A derivative-free algorithm for nonlinear equations and its applications in multibody dynamics

Local floating coordinate system is used to represent the deployment motion of each rigid and flexible body of multibody system dynamics. Normal substructure modes are employed to describe the flexibility of a flexible body. Constraint equations establish the linkage between different bodies, part o...

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Bibliographic Details
Published in:Journal of algorithms & computational technology Vol. 12; no. 1; pp. 30 - 42
Main Authors: Tang, Di, Bao, Shiyi, Lv, Binbin, Guo, Hongtao, Luo, Lijia, Mao, Jianfeng
Format: Journal Article
Language:English
Published: London, England SAGE Publications 01.03.2018
Sage Publications Ltd
SAGE Publishing
Subjects:
Algebra
Algorithms
Coordinates
Differential equations
Efficiency
Flexible bodies
Jacobi matrix method
Jacobian matrix
Mathematical analysis
Multibody systems
Nonlinear equations
Quasi Newton methods
Substructures
System dynamics
Derivative-free algorithm
nonlinear equations
multibody dynamics
differential-algebraic equations
ISSN:1748-3026, 1748-3018, 1748-3026
Online Access:Get full text
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Summary:Local floating coordinate system is used to represent the deployment motion of each rigid and flexible body of multibody system dynamics. Normal substructure modes are employed to describe the flexibility of a flexible body. Constraint equations establish the linkage between different bodies, part of them to specify positions and the others to specify orientations. System's governing equations are then derived using generalized coordinates by Lagrange methods. The resulting differential-algebraic equations are transformed to algebraic equations using backward differential formula corrector method, thus highly coupled nonlinear equations are obtained. However, Jacobian matrix of the nonlinear equations is hard to calculate, and then a quasi-Newton method based on Broyden–Fletcher–Goldfarb–Shanno update approach for the solution of the nonlinear equations is proposed. And a suitable line search approach is combined with the Broyden–Fletcher–Goldfarb–Shanno method to improve its efficiency. Some numerical results are reported to show efficiency of the proposed method. Afterwards, the Broyden–Fletcher–Goldfarb–Shanno method is integrated into multibody dynamics method. A rigid multibody case and a rigid-flex multibody case are further studied to show the efficiency of the proposed multibody solver.
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ISSN:1748-3026
1748-3018
1748-3026
DOI:10.1177/1748301817729990