多柔体系统响应计算的子循环计算方法研究

STUDY ON SUB-CYCLING ALGORITHM FOR A FLEXIBLE MULTI-BODY SYSTEM

过去近30年中,柔性多体系统动力学研究取得了巨大的进展,人们的兴趣集中在柔性多体系统建模、计算及实验研究等3个方面.Belytschko等于1979年提出的子循环算法已经成功地应用于结构动力响应的有限元计算中,然而有关柔性多体动力学的子循环算法研究尚未见报道.该文提出了一种适合于柔性多体系统响应计算的中心差分类子循环算法,在将非线性微分-代数混合方程组(DAEs)缩并为纯微分方程组(ODE)的基础上,推导出快、慢变分量的同步更新公式和子步更新公式;在变量的数值积分过程中,采用能量平衡计算检查算法的稳定性;算例结果表明该算法可以在保持合适的精度要求下,有效地提高响应的计算效率;对积分步长进行摄动修正可以保持算法的稳定性.

Great developments have been made in the field of flexible multi-body system （FMS） with mod- eling, computational and experimental studies for nearly 30 years. The subcycling algorithms, which were firstly presented by Belytschko T. et al. in 1979, have been successfully applied in the structural dynamic analysis of FMS. However, subcycling algorithms for the FMS are still not presented up to now. This paper introduces a central difference method based sub-cycling algorithm for the FMS. First, common update for- mulae and sub-step update formulae for quickly changing variables and slowly changing variables of the FMS are established. Second, the nonlinear differential-algebraic equations are contracted to the original differential equations. Third, algorithm stability is validated with an energy balance computation during the integration procedure. Numerical results indicate that the sub-cycling algorithm is available to enhance the computational efficiency with appropriate computational accuracy. Furthermore, the algorithm stability can be determined by means of modifying the integral step sizes with the perturbation method.