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

作者：Tang Di; Bao Shiyi; Lv Binbin; Guo Hongtao; Luo Lijia; Mao Jianfeng

来源：Journal of Algorithms and Computational Technology, 2018, 12(1): 30-42.

DOI：10.1177/1748301817729990

• Coupled nonlinear equations
• Derivative-free algorithm
• Differential algebraic equations
• Generalized coordinates
• Multi-body dynamic
• Multi-body system dynamics
• Multibody dynamics method
• Quasi-Newton methods

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.

• 出版日期2018
• 单位浙江大学