绝对节点坐标列式实体梁单元建模方法及应用

doi:10.7527/S1000-6893.2015.0201

ACTA AERONAUTICAET ASTRONAUTICA SINICA ›› 2015, Vol. 36 ›› Issue (10): 3316-3326.doi: 10.7527/S1000-6893.2015.0201

• Solid Mechanics and Vehicle Conceptual Design • Previous Articles Next Articles

Modelling method and application of solid beam element based on absolute nodal coordinate formulation

MA Chao, WEI Cheng, ZHAO Yang, WANG Ran

Department of Aerospace Engineering, Harbin Institute of Technology, Harbin 150001, China

Received:2014-09-28 Revised:2015-07-16 Online:2015-10-15 Published:2015-07-21
Supported by:
National Basic Research Program of China (2013CB733004); National Key Discipline Laboratory Open Fundation (HIT.KLOF.MST.201508); Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIF.NSRIF.201515)

Abstract

Abstract:

In the multibody system dynamics formulations, the modeling of classical non-isoparametric beam element is mainly based on the Euler-Bernoulli and Timoshenko beam theories, which cannot accurately describe the deformation of the beam cross section. Although the absolute node coordinate formulation beam element is able to achieve section description, it is necessary to introduce additional description frames and deal with series locking problems. Different from the elements mentioned above, the absolute nodal coordinate formulation solid element directly describes the section deformation through the node coordinates without the locking problems. Based on the solid element, the absolute nodal coordinate solid beam element considering the continuity condition and internal viscoelastic damping, has been provided and achieved for the first time. With the solid beam element, the modelling of a multibody system is realized. According to numerical simulations, it is able to obtain some nonlinearity results with solid beam element and the precision is much higher than traditional finite element and absolute nodal coordinate formulation element.

Key words: multibody system dynamics, absolute nodal coordinate formulation, continuity condition, geometric nonlinearity, internal damping model

CLC Number:

MA Chao, WEI Cheng, ZHAO Yang, WANG Ran. Modelling method and application of solid beam element based on absolute nodal coordinate formulation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(10): 3316-3326.

References

[1] Shabana A A. Flexible multibody dynamics: Review of past and recent developments[J]. Multibody System Dynamics, 1997, 1(2): 189-222.
[2] Shabana A A. Definition of the slopes and the finite element absolute nodal coordinate formulation[J]. Multibody System Dynamics, 1997, 1(3): 339-348.
[3] Omar M A, Shabana A A. A two-dimensional shear deformable beam for large rotation and deformation problems[J]. Journal of Sound and Vibration, 2001, 243(3): 565-576.
[4] Shabana A A, Yakoub R Y. Three dimensional absolute nodal coordinate formulation for beam elements: Theory[J]. Journal of Mechanical Design, 2001, 123(4): 606-613.
[5] Yakoub R Y, Shabana A A. Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications[J]. Journal of Mechanical Design, 2001, 123(4): 614-621.
[6] Dombrowski S V. Analysis of large flexible body deformation in multibody systems using absolute coordinates[J]. Multibody System Dynamics, 2002, 8(4): 409-432.
[7] Kerkkänen K S, Sopanen J T, Mikkola A M. A linear beam finite element based on the absolute nodal coordinate formulation[J]. Journal of Mechanical Design, 2005, 127(4): 621-630.
[8] Gerstmayr J, Shabana A A. Analysis of thin beams and cables using the absolute nodal coordinate formulation[J]. Nonlinear Dynamics, 2006, 45(1): 109-130.
[9] Gerstmayr J, Matikainen M K. Analysis of stress and strain in the absolute nodal coordinate formulation[J]. Mechanics Based Design of Structures and Machines,2006, 34(4): 409-430.
[10] García-Vallejo D, Mikkola A M, Escalona J L. A new locking-free shear deformable finite element based on absolute nodal coordinates[J]. Nonlinear Dynamics, 2007, 50(1): 249-264.
[11] Zhu D P, Lu Y J, Tang J L, et al. Application of large deformation cable beam element in multibody dynamics[C]//Proceedings of the 2007 National Symposium on Structural Dynamics. Beijing: Chinese Society for Vibration Engineering, 2007: 81-107 (in Chinese). 朱大鹏, 路英杰, 汤家力, 等. 大变形索梁单元在多体动力学框架下的应用[C]//2007全国结构动力学学术研讨会论文集. 北京: 中国振动工程学会, 2007: 81-107.
[12] Tang J L, Ren G X, Zhu W D, et al. Dynamics of variable-length tethers with application to tethered satellite deployment[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(8): 3411-3424.
[13] Zhao C Z, Yu H D, Wang H, et al. Dynamic modeling and kinematic behavior of variable cross-section beam based on the absolute nodal coordinate formulation[J]. Journal of Mechanical Engineering, 2014, 50(17): 38-45 (in Chinese). 赵春璋, 余海东, 王皓, 等. 基于绝对节点坐标法的变截面梁动力学建模与运动变形分析[J]. 机械工程学报, 2014, 50(17): 38-45.
[14] Kübler L, Eberhard P, Geisler J. Flexible multibody systems with large deformations and nonlinear structural damping using absolute nodal coordinates[J]. Nonlinear Dynamics, 2003, 34(1): 31-52.
[15] Yu L, Ren G X. Application of solid elements using absolute coordinates in multibody systems dynamics[J]. Journal of System Simulation, 2012, 24(3): 733-739 (in Chinese). 虞磊, 任革学. 基于绝对坐标的实体单元在多体系统动力学中的应用[J]. 系统仿真学报, 2012, 24(3): 733-739.
[16] Olshevskiy A, Dmitrochenko O, Kim C W. Three-dimensional solid brick element using slopes in the absolute nodal coordinate formulation[J]. Journal of Computational and Nonlinear Dynamics, 2014, 9(2): 021001-1-10.
[17] Shabana A A. Dynamics of multibody systems[M]. 3rd ed. Cambridge/New York: Cambridge University Press, 2005: 267-304.
[18] Shabana A A. Computational continuum mechanics[M]. 2nd ed. New York: Cambridge University Press, 2012: 146-217.
[19] Mohamed A A, Shabana A A. A nonlinear visco-elastic constitutive model for large rotation finite element formulations[J]. Multibody System Dynamics, 2011, 26(1): 57-79.
[20] Irgens F. Continuum mechanics[M]. Berlin: Springer-Verlag, 2008: 372-375.

Modelling method and application of solid beam element based on absolute nodal coordinate formulation

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