关键词: HHT方法, 多体动力学, 广义-方法, 时间积分算法, 微分—代数方程, 隐式数值积分解耦法

Abstract: For analysis of multibody dynamics, a new generalized-α algorithm is proposed on the basis of implicit numerical integration decoupling algorithms. By applying the new generalized-α algorithm and introducing the scaling factor h or h2 of integration stepsize into the calculations of Jacobian matrix, discrete equations of multi-body dynamics and constraints equations are obtained. Decoupling equations for systems’ variables and decoupling Jacobian matrix are obtained on the basis of implicit numerical integration decoupling algorithms, thereby improving the efficiency of calculation and avoiding poor Jacobian matrix. Accuracy, convergence, stability and efficiency analysis of the new generalized-α algorithm are carried out through numerical examples. Theoretical study and numerical analysis show that the new generalized-α algorithm reduces the number of evaluations of Jacobian matrix function, the iterations of Newton-Raphson and the calculations of dimensions of multi-flexible body dynamics greatly. The new generalized-α algorithm featuring efficiency, accuracy and controllable numerical damping has important theoretical reference meaning and practical application value to mechanical systems with multi flexible bodies, contact-impact and friction.

Key words: Differential algebraic equation, Generalized alpha method, HHT method, Implicit numerical integration decoupling algorithm, Multi-body dynamics, Time integration algorithm