DAEs and PDEs in elastic multibody systems

Numerical Algorithms

Volumn 19, Issue 1-4, 1998, Pages 235-246

  Simeon, B ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

DAEs; Elastic multibody systems; Numerical simulation; Slider crank

Indexed keywords

EID: 0032272585     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019118809892     Document Type: Article

References (23)

1. F. Bornemann and C. Schütte, Homogenization of Hamiltonian systems with a strong constraining potential, Physica D 102 (1997) 57-77.
2. S.L. Campbell and W. Marszalek, The index of an infinite dimensional implicit system, Report, North Carolina State University (1996), to appear in Math. Modelling Systems.
3. P.G. Ciarlet, Mathematical Elasticity, Vol. I (North-Holland, New York, 1988).
4. M. Géradin, Computational aspects of the finite element approach to flexible multibody systems, in: Advanced Multibody System Dynamics, ed. W. Schiehlen (Kluwer Academic, Stuttgart, 1993) pp. 337-354.
5. E. Hairer and G. Wanner, Solving Ordinary Differential Equations, Vol. II, 2nd ed. (Springer, Berlin/Heidelberg, 1996).
6. E. Haug, Computer Aided Kinematics and Dynamics of Mechanical Systems: Basic Methods (Allyn and Bacon, Boston, 1989).
7. T.J. Hughes, The Finite Element Method (Prentice-Hall, Englewood Cliffs, NJ, 1987).
8. M. Jahnke, K. Popp and B. Dirr, Approximate analysis of flexible parts in multibody systems using the finite element method, in: Advanced Multibody System Dynamics, ed. W. Schiehlen (Kluwer Academic, Stuttgart, 1993) pp. 237-256.
9. N. Kikuchi and J. Oden, Conctact Problems in Elasticity (SIAM, Philadelphia, PA, 1988).
10. C. Lubich, Integration of stiff mechanical systems by Runge-Kutta methods, Z. Angew. Math. Phys. 44 (1993) 1022-1053.
11. A. Noor, Recent advances and applications of reduction methods, Appl. Mech. Rev. 47 (1994) 125-146.
12. A. Nordmark, The Matlab PDE Toolbox (The Mathworks Inc., 1995).
13. P.J. Rabier and W.C. Rheinboldt, On the numerical solution of the Euler-Lagrange equations, SIAM J. Numer. Anal. 32 (1995) 318-329.
14. S. Reich, Smoothed dynamics of highly oscillatory Hamiltonian systems, Physica D 89 (1995) 28-42.
15. D. Sachau, Berücksichtigung von flexiblen Körpern und Fügestellen in Mehrkörpersystemen zur Simulation aktiver Raumfahrtstrukturen, Dissertation, Universität Stuttgart (1996).
16. W.O. Schiehlen, ed., Multibody System Handbook (Springer, Berlin, 1990).
17. B. Simeon, MBSPACK - Numerical integration software for constrained mechanical motion, Surv. Math. Ind. 5 (1995) 169-202.
18. B. Simeon, Modelling a flexible slider crank mechanism by a mixed system of DAEs and PDEs, Math. Modelling Systems 2 (1996) 1-18.
19. B. Simeon, Order reduction of stiff solvers at elastic multibody systems, to appear in Appl. Numer. Math.
20. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1993).
21. O. Wallrapp, Standardization of flexible body modelling in MBS codes, Mech. Struct. Mach. 22 (1994) 283-304.
22. K. Washizu, Variational Methods in Elasticity and Plasticity (Pergamon, Oxford, 1982).
23. J. Yen, L. Petzold and S. Raha, A time integration algorithm for flexible mechanism dynamics: the DAE α-method, SIAM J. Sci. Comput. 19 (1998) 1513-1534.