Abstract
The paper describes a finite element formulation of flexible multibody systems. The discretized equations of motion are formulated using the augmented lagrangian approach and are solved in an implicit manner. Symbolic computation is utilized to develop the element models. Flexible members are treated in two ways: either in a fully nonlinear manner using a geometrically exact beam model, or through the substructuring concept. Two complex joint models are presented: a cam pair with double curvature and a flexible slider. Dry friction effects are taken into account using a regularization procedure.
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references
Cardona A., An integrated approach to mechanism analysis,PhD thesis, Université de Liège, Faculté des Sciences Appliquées (1989).
Geradin M., Park K.C. and Cardona A., On the representation of finite rotations in spatial kinematics, LTAS report, University of Liège, Belgium (1988).
Cardona A. and Geradin M., A beam finite element non linear theory with finite rotations, Int. Jour. Num. Meth. Engng. Vol. 26, pp. 2403–2438 (1988).
Cardona A., Geradin M., Granville D. and Raeymaekers V., Module d’analyse de mécanismes flexibles MECANO - Manuel d’utilisation, LTAS report, Université de Liège (1988).
Cardona A., Geradin M. and Doan D.B., Rigid and flexible joint modelling in multibody dynamics using finite elements, Comp. Meth. Appl. Mech. Engng., Vol. 89, pp. 395–418 (1991).
Newmark N.M., A method of computation for structural dynamics, Jnl. Eng. Mch. Div. ASCE, No. 85 (EM3), proc. paper 2094, pp. 67–94 (1959).
Geradin M., Rixen D., Théorie des Vibrations. Masson Ed., Paris (1992).
Farhat C.,Grivelli L. and Geradin M., On the spectral stability of time integration algorithms for a class of constrained dynamics problems, AIAA paper 93–1306,SDM 93 conference, La Jolla, CA, (AIAA, 1993).
Cassano A. and Cardona A., A comparison between three variable-step algorithms for the integration of the equations of motion in structural dynamics, Jnl of Latin American Research, Vol. 21, pp. 187–197 (1991).
Cardona A. and Geradin M., Numerical integration of second order differential algebraic systems in flexible mechanism dynamics, Computer Aided Analysis of Rigid and Flexible Mechanical Systems, NATO/ASI, Troia, Portugal (1993).
Duysens J. and Geradin M., Contribution of a symbolic calculation code to the elaboration of a finite element calculation code: a first application to the dynamic behavior of flexible mechanisms, LTAS report VA 87, University of Liège, Belgium (1992).
Duysens J. and Geradin M., Flexible multibody dynamics analysis: a finite element approach aided by computer algebra, Proc. Int. Workshop on Mechanism Design and Analysis (COMES’93), Clermont-Fd, France, 17–18 May 1993.
Chart B. et al., MAPLE V - Language reference manual, Springer-Verlag (1991).
Simo J. C., A finite strain beam formulation. The three-dimensional dynamic problem. Part I, Comp. Meth. Appl. Mech. Engng., Vol. 49, pp. 55–70 (1985).
Simo J. C. and Vu-Quoc L., A three-dimensional finite strain rod model. Part II: computational aspects, Comp. Meth. Appl. Mech. Engng., Vol. 58, pp. 79–116 (1986).
Park K.C., Flexible beam dynamics: part I - formulation, Center for Space Structures and Control, University of Colorado, Boulder (1986).
Hughes T.J.R., The finite element method: linear static and dynamic finite element analysis, Prentice Hall, Englewood Cliffs, NJ (1987).
Geradin M. and Cardona A., Substructuring techniques in flexible multibody systems, Eight VPI & SU Symposium on Dynamics and Control of Large Space Structures, May 6–8, 1991.
Craig R. and Bampton M., Coupling of substructures for dynamic analysis, AIAA jnl, vol. 6, No. 7, pp.1313–1319 (1968).
Cardona A. and Geradin M., Finite element modeling of flexible tracks. Proc. Int. Conference: Dynamics of flexible structures in space, Cranfield, UK, 15–18 May 1990.
Cardona A. and Geradin M., Kinematic and dynamic analysis of mechanisms with cams, Comp. Methods Appl. Mech. Eng., No. 103, pp. 115–134 (1993)
Housner J., Private communication (1987).
Geradin M. and Cardona A., Analysis of the retraction of a deployable three longeron truss, LTAS report, University of Liège (1987).
Geradin M., Cardona A. and Granville D., Deployment of large flexible space structures, in space vehicle flight mechanics, Agard conf. proceedings, pp 28–1–28–11 (1989).
Granville D. and Geradin M., Calcul de déploiements d’antennes par MECANO, LTAS report VF 62, Université de Liège (1989).
Cardona A and Geradin M., Time integration of the equations of motion in mechanisms analysis, Computers and Stuctures, Vol.33, No. 3, pp. 801–820 (1989).
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© 1994 Springer Science+Business Media Dordrecht
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Géradin, M., Cardona, A., Doan, D.B., Duysens, J. (1994). Finite Element Modeling Concepts in Multibody Dynamics. In: Seabra Pereira, M.F.O., Ambrósio, J.A.C. (eds) Computer-Aided Analysis of Rigid and Flexible Mechanical Systems. NATO ASI Series, vol 268. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1166-9_8
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DOI: https://doi.org/10.1007/978-94-011-1166-9_8
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