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Research Papers

A Formulation on the Special Euclidean Group for Dynamic Analysis of Multibody Systems

[+] Author and Article Information
Valentin Sonneville

Department of Aerospace and
Mechanical Engineering (LTAS),
University of Liège,
Chemin des Chevreuils 1,
Liège 4000, Belgium
e-mail: v.sonneville@ulg.ac.be

Olivier Brüls

Department of Aerospace and
Mechanical Engineering (LTAS),
University of Liège,
Chemin des Chevreuils 1,
Liège 4000, Belgium
e-mail: o.bruls@ulg.ac.be

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received July 8, 2013; final manuscript received January 22, 2014; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 041002 (Jul 11, 2014) (8 pages) Paper No: CND-13-1173; doi: 10.1115/1.4026569 History: Received July 08, 2013; Revised January 22, 2014

This paper presents a finite element approach of multibody systems using the special Euclidean group SE(3) framework. The development leads to a compact and unified mixed coordinate formulation of the rigid bodies and the kinematic joints. Flexibility in the kinematic joints is also easily introduced. The method relies on local description of motions, so that it provides a singularity-free formulation and exhibits important advantages regarding numerical implementation. A practical case is presented to illustrate the method.

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References

Géradin, M. and Cardona, A., 2001, Flexible Multibody Dynamics: A Finite Element Approach, John Wiley and Sons, Chichester, UK.
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Brüls, O., Arnold, M., and Cardona, A., 2011, “Two Lie Group Formulations for Dynamic Multibody Systems With Large Rotations,” Proceedings of the IDETC/MSNDC Conference, Washington, DC, August 28–31, 2011, ASME, Paper No. DETC2011-48132, pp. 85–94. [CrossRef]
Brüls, O., Cardona, A., and Arnold, M., 2012, “Lie Group Generalized-α Time Integration of Constrained Flexible Multibody Systems,” Mech. Mach. Theory, 48, pp. 121–137. [CrossRef]
Brüls, O. and Cardona, A., 2010, “On the Use of Lie Group Time Integrators in Multibody Dynamics,” ASME J. Comput. Nonlinear Dyn., 5(3), p. 031002. [CrossRef]
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Sonneville, V. and Brüls, O., 2012, “Formulation of Kinematic Joints and Rigidity Constraints in Multibody Dynamics Using a Lie Group Approach,” Proceedings of the 2nd Joint International Conference on Multibody System Dynamics (IMSD), Stuttgart, Germany, May, 2012. Available at: http://hdl.handle.net/2268/120012.
Park, J. and Chung, W., 2005, “Geometric Integration on Euclidean Group With Application to Articulated Multibody Systems,” IEEE Trans. Rob., 21(5), pp. 850–863. [CrossRef]
Haug, E. J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems , Vol. 1: Basic Methods, Allyn and Bacon, Needham Heights, MA.
Sonneville, V., Cardona, A., and Brüls, O., 2014, “Geometrically Exact Beam Finite Element Formulated on the Special Euclidean Group SE(3),” Comput. Methods Appl. Mech. Eng., 268, pp. 451–474. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Representation of the nodes and the relationships involved in the finite element approach of multibody systems

Grahic Jump Location
Fig. 2

Model of the spatial slider crank mechanism

Grahic Jump Location
Fig. 3

Simulation results

Grahic Jump Location
Fig. 4

Velocity of node 3: stars (red), x; circles (green), y; solid line (blue), z

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