An invariant-preserving approach to robust finite-element multibody simulation

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 83, Issue 10, 2003, Pages 663-676

  Borri, Marco ^a   Bottasso, Carlo L ^a   Trainelli, Lorenzo ^a  

^a POLITECNICO DI MILANO   (Italy)

Author keywords

Cayley parametrization; Energy momentum conserving dissipating algorithms; Flexible multibody systems; Non linear finite elements; Non linear stability

Indexed keywords

EID: 21144443065     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200310065     Document Type: Article

References (29)

1. M. Boni, C.L. Bottasso, and L. Trainelli, A novel momentum-preserving energy-decaying algorithm for finite-element multibody procedures, Comput. Assist. Mech. Eng. Sci. 9, 315-340 (2002).
2. M. Boni, C. L. Bottasso, and L. Trainelli, Integration of elastic multibody systems by invariant conserving/dissipating algorithms - Part I: Formulation, Comput. Methods Appl. Mech. Eng. (Netherlands) 190, 3669-3699 (2001).
3. C. L. Bottasso, M. Borri, and L. Trainelli, Integration of elastic multibody systems by invariant conserving/dissipating algorithms - Part II: Numerical schemes and applications, Comput. Methods Appl. Mech. Eng. (Netherlands) 190, 3701-3733 (2001).
4. C. L. Bottasso and M. Borri, Integrating finite rotations, Comput. Methods Appl. Mech. Eng. (Netherlands) 164, 307-331 (1998).
5. C. L. Bottasso and M. Borri, Energy preserving/decaying schemes for non-linear beam dynamics using the helicoidal approximation, Comput. Methods Appl. Mech. Eng. (Netherlands) 143, 393-415 (1997).
6. O. A. Bauchau, Computational schemes for flexible, nonlinear multibody dynamics, Multibody Syst. Dyn. 2, 169-225 (1998).
7. O. A. Bauchau and N. J. Theron, Energy decaying scheme for nonlinear beam models, Comput. Methods Appl. Mech. Eng. (Netherlands) 134, 37-56 (1996).
8. O.A. Bauchau and N.J. Theron, Energy decaying scheme for nonlinear elastic multibody systems, Comput. Struct. 59, 317-331 (1996).
9. O. A. Bauchau, G. Damilano, and N. J. Theron, Numerical integration of nonlinear elastic multibody systems, Int. J. Numer. Methods Eng. 38, 2727-2751 (1995).
10. O. A. Bauchau, C. L. Bottasso, and L. Trainelli, Robust integration schemes for flexible multibody systems, Comput. Methods Appl. Mech. Eng. (Netherlands), to appear.
11. O. A. Bauchau, C. L. Bottasso, and J. Y. Choi, On the modeling of shells in multibody dynamics, Multibody Syst. Dyn., to appear.
12. C. L. Bottasso, O. A. Bauchau, and J. Y. Choi, An energy decaying scheme for nonlinear dynamics of shells, Comput. Methods Appl. Mech. Eng. (Netherlands) 191, 3099-3121 (2002).
13. O.A. Bauchau and C. L. Bottasso, On the design of energy preserving and decaying schemes for flexible non-linear multi-body systems, Comput. Methods Appl. Mech. Eng. (Netherlands) 169, 61-79 (1998).
14. C.J. Budd and A. Iserles, Geometric integration: numerical solution of differential equations on manifolds, Philos. Trans. R. Soc. Lond. A, Math. Phys. Eng. Sci. 357, 945-956 (1999).
15. J. C. Simo and N. Tamow, The discrete energy-momentum method. Conserving algorithms for nonlinear dynamics, Z. Angew. Math. Phys. 43, 757-792 (1992).
16. J. C. Simo, N. Tarnow, and M. Doblare, Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms, Int. J. Numer. Methods Eng. 38, 1431-1473 (1995).
17. D. Kuhl and E. Ramm, Constraint energy momentum algorithm and its application to non-linear dynamics of shells, Comput. Methods Appl. Mech. Eng. (Netherlands) 136, 293-315 (1996).
18. M. Boni, L. Trainelli, and C.L. Bottasso, On the representation and parameterization of motion, Multibody Syst. Dyn. 4, 129-193 (2000).
19. M. Borri, C. L. Bottasso, and L. Trainelli, Geometric invariance, Comput. Mech. 29, 163-169 (2002).
20. O. A. Bauchau and L. Trainelli, The vectorial parametrization of rotation, Nonlinear Dyn., submitted.
21. M. Borri and L. Trainelli, The vectorial parametrization of motion, in preparation.
22. M. Borri, C. L. Bottasso, and L. Trainelli, An embedded projection method for index-3 constrained mechanical systems, in: Computational Aspects of Nonlinear Multibody Systems with Large Rigid Body Motion, edited by J. A. C. Ambrosio and M. Kleiber (IOS Press, Amsterdam, 2001).
23. M. Borri, L. Trainelli, and A. Croce, The embedded projection method: A general index reduction procedure for constrained system dynamics, Appl. Numer. Math., submitted.
24. H. M. Hilber, T. J. R. Hughes, and R. L. Taylor, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthq. Eng. Struct. Dyn. 5, 282-292 (1977).
25. J. Chung and G. M. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method, Trans. ASME, J. Appl. Mech. 60, 371-375 (1993).
26. T. Belytschko and T. J. R. Hughes, eds., Computational Methods for Transient Analysis (North-Holland, Amsterdam, 1983).
27. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations - I: Non-stiff Problems (Springer, Berlin, 1987).
28. E. Hairer and G. Wanner, Solving Ordinary Differential Equations - II: Stiff Problems (Springer, Berlin, 1991).
29. C. Lubich, Integration of stiff mechanical systems by Runge-Kutta methods, Z. Angew. Math. Phys. 44, 1022-1053 (1993).