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Research Papers

An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Qiang Tian

Center for Computer-Aided Design, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. Chinatianqiang_hust@yahoo.com.cn

Li Ping Chen1

Center for Computer-Aided Design, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. Chinachenlp@hustcad.com

Yun Qing Zhang

Center for Computer-Aided Design, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. Chinazhangyq@hust.edu.cn

Jingzhou Yang

Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409james.yang@ttu.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 4(2), 021009 (Mar 10, 2009) (14 pages) doi:10.1115/1.3079783 History: Received November 30, 2007; Revised April 28, 2008; Published March 10, 2009

This paper presents an efficient hybrid method for dynamic analysis of a flexible multibody system. This hybrid method is the combination of a penalty and augmented Lagrangian formulation with the mass-orthogonal projections method based on the absolute nodal coordinate formulation (ANCF). The characteristic of the ANCF that the mass matrix is constant and both Coriolis and centrifugal terms vanish in the equations of motion make the proposed method computationally efficient. Within the proposed method, no additional unknowns, such as the Lagrange multipliers in the Newmark method, are introduced, and the number of equations does not depend on the number of constraint conditions. Furthermore, conventional integration stabilization methods, such as Baumgarte’s method. are unnecessary. Therefore, the proposed method is particularly suitable for systems with redundant constraints, singular configurations, or topology changes. Comparing results from different methods in terms of efficiency and accuracy has shown that the proposed hybrid method is efficient and has good convergence characteristics for both stiff and flexible multibody systems.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The beam element with shear deformation

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Figure 2

Flexible double pendulum

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Figure 3

Tip point B X-displacement error with respect to RKF45 results

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Figure 4

Tip point B X-displacement error with respect to MSC.ADAMS results (four elements, E=2.07×1011 Pa)

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Figure 5

Tip point B X-displacement error with respect to MSC.ADAMS results (eight elements, E=2.07×1011 Pa)

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Figure 6

Incorrect results of the Newmark method (γ=56 and η=49)

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Figure 7

The system energy variation using the Newmark method (E=2.07×1011 Pa, four elements)

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Figure 14

Tip point B X-displacement variation (8 elements, E=7×109 Pa)

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Figure 15

Tip point B X-displacement error with respect to Newmark results (γ=1/2, η=1/4, eight elements, and E=7×109 Pa)

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Figure 16

Tip point B transverse displacements obtained by using different element number models (E=7×109 Pa)

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Figure 17

Double pendulum configuration (Index 1 ALF method, four elements, and E=2.07×1011 Pa)

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Figure 18

Double pendulum configuration (Index 1 ALF method, eight elements, E=7×109 Pa)

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Figure 19

Double pendulum configuration (Index 1 ALF method, eight elements, E=2×108 Pa)

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Figure 8

The system energy variation using the Newmark method and Baumgarte’s method (four elements, E=2.07×1011 Pa)

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Figure 9

The system energy variation using the ALF-based method (four elements, E=2.07×1011 Pa)

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Figure 10

Point A X-displacement constraint violation

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Figure 11

Point A X-velocity constraint violation

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Figure 12

Point A X-acceleration constraint violation

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Figure 13

Tip point B transverse displacements obtained by using models with different numbers of elements (E=2.07×1011 Pa)

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