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Liu Cheng, Hu Haiyan. DYNAMIC MODELING AND COMPUTATION FOR FLEXIBLE MULTIBODY SYSTEMS BASED ON THE LOCAL FRAME OF LIE GROUP[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(1): 213-233. DOI: 10.6052/0459-1879-20-292
Citation: Liu Cheng, Hu Haiyan. DYNAMIC MODELING AND COMPUTATION FOR FLEXIBLE MULTIBODY SYSTEMS BASED ON THE LOCAL FRAME OF LIE GROUP[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(1): 213-233. DOI: 10.6052/0459-1879-20-292
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DYNAMIC MODELING AND COMPUTATION FOR FLEXIBLE MULTIBODY SYSTEMS BASED ON THE LOCAL FRAME OF LIE GROUP

  • Department of Mechanics, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

  • Received Date: August 16, 2020
    Graphical Abstract
    • Abstract
  • The main content of the dynamics of flexible multibody systems focuses on the dynamic modeling, computation and control of complex systems composed of flexible components, which are subjected to the relative overall motion and connected by kinematical constraints. Compared with the computational structural mechanics, the multibody dynamics issues have high geometrically nonlinear, which is not only deduced by the large rotation caused from the large deformation of flexible components, but also is deduced by the overall rigid body motion. Under the concept of the local frame of Lie group (LFLG), the topic that how to develop a new modeling and computational method for flexible multibody dynamics is discussed. The major studies of this paper include the following aspects: the modelling methods of beam elements and plate/shell elements based on the LFLG, the long-time integration algorithm for the flexible multibody systems including collision problems, the parallel algorithm for multibody systems based on the domain decomposition method, and several numerical examples to verify the feasibility of the proposed method. The unique feature of the new method can eliminate the geometrically nonlinear of the overall rigid motion for flexible components. Therefore, the generalized inertial forces and internal forces as well as their Jacobian matrices are invariable under the arbitrary rigid body motion. The proposed method can motivate the integration of the modeling method of the flexible multibody dynamics and the computational structural dynamics with large deformation components and is expected to promote the development of the next-generation software of multibody system dynamics.
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  • [1]
    Simo JC, Vu-Quoc L . On the Dynamics in space of rods undergoing large motions-a geometrically exact approach. Computer Methods in Applied Mechanics and Engineering, 1988, 66 (2): 125-161
    [2]
    Shabana AA . An absolute nodal coordinates formulation for the large rotation and deformation analysis of flexible bodies. . Chicago: University of Illinois at Chicago, 1996
    [3]
    Meier C, Popp A, Wall WA . Geometrically exact finite element formulations for slender beams: Kirchhoff-Love theory versus Simo-Reissner theory. Archives of Computational Methods in Engineering, 2019,26(1):163-243
    [4]
    Gerstmayr J, Sugiyama H, Mikkola A . Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems.  Journal of Computational and Nonlinear Dynamics, 2013,8(3):031016
    [5]
    Romero I . A comparison of finite elements for nonlinear beams: The absolute nodal coordinate and geometrically exact formulations.  Multibody System Dynamics, 2008,20(1):51-68
    [6]
    Bauchau OA, Han SL, Mikkola A , et al. Comparison of the absolute nodal coordinate and geometrically exact formulations for beams.  Multibody System Dynamics, 2014,32(1):67-85
    [7]
    王珍, 刘铖 . 几何精确方法与绝对节点坐标方法对比研究//第十届全国多体动力学与控制暨第五届全国航天动力学与控制学术会议, 青岛 , 2017 年9月22-25日.

    ( Wang Zhen, Liu Cheng. Comparison of the geometrically exact formulation and the absolute nodal coordinate formulation//The 10th National Conference on Multibody dynamics and Control & the 5th National Conference on Astrodynamics and Control, Qingdao, 2017-9-22-25 (in Chinese))
    [8]
    Reissner E . On one-dimensional finite-strain beam theory: The plane problem.  Zeitschrift Fddotur Angewandte Mathematik und Physik Zamp, 1972,23(5):795-804
    [9]
    Ren H, Fan W, Zhu WD . An accurate and robust geometrically exact curved beam formulation for multibody dynamic analysis.  ASME Journal of Vibration and Acoustics, 2017,140(1):011012
    [10]
    Liu JP, Cheng ZB, Ren GX . An arbitrary Lagrangian--Eulerian formulation of a geometrically exact Timoshenko beam running through a tube.  Acta Mechanica, 2018,229(8):3161-3188
    [11]
    Cardona A , Gacuteeradin M. A beam finite element non-linear theory with finite rotations. International Journal for Numerical Methods in Engineering, 1988,26:2403-2438
    [12]
    Sonneville V, Cardona A , Brddotuls O. Geometrically exact beam finite element formulated on the special Euclidean group SE(3). Computer Methods in Applied Mechanics and Engineering, 2014,268:451-474
    [13]
    刘铖, 胡海岩. 浅谈多体系统动力学几何非线性与转动非线性// 第十一届全国多体动力学与控制暨第六届全国航天动力学与控制和第十四届全国分析力学联合学术会议, 长沙, 2019 -09-20-23日.

    Liu Cheng, Hu Haiyan. A brief discussion on the geometrically nonlinear and rotational nonlinear of the multibody systems//The 11th National Conference on Multibody dynamics and Control & the 6th National Conference on Astrodynamics and Control & the 14th National Conference on analytical dynamics, Changsha, 2019-09-20-23 (in Chinese))
    [14]
    Hughes TJR, Cottrell JA, Bazilevs Y . Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 2005,194(39-41):4135-4195
    [15]
    Simo JC, Fox DD . On a stress resultant geometrically exact shell model Part I: Formulation and optimal parametrization.  Computer Methods in Applied Mechanics and Engineering, 1989,72(3):267-304
    [16]
    Simo JC, Rifai MS, Fox DD . On a stress resultant geometrically exact shell model Part IV: Variable thickness shells with through-the-thickness stretching.  Computer Methods in Applied Mechanics and Engineering, 1990,81(1):91-126
    [17]
    Simo JC, Kennedy JG . On a stress resultant geometrically exact shell model Part V: Nonlinear plasticity formulation and integration algorithms.  Computer Methods in Applied Mechanics and Engineering, 1992,96:133-171
    [18]
    Simo JC, Fox DD, Hughes TJR . Formulations of finite elasticity with independent rotations.  Computer Methods in Applied Mechanics and Engineering, 1992,95(2):277-288
    [19]
    Fox DD, Simo JC . A drill rotation formulation for geometrically exact shells.  Computer Methods in Applied Mechanics and Engineering, 1992,98(3):329-343
    [20]
    潘亦甦, 陈大鹏 . 具有Drilling自由度的膜单元的杂交／混合有限元法. 西南交通大学学报, 1995,30(2):128-134.

    (Pan Yisu, Chen Dapeng . A hybrid/mixed model for membrane elements with drilling degrees of freedom. Journal of Southwest Jiaotong University, 1995,30(2):128-134 (in Chinese))
    [21]
    Sonneville V . A geometric local frame approach for flexible multibody systems.  Liege, Belgique: University of Liege, 2015
    [22]
    Shabana AA, Yakoub RY . Three-dimensional absolute nodal coordinate formulation for beam elements: Theory.  ASME Journal of Mechanical Design, 2001,123(4):606-613
    [23]
    Yakoub RY, Shabana AA . Three-dimensional absolute nodal coordinate formulation for beam elements implementation and applications.  ASME Journal of Mechanical Design, 2001,123:614-621
    [24]
    Garcacuteia De Jal'{o}n J, Bayo E . Kinematic and Dynamic Simulation of Multibody Systems the Real-Time Challenge. New York: Springer, 1994
    [25]
    Bauchau OA . Flexible Multibody Dynamics. Springer Science & Business Media, 2010
    [26]
    Jeleniacutec G, Cristfield MA . Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for statics and dynamics.  Computer Methods in Applied Mechanics and Engineering, 1999,171(1):141-171
    [27]
    Ibrahimbegovic A, Taylor RL . On the role of frame-invariance in structural mechanics models at finite rotations.  Computer Methods in Applied Mechanics and Engineering, 2002,191(45):5159-5176
    [28]
    Bauchau OA, Han SL . Interpolation of rotation and motion.  Multibody System Dynamics, 2014,31(3):339-370
    [29]
    Patel M, Shabana AA . Locking alleviation in the large displacement analysis of beam elements: the strain split method.  Acta Mechanica, 2018,229(7):2923-2946
    [30]
    刘铖, 田强, 胡海岩 . 基于绝对节点坐标的多柔体系统动力学高效计算方法. 力学学报, 2010,42(6):1197-1205.

    (Liu Cheng, Tian Qiang, Hu Haiyan . Efficient computational method for dynamics of flexible multibody systems based on absolute nodal coordinate. Chinese Journal of Theoretical and Applied Mechanics, 2010,42(6):1197-1205 (in Chinese))
    [31]
    Liu C, Tian Q, Hu HY . New spatial curved beam and cylindrical shell elements of gradient-deficient absolute nodal coordinate formulation.  Nonlinear Dynamics, 2012,70(3):1903-1918
    [32]
    Zhao ZH, Ren GX . A quaternion-based formulation of Euler--Bernoulli beam without singularity.  Nonlinear Dynamics, 2012,67(3):1825-1835
    [33]
    Bergou M, Wardetzky M, Robinson S , et al. Discrete elastic rods.  ACM Transactions on Graphics, 2008,27(3):459-470
    [34]
    Liu C, Tian Q, Hu HY . Dynamics of a large scale rigid--flexible multibody system composed of composite laminated plates.  Multibody System Dynamics, 2011,26(3):283-305
    [35]
    Liu C, Tian Q, Yan D , et al. Dynamic analysis of membrane systems undergoing overall motions, large deformations and wrinkles via thin shell elements of ANCF.  Computer Methods in Applied Mechanics and Engineering, 2013,258:81-95
    [36]
    Hou YS, Liu C, Hu HY . Component-level proper orthogonal decomposition for flexible multibody systems.  Computer Methods in Applied Mechanics and Engineering, 2020,361:112691
    [37]
    Simo JC, Tarnow N, Doblare M . Nonlinear dynamic of three-dimensional rods: Exact energy and momentum conserving algorithm.  International Journal for Numerical Methods in Engineering, 1995,38(9):1431-1473
    [38]
    Romero I, Armero F . An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy--momentum conserving scheme in dynamics.  International Journal for Numerical Methods in Engineering, 2002,54:1683-1716
    [39]
    Marsden JE, West M . Discrete mechanics and variational integrators.  Acta Numerica, 2001: 357-514
    [40]
    Betsch P, Hesch C, Sanger N , et al. Variational integrators and energy-momentum schemes for flexible multibody dynamics.  Journal of Computational and Nonlinear Dynamics, 2010,5(3):031001
    [41]
    Schwarze M, Reese S . A reduced integration solid-shell finite element based on the EAS and the ANS concept-Large deformation problems.  International Journal for Numerical Methods in Engineering, 2011,85:289-329
    [42]
    Luo K, Liu C, Tian Q , et al. An efficient model reduction method for buckling analyses of thin shells based on IGA.  Computer Methods in Applied Mechanics and Engineering, 2016,309:243-268
    [43]
    Sun DW, Liu C, Hu HY . Dynamic computation of 2D segment-to-segment frictionless contact for a flexible multibody system subject to large deformation.  Mechanism and Machine Theory, 2019,140:350-376
    [44]
    Heyn T . On the modeling, simulation, and visualization of many-body dynamics problems with friction and contact. [PhD Thesis]. University of Wisconsin-Madison, 2013
    [45]
    Lew AJ, Marsden JE, Ortiz M , et al. Asynchronous variational integrators.  Archive for Rational Mechanics and Analysis, 2003,167(2):85-146
    [46]
    许焕宾, 李伟杰, 史文华 等.  一种可重复展收的桁架结构及其胞元, 中国专利, 公开号: CN105923170B, 2016 -04-26
    [47]
    Farhat C, Lesoinne M, Letallec P , et al. FETI-DP: a dual--primal unified FETI method-part I: A faster alternative to the two-level FETI method.  International Journal for Numerical Methods in Engineering, 2001,50(7):1523-1544
    [48]
    刘铖, 叶子晟, 胡海岩 . 基于区域分解的柔性多体系统高效并行算法. 中国科学: 物理学力学天文学, 2017,47(10):12-22.

    (Liu Cheng, Ye Zisheng, Hu Haiyan . An efficient parallel algorithm for flexible multibody systems based on domain decomposition method, Scientia Sinica Physica, Mechanica and Astronomica, 2017,47(10):12-22 (in Chinese))
    [49]
    李培, 马沁巍, 宋燕平  等. 大型空间环形桁架天线反射器展开动力学模拟与实验研究. 中国科学: 物理学力学天文学, 2017,47(10):3-11.

    (Li Pei, Ma Qinwei, Song Yanping , et al. Deployment dynamics simulation and ground test of a space hoop trus antenna reflector. Scientia Sinica Physica, Mechanica and Astronomica, 2017,47(10):3-11 (in Chinese))
    [50]
    Li P, Liu C, Tian Q , et al. Dynamics of a deployable mesh reflector of satellite antenna: Parallel computation and deployment simulation.  Journal of Computational and Nonlinear Dynamics, 2016,11(6):061005
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