The analysis of the Generalized-α method for non-linear dynamic problems

Computational Mechanics

Volumn 28, Issue 2, 2002, Pages 83-104

  Erlicher, S ^a   Bonaventura, L ^a   Bursi, O S ^a  

^a UNIVERSITY OF TRENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DIFFERENTIAL EQUATIONS; DYNAMICS; NONLINEAR EQUATIONS;

STRUCTURAL DYNAMICS;

NONLINEAR SYSTEMS;

EID: 0345668472     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-001-0273-z     Document Type: Article

References (36)

1. Abramowitz M, Stegun LA (1964) Handbook of Mathematical Functions. National Bureau of Standards, Appl. Math. Series 55, Washington D.C
2. Bauchau OA, Damilano G, Theron NJ (1995) Numerical integration of non-linear elastic multi-body systems. Int. J. Num. Meth. Eng. 38: 2727-2751
3. Belytschko T, Schoeberle DF (1975) On the unconditional stability of an implicit algorithm for nonlinear structural dynamics. Trans. ASME J. Appl. Mech. 42: 865-869
4. Chung J, Hulbert GM (1993) A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J. Appl. Mech. 60: 371-375
5. Crisfield MA, Galvanetto U, Jelenic G (1997) Dynamics of 3-D co-rotational beams. Comput. Mech. 20: 507-519
6. Chrisfield MA, Shi J (1994) A co-rotational element/time-integration strategy for non-linear dynamics. Int. J. Numer. Meth. Eng. 37: 1897-1913
7. Hairer E, Nørsett SP, Wanner G (1987) Solving Ordinary Differential Equations I. Springer-Verlag, Berlin
8. Hairer E, Wanner G (1991) Solving Ordinary Differential Equations II. Springer-Verlag, Berlin
9. Hilber HM, Hughes TJR (1978) Collocation, dissipation and "overshoot" for time integration schemes in structural dynamics. Earthquake Eng. Struct Dynam. 6: 99-117
10. Hilber HM, Hughes TJR, Taylor RL (1977) Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng. Struct. Dynam. 5: 283-292
11. Hoff C, Pahl PJ (1988a) Development of an implicit method with numerical dissipation for time integration algorithms in structural dynamics. Comput. Meth. Appl. Mech. Eng. 67: 367-385
12. 1-method and comparison with other dissipative algorithms in structural dynamics. Comput. Meth. Appl. Eng. 67: 87-110
13. Houbolt JC (1950) A recurrence matrix solution for the dynamic response of elastic aircraft. J. Aeronaut. Sci. 17: 540-550
14. Hughes TJR (1977) A note on the stability of Newmark's Algorithm in nonlinear structural dynamics. Int. J. Num. Meth. Eng. 11(2): 383-386
15. Hughes TJR (1976) Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics. Comput. Struct. 6: 313-324
16. Hughes TJR (1987) The Finite Element Method, Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Upper Saddle River, New Jersey
17. Hughes TJR, Liu WK (1978) Implicit-explicit finite elements in transient analysis: implementation and numerical examples. J. Appl. Mech. (60): 371-375
18. Hulbert GM (1991) Limitations on linear multistep method for structural dynamics. Earthquake Eng. Struct. Dynam. 20: 191-196
19. Hulbert GM, Hughes TJR (1987) An error analysis of truncated starting conditions in step-by-step time integration: consequences for structural dynamics. Earthquake Eng. Struct. Dynam. 15: 901-910
20. Hulbert GM, Jang I (1995) Automatic time step control algorithms for structural dynamics. Comp. Meth. Appl. Mech. Eng. 126: 155-178
21. Karabalis DL, Beskos DE (1997) Numerical Methods in Earthquake engineering in Computer Analysis and Design of Earthquake Resistant Structures: a Handbook. Computational Mechanics Publications, WIT Press, Southampton, UK
22. Kuhl D, Crisfield MA (1999) Energy conserving and decaying algorithms in non-linear structural dynamics. Int. J. Numer. Meth. Eng. 45: 569-599
23. Kuhl D, Ramm E (1996) Constraint energy momentum algorithm and its application to non-linear dynamics of shells. Comput. Meth. Appl. Mech. Eng.
24. Kuhl D, Ramm E (1999) Generalized energy-momentum method for non-Linear adaptive shell dynamics. Comput. Meth. Appl. Mech. Eng. 178: 343-366
25. Lambert JD (1991) Numerical Methods for Ordinary Differential Systems. John Wiley & Sons, New York
26. Newmark NM (1959) A method of computation for structural dynamics. J. Eng. Mech. Div. ASCE 85(EM3): 67-94
27. Owren B, Simonsen HH (1995) Alternative integration methods for problems in structural dynamics. Comput. Meth, Appl. Mech. Eng. 122: 1-10
28. Park KC (1975) An improved stiffy stable method for direct integration of nonlinear structural dynamic equations. Trans. ASME J. Appl. Mech. 42: 464-470
29. Piché R (1995) An L-stable Rosenbrock method for step-by-step time integration in structural dynamics. Comput. Math. Appl. Mech. Eng. 126: 343-354
30. Simo JC, Tarnow N (1992) The discrete energy-momentum method: conserving algorithms for nonlinear elastodynamics. Z. Angew. Math. Phys. 43: 757-792
31. Stuart AM, Humphries AR (1996) Dynamical Systems and Numerical Analysis. Cambridge University Press, New York
32. Tamma KK, Zhou X, Sha D (2000) The time dimension: a theory towards the evolution, classification, characterization and design of computational algorithms for transient/dynamic applications. Arch. Comput. Meth. Eng. 7: 67-290
33. Wood WL (1990) Practical Time-Stepping Schemes. Clarendon Press, Oxford
34. Wood WL, Bossak M, Zienkiewicz OC (1981) An alpha modification of Newmark's method. Int. J. Numer. Meth. Eng. 15: 1562-1566
35. Wood WL, Oduor ME (1988) Stability properties of some algorithms for the solution of nonlinear dynamics vibration equations. Comm. Appl. Numer. Meth. 4: 205-212
36. Zhong HG, Crisfield MA (1998) An energy conserving co-rotational procedure for the dynamics of shell structures. Eng. Comput. 15(5): 552-576