基于几何精确理论的大变形柔性多体系统动力学变分李群模型及算法

项目名称： 基于几何精确理论的大变形柔性多体系统动力学变分李群模型及算法

项目编号： No.11472144

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： 潘振宽

作者单位： 青岛大学

项目金额： 86万元

中文摘要： 含梁、板、壳、缆、膜等柔性部件大变形柔性多体系统动力学分析的关键是这些部件连续与离散模型的精确描述及稳定、精确、高效的数值积分方法的设计。本项目拟采用几何精确梁、板、壳模型描述大尺度变形部件柔性变形，采用李群方法描述变形体和刚体有限转动；采用离散力学变分原理、李群数值积分方法、多项式插值与高阶求积公式等关键技术针对保守系统设计辛-能量-动量-李群结构保持的高阶变分李群数值积分方法，并将其自然拓展到受非保守力、非完整约束的大变形柔性多体系统。所设计模型与传统多体系统动力学方程兼容，并可自然拓展到绳索、缆、膜等大变形部件描述，几何精确模型为部件大变形精确描述提供保障；有限转动的李群表示使得系统的动力学方程与转动参数无关，且其广义质量阵为常值阵，提高了计算效率；高阶变分李群数值积分方法保证了数值积分的精度和稳定性。研究结果可为大变形柔性多体系统系统动力学分析提供高效的理论建模与数值算法。

中文关键词： 柔性多体系统动力学；大变形；几何精确模型；变分数值积分方法；李群方法

英文摘要： The dynamic analyses of flexible multibody systems(FMS) including large scale components such as beams, plates, shells, cables and membranes depend on exact continuous and discrete mathematical models and stable, accurate and efficient numerical methods. We use geometrically exact beam,plate and shell models under Lie group to descript the large deflection of flexible components in the system and propose the higher order vatiational Lie group integrators for the conservative FMS based on discrete variational principle,Lie Group integrators,polynomial interplation and higher order quadrature techniques, which can be extended to systems with non-holonomic constraints and non-conservative forces. The dynamic equations derived are consistent with traditional multibody systems and can be used naturally to systems including cables, membranes, the exactness of large deflection can be guaranteed by geometrically exact models also. The Lie group method for finite rotation leads to constant generalized mass matrix with higher computation efficiency. Higher order variational Lie group integrators support the stability and accuracy of integration. The models and integrators can be employed to long term simulations of flexible multibody systems with large deflection components. The achievements extend the scope of traditional investigations on dynamics of FMS.

英文关键词： Dynamics of Flexible Multibody Systems;Large Deflection;Geometrically Exact Theory;Variational Integrators;Lie Group Methods