Properties of time integration with first order filter damping

International Journal for Numerical Methods in Engineering

Volumn 64, Issue 4, 2005, Pages 547-566

  Krenk, S ^a   Hogsberg J R ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Algorithmic damping; Structural dynamics; Time integration

Indexed keywords

ALGORITHMS; DYNAMICS; EQUATIONS OF MOTION; INTEGRATION; LINEAR EQUATIONS; MATRIX ALGEBRA; STRUCTURAL ANALYSIS;

ALGORITHMIC DAMPING; FIRST ORDER FILTER DAMPING; STRUCTURAL DYNAMICS; TIME INTEGRATION;

DAMPING;

ALGORITHM;

EID: 25844459746     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1392     Document Type: Article

References (24)

1. Simo JC, Wong KK. Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum. International Journal for Numerical Methods in Engineering 1991; 31:19-52.
2. Simo JC, Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Zeitschrift für Angewandte Mathematik und Physik 1992; 43:757-792.
3. Puso MA. An energy and momentum conserving method for rigid-flexible body dynamics. International Journal for Numerical Methods in Engineering 2002; 53:1393-1414.
4. Gonzalez O. Exact energy and momentum conserving algorithms for general models in non-linear elasticity. Computer Methods in Applied Mechanics and Engineering 2000; 190:1763-1783.
5. Lens EV, Cardona A, Geradin M. Energy preserving time integration for constrained multibody systems. Multibody System Dynamics 2004; 11:41-61.
6. Betsch P, Steinmann P. Conservation properties of a time FE method. Part I: time-stepping schemes for N-body problems. International Journal for Numerical Methods in Engineering 2000; 49:599-638.
7. Betsch P, Steinmann P. Conservation properties of a time FE method. Part II: time-stepping schemes for non-linear elastodynamics. International Journal for Numerical Methods in Engineering 2001; 50:1931-1955.
8. Krenk S. State-space time integration with energy control and 4th order accuracy for linear dynamic systems. International Journal for Numerical Methods in Engineering, 2005, in press.
9. Newmark NM. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division (ASCE) 1959; 85:67-94.
10. Hughes TJR. Analysis of transient algorithms with particular reference to stability behaviour. In Computational Methods for Transient Analysis, Belytschko T, Hughes TJR (eds). North-Holland: Amsterdam, 1983; 67-155.
11. Hilber HM, Hughes TJR, Taylor RL. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engineering and Structural Dynamics 1977; 5:283-292.
12. Wood WL, Bossak M, Zienkiewicz OC. An alpha modification of Newmark's method. International Journal for Numerical Methods in Engineering 1981; 15:1562-1566.
13. Chung J, Hulbert GM. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized α method. Journal of Applied Mechanics 1993; 60:371-375.
14. Hulbert GM, Chung J. Explicit time integration algorithms for structural dynamics with optimal numerical dissipation. Computer Methods in Applied Mechanics and Engineering 1996; 137:175-188.
15. Hoff C, Pahl PJ. Development of an implicit method with numerical dissipation from a generalized single-step algorithm for structural dynamics. Computer Methods in Applied Mechanics and Engineering 1988; 67:367-385.
16. 1-method and comparison with other dissipative algorithms in structural dynamics. Computer Methods in Applied Mechanics and Engineering 1988; 67:87-110.
17. Zhou X, Tamma KK. Design, analysis and synthesis of generalized single step single solve and optimal algorithms for structural dynamics. International Journal for Numerical Methods in Engineering 2004; 59:597-668.
18. Hulbert GM. Computational structural dynamics. In Encyclopedia of Computational Mechanics, vol. 2: Solids and Structures, Stein E, de Borst R, Hughes TJR (eds). Wiley: Chichester, U.K., 2004; 169-193.
19. Kuhl D, Crisfield MA. Energy-conserving and decaying algorithms in non-linear structural dynamics. International Journal for Numerical Methods in Engineering 1999; 45:569-599.
20. Geradin M, Rixen D. Mechanical Vibrations, Theory and Applications to Structural Dynamics (2nd edn). Wiley: Chichester, 1997.
21. Meirovitch L. Elements of Vibration Analysis. McGraw-Hill: New York, 1986.
22. Czekanski A, El-Abbasi N, Meguid SA. Optimal time integration parameters for elastodynamic contact problems. Communications in Numerical Methods in Engineering 2001; 17:379-384.
23. Hilber HM, Hughes TJR. Collocation, dissipation and 'overshoot' for time integration schemes in structural dynamics. Earthquake Engineering and Structural Dynamics 1978; 6:99-117.
24. Krenk S. Conservation properties of Newmark based time integration algorithms. Department of Mechanical Engineering, Technical University of Denmark, submitted.