An Implicit Multistage Integration Method Including Projection for the Numerical Simulation of Constrained Multibody Systems

Multibody System Dynamics

Volumn 1, Issue 4, 1997, Pages 405-424

  Dehombreux, Pierre ^a   Verlinden, Olivier ^a   Conti, Calogero ^a  

^a UNIVERSITY OF MONS   (Belgium)

Author keywords

Constraint violation; Differential algebraic equations; Numerical integration; Numerical stability; Projection methods

Indexed keywords

EID: 2342524133     PISSN: 13845640     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1009742111828     Document Type: Article

References (29)

1. Gear, C.W., Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1971.
2. Hairer, E., Norsett, S.P. and Wanner, G., Solving Ordinary Differential Equations. I. Nonstiff Problems, Springer-Verlag, Berlin/Heidelberg, 1987.
3. Hairer, E. and Wanner, G., Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems, Springer-Verlag, Berlin/Heidelberg, 1991.
4. Dahlquist, G., 'On accuracy and unconditional stability of linear multistep methods for second order differential equations', BIT 18, 1978, 133-136.
5. Newmark, N.M., 'A method for computation for structural dynamics', Journal of the American Society of Civil Engineers 85, 1959, 67-94.
6. Hilber, H.M. and Hugues, T.J.R., 'Collocation, dissipation and overshoot for time integration schemes in structural dynamics', Earthquake Engineering and Structural Dynamics 6, 1978, 99-117.
7. Bathe, K.J., Finite Element Procedures, Prentice-Hall, Englewood Cliffs, NJ, 1995.
8. Cardona, A. and Géradin, M., 'Numerical integration of second order differential-algebraic systems in flexible mechanisms dynamics', in Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, M.F.O. Seabra Pereira and J.A.C. Ambrósio (eds), NATO ASI Series, Vol. E268, Kluwer Academic Publishers, Dordrecht, 1994, 501-529.
9. Dehombreux, P., 'Simulation du comportement dynamique de systèmes multicorps contraints', Thèse de doctorat, Faculté Polytechnique de Mons, Mons, 1995.
10. Petzold, L.R., 'Differential/algebraic equations are not ODEs', SIAM Journal of Scientific and Statistical Computation 3, 1982, 367-384.
11. Schiehlen, W., Multibody Systems Handbook, Springer-Verlag, Berlin/Heidelberg, 1990.
12. Nikravesh, P.E., Computer Aided Analysis of Mechanical Systems, Prentice-Hall, Englewood Cliffs, NJ, 1988.
13. Haug, E.J. and Deyo, R.C., Real-Time Integration Methods for Mechanical System Simulation, NATO ASI Series, Series F: Computer and Systems Sciences, Vol. 69, Springer-Verlag, Berlin/Heidelberg, 1991.
14. Garcia de Jalon, J. and Bayo, E., Kinematic and Dynamic Simulation of Multibody Systems, Springer-Verlag, Berlin/Heidelberg, 1994.
15. Baumgarte, J., 'Stabilization of constraints and integrals of motion in dynamical systems', Computer Methods in Applied Mechanics and Engineering 1, 1972, 1-16.
16. Hahn, H. and Simeon, B., 'Separation principle of mechanical system models including stabilized constraint relations', Archive of Applied Mechanics 64, 1994, 147-153.
17. Lötstedt, P., 'On a penalty function method for the simulation of mechanical systems subject to constraints', Report TRITA-NA-7919, Royal Institute of Technology, Stockholm, 1979.
18. Bayo, E. and Ledesma, R., 'Augmented Lagrangian and projection methods for constrained multibody dynamics with no constraint violation', Report UCSB-ME-93-1, 1993.
19. Gear, C.W., Leimkuhler, B. and Gupta, G.K., 'Automatic integration of Euler-Lagrange equations with constraints', Journal of Computational and Applied Mathematics 12/13, 1985, 77-90.
20. Führer, C. and Leimkuhler, B., 'Formulation and numerical solution of the equations of constrained mechanical motion', DFVLR-Forschungsbericht, Vol. 89-08, Institut für Dynamik der Flugsysteme, Oberpfaffenhofen, 1989.
21. Wehage, R.A., 'Generalized coordinate partitioning in dynamic analysis of mechanical systems', Ph.D. Dissertation, The University of Iowa, 1980.
22. Singh, R.P. and Likins, P.W., 'Singular value decomposition for constrained dynamical systems', Journal of Applied Mechanics 52, 1985, 943-948.
23. Mani, N.K., Haug, E.J. and Atkinson, K.E., 'Application of singular value decomposition for analysis of mechanical system dynamics', Journal of Mechanisms, Transmissions, and Automation in Design 107, 1985, 82-87.
24. Kim, S.S. and Vanderploeg, M.J., 'QR decomposition for state space representation of constrained mechanical dynamic systems', Journal of Mechanisms, Transmissions and Automation in Design 108, 1986, 183-188.
25. Lubich, C., 'Extrapolation integrators for constrained multibody systems', Impact of Computing in Science and Engineering 3, 1991, 213-234.
26. Dehombreux, P., Conti, C. and Verlinden, O., 'A numerical integration algorithm based on the introduction of a constraint violation factor', in Dynamical Problems of Rigid-Elastic Systems and Structures, N.V. Banichuk, D.M. Klimov and W. Schiehlen (eds), Springer-Verlag, Berlin/Heidelberg/New York, 1991, 73-82.
27. Eich, E., 'Convergence results for a coordinate projection method applied to mechanical systems with algebraic constraints', SIAM Journal of Numerical Analysis 30, 1993, 1467-1482.
28. Bayo, E. and Ledesma, R., 'Augmented Lagrangian and NLMS-orthogonal projection methods for constrained multibody dynamics', Nonlinear Dynamics 9, 1996, 113-130.
29. Hiller, M. and Frik, S., 'Road vehicle benchmark 2: Five-link suspension', in Multibody Computer Codes in Vehicle System Dynamics, W. Kortüm, S. Sharp and A. de Pater (eds), Swets & Zeitlinger, Amsterdam, 1993, 254-262.