基于区域分解的柔性多体系统高效并行算法

发布时间：2018-05-12 01:08

本文选题：大变形柔性多体系统 + 区域分解　；参考：《中国科学:物理学力学天文学》2017年10期

【摘要】：近年来,大量轻质柔性结构成功应用于航空航天、智能机器人以及3D打印等领域,使得这些机械系统呈现出典型的刚柔耦合动力学特性.已有研究表明,基于小变形、小转动假设的传统柔性多体系统建模方法,如浮动坐标系方法,已无法精确描述上述大变形柔性构件的动力学特性.本文在等几何分析体系下,采用非均匀有理B样条(Non-Uniform Rational B-Splines,NURBS)插值函数离散平面柔性结构位移场,基于连续介质力学大变形理论,建立了能够精确描述大转动与大变形耦合的平面板单元.为了提高大变形柔性多体系统仿真效率,本文首先采用不变矩阵法,推导了大变形柔性体的非线性弹性力与切向刚度矩阵的高效计算公式.其次,基于有限元撕裂对接(Finite Element Tearing and Interconnecting,FETI)区域分解技术,提出了一种大变形柔性多体系统动力学方程高效求解算法.该算法中,首先通过空间离散与时间离散将多体系统动力学方程转化为一组非线性代数方程,然后采用含预条件的共轭梯度(Preconditioned Conjugate Gradients,PCG)迭代算法并行求解线性化后的线性方程组.较以往多体系统常用的并行直接算法,能够显著地提高计算效率.最后,通过若干数值算例验证了所提出并行算法的有效性,并分析了该算法的复杂度,加速比以及可扩展性.
[Abstract]:In recent years, a large number of lightweight flexible structures have been successfully applied in aerospace, intelligent robots and 3D printing, which make these mechanical systems exhibit typical rigid-flexible coupling dynamics. It has been shown that the traditional modeling method of flexible multi-body system based on the assumption of small deformation and small rotation, such as floating coordinate system, can no longer accurately describe the dynamic characteristics of the large deformation flexible member mentioned above. In this paper, based on the theory of large deformation in continuum mechanics, the displacement field of planar flexible structures is discretized by non-uniform rational B-spline Rational B-SplinesNURBS interpolation function in the isometric analysis system. A planar plate element which can accurately describe the coupling of large rotation and large deformation is established. In order to improve the simulation efficiency of flexible multi-body system with large deformation, this paper first uses the invariant matrix method to derive the high efficiency formulas for calculating the nonlinear elastic force and tangential stiffness matrix of the large deformation flexible body. Secondly, an efficient algorithm for solving the dynamic equations of flexible multi-body systems with large deformation is proposed based on the finite element tearing and docking finite Element Tearing and interconnecting FETI domain decomposition technique. In this algorithm, the dynamic equations of multibody systems are firstly transformed into a set of nonlinear algebraic equations by spatial and temporal discretization, and then the linear equations after linearization are solved in parallel by the conjugate gradient Conjugate radientsl (PCG) iterative algorithm with preconditioned conditions. Compared with the parallel direct algorithm commonly used in multibody systems, the computational efficiency can be improved significantly. Finally, several numerical examples are given to verify the effectiveness of the proposed parallel algorithm, and the complexity, speedup and scalability of the algorithm are analyzed.
【作者单位】：北京理工大学宇航学院力学系深空自主导航与控制工信部重点实验室;
【基金】：国家自然科学基金(编号:11290151,11672034) 上海航天科技创新项目资助
【分类号】：O313.7

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