Abstract
This paper describes an energy preserving integration method for thedynamic analysis of nonlinear multibody systems in the presence ofnonlinear constraints. The aspects of finite rotation incrementation,discrete energy conservation and the most common constraint types areexamined in detail. The application is made to several rigid bodyexamples, including an intermittent contact problem.
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References
Bauchau, O., ‘Computational schemes for flexible, nonlinear multi-body systems’, Multibody System Dynam. 2, 1998, 169–225.
Bauchau, O., ‘Flexible multibody systems with intermittent contacts’, Multibody System Dynam. 4, 2000, 23–54.
Bauchau, O. and Joo, T., ‘Computational schemes for nonlinear elasto-dynamics, Internat. J. Numer. Meth. Engrg. 45, 1999, 693–719.
Betsch, P. and Steinmann, P., ‘Conservation properties of a time FE method. Part I: Time-stepping schemes for N-body problems’, Internat. J. Numer. Meth. Engrg. 49, 2000, 599–638.
Betsch, P. and Steinmann, P., ‘Conservation properties of a time FE method. Part II: Time-stepping schemes for non-linear elastodynamics’, Internat. J. Numer. Meth. Engrg. 50, 2001, 1931–1955.
Betsch, P. and Steinmann, P., ‘Conservation properties of a time FE method. Part III: Mechanical systems with holonomic constraints, Internat. J. Numer. Meth. Engrg., to appear.
Betsch, P. and Steinmann, P., ‘Constrained integration of rigid body dynamics’, Comput. Methods Appl. Mech. Engrg. 191, 2001, 467–488.
Cardona, A., ‘An integrated approach to mechanism analysis’, Ph.D. Thesis, Faculté des Sciences Appliquées, Université of Liège, 1989.
Cardona, A. and Géradin, M., ‘Time integration of the equations of motion in mechanism analysis, Comput. & Structures Multibody 33, 1989, 801–820.
Chung, J. and Hulbert, G.M., ‘A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized α method’, J. Appl. Mech. 60, 1993, 371–375.
Géradin, M. and Cardona, A., Flexible Multibody Dynamics: A Finite Element Approach, John Wiley & Sons, New York, 2000.
Gonzalez, O., ‘Mechanical systems subject to holonomic constraints: Differential-algebraic formulations and conservative integration’, Physica D 132, 1999, 165–174.
Greenspan, D., ‘Conservative numerical methods for \(\ddot x = f(x)\)’, J. Comput. Phys. 56, 1984, 28–41.
Laursen, T.A. and Love, G.R., ‘Improved implicit integrators for transient impact problems — Geometric admissibility within the conserving framework, Internat. J. Numer. Meth. Engrg. 53, 2002, 245–274.
Puso, M., ‘An energy and momentum conserving method for rigid-flexible body dynamics’, Internat. J. Numer. Meth. Engrg. 53, 2002, 1393–1414.
Simo, J.C., Tarnow, N. and Wong, K.K., ‘Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics’, Comput. Methods Appl. Mech. Engrg. 100, 1992, 63–116.
Whittaker, E.T., Treatise on the Analytical Dynamics of Particles and Rigid Bodies, fourth edition, Cambridge University Press, Cambridge, 1998.
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Lens, E.V., Cardona, A. & Géradin, M. Energy Preserving Time Integration for Constrained Multibody Systems. Multibody System Dynamics 11, 41–61 (2004). https://doi.org/10.1023/B:MUBO.0000014901.06757.bb
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DOI: https://doi.org/10.1023/B:MUBO.0000014901.06757.bb