• CN：11-2187/TH
• ISSN：0577-6686

• 机械动力学 •

基于向后差分法求解多体系统动力学微分-代数方程组的双循环隐式积分方法

1. 南京理工大学理学院 南京 210094
• 出版日期:2016-04-05 发布日期:2016-04-05
• 作者简介:张乐,男,1988年出生,博士研究生。主要研究方向为多体系统动力学。E-mail：zhangleatnjust@gmail.com;章定国(通信作者),男,1967年出生,博士,教授,博士研究生导师。主要研究方向为多体系统动力学,柔性机器人动力学。E-mail：zhangdg419@mail.njust.edu.cn
• 基金资助:
国家自然科学基金项目(11272155, 11132007)、江苏省“333工程”(BRA2011172)和中央高校基本科研业务费专项资金(30920130112009)资助项目

Two-loop Implicit Integration Method Based on Backward Differential Formulation for Differential-algebraic Equations of Multibody System Dynamics

ZHANG Le, ZHANG Dingguo

1. School of Science, Nanjing University of Science and Technology, Nanjing 210094
• Online:2016-04-05 Published:2016-04-05

Abstract: An iterative method is needed when implicit integration method is used to integrate the independent coordinates of differential-algebraic equations (DAEs) which come from multibody system dynamics. If the iterative method is Newton’s method, numerical differentiation is needed to obtain the Jacobian matrix. A fixed-point iterative method without the using of the Jacobian matrix can simplify the progress. The nonlinear algebraic constraint equations in DAEs are also solved by iteration to obtain the dependent coordinates. A two-loop structure is designed to manage those two iterations. The numerical accuracy of the integration method influences the numbers of iteration of implicit integration method which is called as the outer loop. Backward differential formulation (BDF) is introduced as the integration method into the two-loop method. New strategy is proposed to constitute the new two-loop method. The numbers of iteration of outer loop in the new two-loop method are reduced, and the computational efficiency is improved. The new two-loop method can solve the DAEs of multibody system dynamics well, and its universality is good. Numerical examples are provided.