Energy conservation in Newmark based time integration algorithms

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 44-47, 2006, Pages 6110-6124

  Krenk, Steen ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Energy conservation; Numerical integration; Structural dynamics; Time integration

Indexed keywords

ALGORITHMS; DAMPING; DYNAMICS; EQUATIONS OF MOTION; INTEGRATION;

NUMERICAL INTEGRATION; STRUCTURAL DYNAMICS; TIME INTEGRATION;

ENERGY CONSERVATION;

ALGORITHMS; DAMPING; DYNAMICS; ENERGY CONSERVATION; EQUATIONS OF MOTION; INTEGRATION;

EID: 33745960193     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.12.001     Document Type: Article

References (20)

1. Newmark N.M. A method of computation for structural dynamics. J. Engrg. Mech. Div., ASCE 85 (1959) 67-94
2. Hulbert G.M. Computational structural dynamics. Solids and Structures. In: Stein E., de Borst R., and Hughes T.J.R. (Eds). Encyclopedia of Computational Mechanics vol. 2 (2004), Wiley, Chichester, UK 169-193
3. Hilber H.M., Hughes T.J.R., and Taylor R.L. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engrg. Struct. Dyn. 5 (1977) 282-292
4. Wood W.L., Bossak M., and Zienkiewicz O.C. An alpha modification of Newmark's method. Int. J. Numer. Methods Engrg. 15 (1981) 1562-1566
5. Chung J., and Hulbert G.M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized α method. J. Appl. Mech. 60 (1993) 371-375
6. Hilber H.M., and Hughes T.J.R. Collocation, dissipation and 'overshoot' for time integration schemes in structural dynamics. Earthquake Engrg. Struct. Dyn. 6 (1978) 99-117
7. Zhou X., and Tamma K.K. Design, analysis and synthesis of generalized single step single solve and optimal algorithms for structural dynamics. Int. J. Numer. Methods Engrg. 59 (2004) 597-668
8. Simo J.C., and Wong K.K. Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum. Int. J. Numer. Methods Engrg. 31 (1991) 19-52
9. Simo J.C., and Tarnow N. The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics. Z. Angew. Math. Phys. 43 (1992) 757-792
10. Puso M.A. An energy and momentum conserving method for rigid-flexible body dynamics. Int. J. Numer. Methods Engrg. 53 (2002) 1393-1414
11. Gonzalez O. Exact energy and momentum conserving algorithms for general models in non-linear elasticity. Comput. Methods Appl. Mech. Engrg. 190 (2000) 1763-1783
12. Lens E.V., Cardona A., and Geradin M. Energy preserving time integration for constrained multibody systems. Multibody Syst. Dyn. 11 (2004) 41-61
13. Betsch P., and Steinmann P. Conservation properties of a time FE method. Part I: Time-stepping schemes for N-body problems. Int. J. Numer. Methods Engrg. 49 (2000) 599-638
14. Betsch P., and Steinmann P. Conservation properties of a time FE method. Part II: Time-stepping schemes for non-linear elastodynamics. Int. J. Numer. Methods Engrg. 50 (2001) 1931-1955
15. Krenk S. State-space time integration with energy control and 4th order accuracy for linear dynamic systems. Int. J. Numer. Methods Engrg. 65 (2006) 595-619
16. Krenk S., and Høgsberg J.R. Properties of time integration with first order filter damping. Int. J. Numer. Methods Engrg. 64 (2005) 547-566
17. Geradin M., and Rixen D. Mechanical Vibrations. second ed. (1997), Wiley, Chichester, UK
18. Hughes T.J.R. A note on the stability of Newmark's algorithm in non-linear structural dynamics. Int. J. Numer. Methods Engrg. 11 (1977) 383-386
19. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (1987), Prentice-Hall, Englewood Cliffs, NJ
20. Kuhl D., and Crisfield M.A. Energy conserving and decaying algorithms in non-linear structural dynamics. Int. J. Numer. Methods Engrg. 45 (1999) 569-599