Solving constrained mechanical systems by the family of Newmark and α-methods

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 86, Issue 10, 2006, Pages 772-784

  Lunk, Christoph ^a   Simeon, Bernd ^a  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Constrained mechanical system; Differential algebraic equations; Generalized method; Newmark method; Structural dynamics

Indexed keywords

EID: 33750557231     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.200610285     Document Type: Conference Paper

References (24)

1. M. Arnold, Half-explicit Runge-Kutta methods with explicit stages for differential-algebraic systems of index 2, BIT Numerical Mathematics (Netherlands) 38, 415-138 (1998).
2. M. Arnold and B. Simeon, Pantograph and catenary dynamics: a benchmark problem and its numerical solution. Appl. Numer. Math. 34, 345-362 (2000).
3. U. Ascher and P. Lin, Sequential Regularization Methods for Nonlinear Higher Index DAEs, SIAM J. Sci. Comput. 18, 160-181 (1997).
4. O. A. Bauchau and C. L. Bottasso, and L. Trainelli, Robust Integration Schemes for Flexible Multibody Systems, Comput. Methods Appl. Mech. Eng. (Netherlands) 192, 395-420 (2003).
5. P. Betsch, Energy-consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraints., Comput. Methods Appl. Mech. Eng. (Netherlands), in print.
6. K..E. Brenan, S.L. Campbell, and L. R. Petzold, The Numerical Solution of Initial Value Problems in Ordinary Differential-Algebraic Equations (SIAM, Philadelphia, 1996).
7. O. Brüls, Integrated Simulation and Reduced-Order Modeling of Controlled Flexible Multibody Systems, Ph.D. Thesis, Université de Liège 2005.
8. J. Chung and G. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: The generalized α-method. J. Appl. Mech. 60, 371-375 (1993).
9. E. Eich-Soellner and C. Führer, Numerical Methods in Multibody Dynamics (Teubner, Stuttgart, 1998).
10. S. Erlicher, L. Bonaventura, and O. S. Bursi, The analysis of the Generalized-a method for non-linear dynamic problems. Comput. Mech. 28, 83-104 (2002).
11. C. Führer, B. Leimkuhler, Numerical Solution of Differential- Algebraic Equations for Constrained Mechanical Motion. Numer. Math. 59, 55-69 (1991).
12. C. Gear, G. Gupta, and B. Leimkuhler, Automatic Integration of the Euler-Lagrange Equations with Constraints. J. Comput. Appl. Math. 12-13, 77-90 (1985).
13. M. Géradin and A. Cardona, Flexible Multibody Dynamics (John Wiley, New York, 2000).
14. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, 2nd ed. (Springer, Berlin, Heidelberg, 1996).
15. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration (Springer, Berlin, Heidelberg, 2002).
16. H. Hilber, T. Hughes, and R. Taylor, Improved numerical dissipation for time integration algorithms in structural dynamics., Earthqu. Eng. Struct. Dyn. 5, 283-292 (1977).
17. G. Hulbert and I. Jang, Automatic time step control algorithms for structural dynamics, Comput. Methods Appl. Mech. Eng. (Netherlands) 126, 155-178 (1995).
18. L. O. Jay and D. Negrut, Extensions of the HHT-a Method to Differential-Algebraic Equations in Mechanics, Tech. Rep., University of Iowa (2006).
19. Ch. Lubich, U. Nowak, U. Pöhle, and Ch. Engstier, MEXX - Numerical software for the integration of constrained mechanical multibody systems., Mech. Struct. Mach. 23, 473-495 (1995).
20. Ch. Lunk and B. Simeon, Solving Constrained Mechanical Systems by the Family of Newmark and α-Methods, Tech. Rep., Center of the Mathematical Sciences, TU Munich (2006).
21. A. Murua, Partitioned half-explicit Runge-Kutta methods for differential algebraic systems of index 2. Computing 59, 43-61 (1997).
22. P. Rabier and W. C. Rheinboldt, On the numerical solution of the Euler-Lagrange equations., SIAM J. Numer. Anal. 32, 318-329 (1995).
23. B. Simeon, MBSPACK - Numerical integration software for constrained mechanical motion. Surv. Math. Ind. 5, 169-202 (1995).
24. J. Yen, L. Petzold, and S. Raha, A Time Integration Algorithm for Flexible Mechanism Dynamics: The DAE-Alpha Method., Comput. Methods Appl. Mech. Eng. (Netherlands) 158, 341-355 (1998).