本文選題：大變形柔性多體系統(tǒng) + 區(qū)域分解��； 參考：《中國科學:物理學 力學 天文學》2017年10期

【摘要】：近年來,大量輕質柔性結構成功應用于航空航天、智能機器人以及3D打印等領域,使得這些機械系統(tǒng)呈現(xiàn)出典型的剛柔耦合動力學特性.已有研究表明,基于小變形、小轉動假設的傳統(tǒng)柔性多體系統(tǒng)建模方法,如浮動坐標系方法,已無法精確描述上述大變形柔性構件的動力學特性.本文在等幾何分析體系下,采用非均勻有理B樣條(Non-Uniform Rational B-Splines,NURBS)插值函數(shù)離散平面柔性結構位移場,基于連續(xù)介質力學大變形理論,建立了能夠精確描述大轉動與大變形耦合的平面板單元.為了提高大變形柔性多體系統(tǒng)仿真效率,本文首先采用不變矩陣法,推導了大變形柔性體的非線性彈性力與切向剛度矩陣的高效計算公式.其次,基于有限元撕裂對接(Finite Element Tearing and Interconnecting,FETI)區(qū)域分解技術,提出了一種大變形柔性多體系統(tǒng)動力學方程高效求解算法.該算法中,首先通過空間離散與時間離散將多體系統(tǒng)動力學方程轉化為一組非線性代數(shù)方程,然后采用含預條件的共軛梯度(Preconditioned Conjugate Gradients,PCG)迭代算法并行求解線性化后的線性方程組.較以往多體系統(tǒng)常用的并行直接算法,能夠顯著地提高計算效率.最后,通過若干數(shù)值算例驗證了所提出并行算法的有效性,并分析了該算法的復雜度,加速比以及可擴展性.
[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.
【作者單位】： 北京理工大學宇航學院力學系深空自主導航與控制工信部重點實驗室;
【基金】：國家自然科學基金(編號:11290151,11672034) 上海航天科技創(chuàng)新項目資助
【分類號】：O313.7

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