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Component mode synthesis with constant mass and stiffness matrices applied to flexible multibody systems. (English) Zbl 1162.74019
Summary: In flexible multibody systems, component mode synthesis is used to reduce the size of system matrices of single bodies from millions to a few hundred, while maintaining the full coupling between body deformation and overall rigid body motion. The combination of clamped eigenmodes and static deformation modes results in a dense non-diagonal structure of system matrices which is computationally costly. In the present paper, the conventional concept of the floating frame of reference is transformed to a description based on absolute coordinates and a corotational linearization of the deformation. The constant mass matrix and the corotated stiffness matrix need to be factorized only once for the whole simulation. In a planar example, component mode synthesis is applied to this absolute coordinate formulation by using twice as many deformation modes as usual, while the solution of the overall system becomes less expensive due to efficient factorization. The size of the system matrices needs to be increased considerably for each axis of rotation. However, the computational complexity for the factorization reduces from cubic to quadratic. Numerical examples are presented in order to demonstrate the difference between standard procedures and the methodology now proposed.

74H45 Vibrations in dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
Full Text: DOI
[1] Craig, AIAA Journal 6 pp 1313– (1968)
[2] Song, Computer Methods in Applied Mechanics and Engineering 24 pp 359– (1980)
[3] Shabana, Journal of Structural Mechanics 11 pp 401– (1983) · doi:10.1080/03601218308907450
[4] . Flexible Multibody Dynamics–A Finite Element Approach. Wiley: New York, 2001.
[5] Géradin, International Journal for Numerical Methods in Engineering 32 pp 1565– (1991)
[6] Geometric and material non-linear deformations in flexible multibody systems. In Computational Aspects of Nonlinear Structural Systems with Large Rigid Body Motion, (eds). IOS: Amsterdam, The Netherlands, 2001; 3–28.
[7] Cardona, International Journal for Numerical Methods in Engineering 26 pp 2403– (1988)
[8] Ambrósio, Nonlinear Dynamics 3 pp 85– (1992) · Zbl 0920.73135
[9] Dynamics of Multibody Systems (3rd edn).Cambridge University Press: New York, 2005. · Zbl 1068.70002 · doi:10.1017/CBO9780511610523
[10] Yakoub, Journal of Mechanical Design 123 pp 606– (2001)
[11] Mikkola, Multibody System Dynamics 9 pp 283– (2003)
[12] . Analysis of higher and lower order elements for the absolute nodal coordinate formulation. In Proceedings of ASME 2005 International Design Engineering Technical Conferences, Long Beach, CA, Paper Number DETC2005-84827, 2005.
[13] Gerstmayr, Multibody System Dynamics 15 pp 309– (2006)
[14] Gerstmayr, International Journal of Nonlinear Dynamics 34 pp 133– (2003) · Zbl 1041.74527
[15] Felippa, Computational Methods in Applied Mechanics and Engineering 194 pp 2285– (2005)
[16] Wempner, International Journal of Solids and Structures 5 pp 117– (1969) · Zbl 0164.26505
[17] Belytschko, International Journal for Numerical Methods in Engineering 7 pp 255– (1973)
[18] Nonlinear Finite Element Analysis of Solids and Structures, vol. 1 and 2. Wiley: Chichester, 1997.
[19] The absolute coordinate formulation with reduced strain for the efficient simulation of flexible multibody systems with nonlinear constraints. In Proceedings of the ECCOMAS 2004, Jyväskylä, Helsinki, Neittaanmäki P, Rossi T, Korotov S, Oñate E, Périaux J, Knörzer D (eds), 2004.
[20] The absolute nodal coordinate formulation with elasto-plastic deformations. In Proceedings of the Multibody Dynamics 2003 Conference, Lisbon, Portugal, Ambrósio JAC (ed.). 2003.
[21] Newmark, Journal of the Engineering Mechanics Division 85 pp 67– (1959)
[22] Finite Element Procedures in Engineering Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1982.
[23] Ambrósio, International Journal of Vehicle Design 26 pp 309– (2001)
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