柔性多体系统动力学仿真算法数值稳定性研究

项目名称： 柔性多体系统动力学仿真算法数值稳定性研究

项目编号： No.11472143

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 丁洁玉

作者单位： 青岛大学

项目金额： 90万元

中文摘要： 本项目针对柔性多体系统动力学仿真算法，以常微分方程、微分-代数方程数值求解经典方法的稳定性分析为基础，研究自由参数的引入对算法稳定区域的影响，进而构造新的自由参数形式，扩大稳定区域。在稳定性分析、收敛性分析和算法复杂度分析的基础上，研究相应的高阶数值求解方法，以保持较高精度和计算效率。针对近年来提出的几何积分方法，进行数值稳定性分析，研究能量、动量、辛结构、李群结构等不变量的保持对数值稳定性的影响。在此基础上，结合分析力学领域对称性和守恒量的研究，尝试设计保持更多不变量的柔性多体系统动力学仿真算法，以期进一步提高柔性多体系统动力学方程数值求解的稳定性。通过简单柔性多体系统的数值仿真和物理实验,验证相关理论分析结果的正确性。本项目的研究成果可以为稳定、高效的柔性多体系统动力学仿真算法设计提供理论依据，促进柔性多体系统动力学的进一步发展，以满足高端装备对仿真分析的更高要求。

中文关键词： 柔性多体动力学；仿真算法；数值稳定性；几何积分方法

英文摘要： Based on the stability analysis of classical numerical methods of ODEs and DAEs, the effects of parameter introducing on the stable region of simulation algorithms is studied for flexible multibody system dynamics. New parameter forms are designed to expand the stable region. Based on stability analysis, convergence analysis and complexity analysis, the corresponding algorithms with higher order are developed to obtain higher accuracy as possible when the stability is improved. Numerical analysis of stability of geometry integrators presented in recent years is studied to find the effects of energy, momentum, symplectic structure and Lie group structure conserving for the stability of the algorithms. Then based on the theories of symmetries and conserved quantities in analytical mechanics, algorithms with more invariants conserving are developed to try to obtain the further stability. Analysis results are verified by numerical simulation and physical experiments of simple flexible multibody systems. These studies can provide theoretical foundation for algorithms design of multibody systems simulation; promote the further development of flexible multibody system dynamics to meet the higher demands of high-end equipment manufacturing simulation.

英文关键词： flexible multibody dynamics;simulation algorithm;numerical stability;geometry integrator