An efficient algorithm based on Broyden's and generalized-α method for large scale flexible multi-body systems

Abstract

This paper designs a novel and efficient numerical strategy based on generalized-α algorithm and Broyden's method to solve dynamic equations of large scale flexible multi-body system. The dynamic models are established in view of Absolute Nodal Coordinate Formulation(ANCF) and the clearance joint model is described by nonlinear contact force model and modified Coulomb's friction model. The proposed strategy only needs a given initial Jacobian matrix and then the numerical solutions can be obtained by using Sherman-Morrison-Woodburg theorem, that can greatly increase the computational efficiency as a result of avoiding solving of the Jacobian matrix in each iteration. Newton-Raphson iteration and Trust-Region-Dogleg algorithm, as two typical numerical solutions for nonlinear dynamic equations of large scale flexible multi-body systems, are selected to be compared the effectiveness and efficiency with the proposed numerical method. Numerical results show that the proposed method is accurate and robust, and can improve the computational efficiency by several or even a dozen times than the other two common methods for large scale flexible multi-body systems including flexible double pendulum model, rigid and rigid-flexible coupling solar array systems.