The newmark integration method for simulation of multibody systems: Analytical considerations

American Society of Mechanical Engineers, Design Engineering Division (Publication) DE

Volumn 118 B, Issue 2, 2005, Pages 1079-1092

  Gavrea, B ^a   Negrut, D ^b   Potra, F A ^a  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; LINEAR ALGEBRA; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS;

DIFFERENTIAL-ALGEBRAIC EQUATIONS; GLOBAL CONVERGENCE ANALYSIS; INDUSTRIAL STRENGTH;

INTEGRATION;

EID: 33645038501     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/IMECE2005-81770     Document Type: Conference Paper

References (30)

1. Newmark, N. M., 1959. "A method of computation for structural dynamics". Journal of the Engineering Mechanics Division, ASCE, pp. 67-94.
2. Ascher, U. M., and Petzold, L. R., 1998. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM, Philadelphia, PA.
3. Hilber, H. M., Hughes, T. J. R., and Taylor, R. L., 1977. "Improved numerical dissipation for time integration algorithms in structural dynamics". Earthquake Eng. and Struct. Dynamics, 5, pp. 283-292.
4. Chung, J., and Hulbert, G. M., 1993. "A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-a method". Transactions of ASME, Journal of Applied Mechanics, 60(2), pp. 371-375.
5. Featherstone, R., 1983. "The calculation of robot dynamics using articulated-body inertias". International Journal of Robotics Research(1), pp. 13-30.
6. de Jalon, J. G., Unda, J., and Avello, A. "Natural coordinates for the computer analysis of multibody systems". Computer Methods in Applied Mechanics and Engineering(56), pp. 309-327.
7. Haug, E. J., 1989. Computer-Aided Kinematics and Dynamics of Mechanical Systems. Prenctice-Hall, Englewood Cliffs, New Jersey.
8. de Jalon, J. G., and Bayo, E., 11994. Kinematic and Dynamic Simulation of Multi-body Systems. The real time challenge. Springer-Verlag, Berlin.
9. Shabana, A. A., 1994. Computational Dynamics. John Wiley & Sons.
10. Brenan, K. E., Campbell, S. L., and Petzold, L. R., 1989. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. North-Holland, New York.
11. Petzold, L. R., 1982. "Differential-algebraic equations are not ODE's". SIAM J. Sci., Stat. Comput., 3(3).
12. Hairer, E., and Wanner, G., 1991. Solving Ordinary Differential Equations, Vol. II of Computational Mathematics, Springer-Verlag.
13. Potra, F. A., 1993. "Implementation of linear multistep methods for solving constrained equations of motion". SIAM. Numer. Anal., 30(3).
14. Lubich, C., Nowak, U., Pohle, U., and Engstler, C., 1995. "Mexx - numerical software for the integration of constrained mechanical multibody systems". Mechanics of Structures and Machines, 23, pp. 473-495.
15. Eich-Sollner, E., and Fuhrer, C., 1998. Numerical Methods in Multibody Dynamics. Teubner-Verlag, Stuttgart.
16. Cardona, A., and Geradin, M., 1994. "Numerical integration of second order differential-algebraic systems in flexible mechanics dynamics". In Computer-Aided Analysis of Rigid and Flexible Mechanical Systems, M. F. O. S. Pereira and J. A. C. Ambrosio, eds., Kluwer Academic Publishers.
17. Yen, J., Petzold, L., and Raha, S., 1996. A time integration algorithm for flexible mechanism dynamics: the DAE a-method. Tech. Rep. TR96-024, Dept. of Comp. Sci., University of Minnesota.
18. Cuadrado, J., Dopico, D., Naya, M. N., and Gonzalez, M., 2004. "Penatly, semi-recursive and hybrid methods for MBS Real-Time dynamics in the context of structural integrators". Multibody Systems Dynamics(12), pp. 117-132.
19. Baumgarte, J., 1972. "Stabilization of constraints and integrals of motion in dynamical systems". Computer Methods in Applied Mechanics and Engineering, 1, pp. 1-16.
20. Owren, B., and Simonsen, H., 1995. "Alternative integration methods for problems in structural dynamics". Structural Dynamics. Comput. Meth. in Appl. Mech. and Eng., 122, pp. 1-10.
21. Jay, L. O., 1998. "Structure preservation for constrained dynamics with super partitioned additive runge-kutta methods". SIAM J. Sci. Comput., 20, pp. 416-446.
22. Schaub, M., and Simeon, B., 2002. "Automatic h-scaling for the efficient time integration of stiff mechanical systems". Multibody System Dynamics, 8, pp. 329-345.
23. Dennis, J., and Schnabel, R., 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ.
24. MSCsoftware, 2005. ADAMS User Manual.
25. Zienkiewicz, O., and Xie, Y., 1991. "A simple error estimator and adaptive time-stepping procedure for dynamic analysis". Earthquake Engineering and Structural Dynamics, 20, pp. 871-887.
26. Atkinson, K. E., 1989. An introduction to numerical analysis, second ed. John Wiley & Sons Inc., New York.
27. Hughes, T. J. R., 1987. Finite Element Method - Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, New Jersey.
28. Negrut, D., Haug, E. J., and German, H. C., 2003. "An implicit Runge-Kutta method for integration of Differential-Algebraic Equations of Multibody Dynamics". Multibody System Dynamics, 9(2), pp. 121-142.
29. Oghbaei, M., and Anderson, K., 2005. "A new implicit integration scheme for the simulation of stiff-complex mechanical systems-DETC2005- 84471". In Proceedings to the Fifth ASME International Conference on Multibody Systems, Nonlinear Dynamics and Control, A. Shabana and K. Anderson, eds., ASME.
30. Negrut, D., Gavrea, B., and Potra, F., 2005. "Multibody dynamics simulation with Newmark integrators". In Preparation.