi: 10.21656/1000-0887.400340

WANG Zhen¹,
DING Jieyu^1,2

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(11772166;11472143)

Received Date: 2019-11-11
Rev Recd Date: 2020-05-09
Publish Date: 2020-12-01

Abstract

Abstract

A multi-body system dynamics model was described with the direction vector method, and the index 3 differential-algebraic equation was reduced to index 1. The multistep block numerical solution scheme was built for the long-time simulation of multi-body systems. The simulation results show that, under the same time step, the multistep block method is better than the classical Runge-Kutta method in terms of the energy error, the position constraint, the speed constraint, the acceleration constraint and the direction vector constraint. The multistep block schemes constructed with the Chebyshev nodes and the Legendre nodes are better than that with the equidistant nodes in terms of the maximum energy error and the direction vector constraint error. The Runge-Kutta method is not suitable for long-time simulation, but the multistep block method can maintain good computational accuracy for long-time simulation.
- multibody system dynamics,
- direction vector method,
- differential-algebraic equation,
- multistep block scheme

FullText(HTML)

References(15)

References

[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))