An asymptotic numerical method for non-linear transient dynamics

Revue Europeenne des Elements

Volumn 9, Issue 1-3, 2000, Pages 113-128

  Cochelin, Bruno ^a   Compain, Christophe ^a  

^a LABORATOIRE DE MÉCANIQUE ET D ACOUSTIQUE   (France)

Author keywords

F.E.M.; Non linear Algorithm; Perturbation methods; Series; Structural Dynamics

Indexed keywords

MATHEMATICAL TRANSFORMATIONS; NEWTON-RAPHSON METHOD; PERTURBATION TECHNIQUES; STIFFNESS MATRIX; STRUCTURAL DYNAMICS;

ASYMPTOTIC NUMERICAL METHOD; NON-LINEAR DYNAMICS; PERTURBATION METHOD; PERTURBATION SERIES; RADIUS OF CONVERGENCE; SERIES; TIME-STEPPING SCHEMES; TRANSIENT DYNAMICS;

ALGORITHMS;

EID: 0009685680     PISSN: 12506559     EISSN: None     Source Type: Journal    
DOI: 10.1080/12506559.2000.10511432     Document Type: Article

References (25)

1. AMMAR S., Méthode asymptotique perturbee appliquee a la resolution de problèmes non lineaires en grandes rotations et deplacements, PhD Thesis, Laval University, QUEBEC, 1996.
2. Azrar L., Cochelin B., Damil N., Potier-Ferry M., "An asymptotic numerical method to compute the post-buckling behavior of elastic plates and shells", Int. J. Numer.Meth.Eng., vol. 36, 1993, p. 1251-1277.
3. Braikat B., Damil N., Potier-Ferry M., "Méthodes asymptotiques numériques pour la plasticité", Revue Européenne des Elements Finis, vol. 6, 1997, p. 337-357.
4. Cochelin B., "A path following technique via an asymptotic numerical method", Computers & Structures, vol. 29, 1994, p. 1181-1192.
5. Cochelin B., Damil N., Potier-Ferry M., "The Asymptotic-Numerical- Method: an efficient perturbation technique for nonlinear structural mechanics", Revue Europeenne des Elements Finis, vol. 3, 1994, p. 281-297.
6. Cochelin B., Damil N.,Potier-Ferry M., "Asymptotic-Numerical Methods and Pade approximants for nonlinear elastic structures", Int. J. Numer. Meth. Eng., vol. 37, 1994, p. 1181-1192.
7. CRISFIELD M. A., Nonlinear Finite Element Analysis of Solids ans Structures, Vol.2, John Wiley and Sons, 1st edition, 1997.
8. Damil N., Potier-Ferry M., "A new method to compute perturbed bifurcations: application to the buckling of imperfect elastic structures", International Journal of Engineering Sciences-N9, vol. 28, 1990, p. 943-957.
9. Elhage-Hussein A., Damil N., Potier-Ferry M., "An asymptotic numerical algorithm for frictionless contact problems", Revue Europeenne des Elements Finis, vol. 7, 1998, p. 119-130.
10. Fafard M., Ammar S., Henchi K., Gendron G., "Application of an asymptotic method to transient dynamic problems", Journal of Sound and Vibration, vol. 208, 1997, p. 73-99.
11. Gallagher R., "Perturbation procedures in nonlinear finite element structural analysis", Computational Mechanics-Lecture Notes in Mathematics, vol. 461, 1975, p. 75-89.
12. Khul D., Ramm E., "Constraint Energy Momentum Algorithm and its application to nonlinear dynamics of shells", Comput. Methods Appl. Mech. Engrg., vol. 136, 1996, p. 293-315.
13. Najah A., Cochelin B.and Damil N., Potier-Ferry M., "A critical review of Asymptotic Numerical Methods", Archives of Computational Methods in Engineering, vol. 5, 1998, p. 31-50.
14. Nayfeh A., Perturbation methods, John Wiley and Sons-New York, 1973.
15. NAYFEH A., MOOK T., Nonlinear Oscillations, Whiley Classic Library, 2nd edition, 1989.
16. NOOR A., PETERS J., "Reduced basis technique for nonlinear analysis of structures", AIAA Journal-N4, vol. 18, 1980, p. 455-462.
17. Noor A., Peters J., "Tracing Post-Limit-Point Paths with reduced Basis Technique", Comput. Methods Appl. Mech. Engrg., vol. 28, 1980, p. 217-240.
18. NOOR A., "Hybrid analytical technique for nonlinear analysis of structures", AIAA Journal-N6, vol. 23, 1985, p. 938-946.
19. Potier-Ferry M., Damil N., Braikat B., Descamps J., Cadou J., Cao H., ElhageHUSSEIN A., "Traitement des fortes non-linearite par la methode asymptotique numerique", C. R. Acad. Sci. Paris, vol. t 314, 1997, p. 171-177, Serie II b.
20. RlKS E., "Some Computational aspects of stability of nonlinear structures", Comput. Methods Appl. Mech. Engrg., vol. 47, 1984, p. 219-259.
21. SlMO J., TARNOW N., "The discrete Energy-Momentum method. Conserving algorithms for nonlinear elastodynamics", Int. J. Numer. Meth. Eng., vol. 136, 1996, p. 293-315.
22. SWEMPLINSKA-STUPNICKA W., The Behavior of Nonlinear Vibrating Systems -Vol. 1 and 2, Kluwer Academic Publisher, 1st edition, 1990.
23. THOMPSON J., Walker A., "The nonlinear perturbation analysis of discrete structural systems", Int. J. Solids Structures, vol. 4, 1968, p. 757-758.
24. Walker A., "A nonlinear finite element analysis of shallow circular arches", Int. J. Solids Structures, vol. 5, 1969, p. 97-107.
25. Zahrouni H., Cochelin B., Potier-Ferry M., "Asymptotic-numerical methods for shells with finite rotations", Comput. Methods Appl. Mech. Engrg., vol. 175, 1999, p. 71-85.