On Lagrange multipliers in flexible multibody dynamics

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 50-51, 2006, Pages 6993-7005

  Simeon, Bernd ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Constraints; Differential algebraic equations (DAEs); Flexible multibody systems; Lagrange multipliers; Numerical simulation; Saddle point problems

Indexed keywords

COMPUTER SIMULATION; CONSTRAINT THEORY; DIFFERENTIAL EQUATIONS; DYNAMICS; ESTIMATION; LINEAR ALGEBRA; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

DIFFERENTIAL-ALGEBRAIC EQUATIONS; FLEXIBLE MULTIBODY SYSTEMS; SADDLE-POINT PROBLEMS;

LAGRANGE MULTIPLIERS;

COMPUTER SIMULATION; CONSTRAINT THEORY; DIFFERENTIAL EQUATIONS; DYNAMICS; ESTIMATION; LAGRANGE MULTIPLIERS; LINEAR ALGEBRA; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES;

EID: 33748032414     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.04.015     Document Type: Article

References (26)

1. Arnold M. A perturbation analysis for the dynamical simulation of mechanical multibody systems. Appl. Numer. Math. 18 (1995) 37-56
2. Bauchau O.A., Bottasso C.L., and Trainelli L. Robust integration schemes for flexible multibody systems. Comput. Methods Appl. Mech. Engrg. 192 (2003) 395-420
3. Braess D. Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics (1997), Cambridge University Press, Cambridge
4. Brenan K.E., Campbell S.L., and Petzold L.R. The Numerical Solution of Initial Value Problems in Ordinary Differential-Algebraic Equations (1996), SIAM, Philadelphia
5. Duvaut B., and Lions J. Inequalities in Mechanics and Physics (1976), Springer, New York
6. Eberhard P. Kontaktuntersuchungen durch hybride Mehrkörpersystem/Finite Element Simulationen (2000), Shaker, Aachen
7. Eich-Soellner E., and Führer C. Numerical Methods in Multibody Dynamics (1998), Teubner, Stuttgart
8. Farhat C., and Roux F. A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Methods Engrg. 32 (1991) 1205-1227
9. Géradin M. Computational aspects of the finite element approach to flexible multibody systems. In: Schiehlen W. (Ed). Advanced Multibody System Dynamics (1993), Kluwer Academic Publishers, Stuttgart 337-354
10. J. Gerstmayr, The absolute nodal coordinate formulation with elasto-plastic deformations. In: Proceedings of ECCOMAS Thematic Conference on Advances in Multibody Dynamics 2003 Conference, 2003, pp. 1-19.
11. Golub G., and van Loan C. Matrix Computations. Second ed. (1989), John Hopkins, Baltimore
12. Hairer E., and Wanner G. Solving Ordinary Differential Equations II. Second ed. (1996), Springer, Berlin, Heidelberg
13. Higueras I. Numerical Methods for Stiff Index 3 DAEs. MCMDS 7 2 (2001) 239-262
14. Hughes T.J. The Finite Element Method (1987), Prentice Hall, Englewood Cliffs
15. Jahnke M., Popp K., and Dirr B. Approximate analysis of flexible parts in multibody systems using the finite element method. In: Schiehlen W. (Ed). Advanced Multibody System Dynamics (1993), Kluwer Academic Publishers, Stuttgart 237-256
16. Kikuchi N., and Oden J. Contact Problems in Elasticity (1988), SIAM, Philadelphia
17. Lubich Ch., Nowak U., Pöhle U., and Engstler Ch. MEXX-numerical software for the integration of constrained mechanical multibody systems. Mech. Struct. Mach. 23 (1995) 473-495
18. Marsden J., and Hughes T.J. Mathematical Foundations of Elasticity (1983), Prentice Hall, Englewood Cliffs
19. Pereia M., and Ambrosio J. Computer Aided Analysis of Rigid and Flexible Mechanical Systems (1994), Kluwer Academic Publishers, Dordrecht
20. Rheinboldt W.C., and Simeon B. On computing smooth solutions of DAE's for elastic multibody systems. Comput. Math. Appl. 37 (1999) 69-83
21. Schwertassek R., and Wallrapp O. Dynamik flexibler Mehrkörpersysteme (1998), Vieweg
22. Shabana A. Dynamics of Multibody Systems (1998), Cambridge University Press, Cambridge
23. Simeon B. MBSPACK-numerical integration software for constrained mechanical motion. Surv. Math. Ind. 5 (1995) 169-202
24. B. Simeon, Numerische Simulation gekoppelter Systeme von partiellen und differential-algebraischen Gleichungen in der Mehrkörperdynamik, Reihe 20, Nr. 325, VDI-Verlag, Düsseldorf, 2000.
25. Simeon B. Numerical analysis of flexible multibody systems. Multibody Syst. Dyn. 6 4 (2001) 305-325
26. Wriggers P. Computational Contact Mechanics (2002), Wiley