Stability and dynamics of a plastic softening oscillator

International Journal of Solids and Structures

Volumn 43, Issue 18-19, 2006, Pages 5867-5885

  Challamel, Noël ^a   Pijaudier Cabot, Gilles ^b  

^a LGCGM   (France)

^b INSTITUT DE RECHERCHE EN GÉNIE CIVIL ET MÉCANIQUE GEM   (France)

Author keywords

Concrete structures; Large displacements; Non linear dynamics; Seismic design; Softening; Stability of inelastic systems; Steel structures

Indexed keywords

CONCRETE CONSTRUCTION; DEGREES OF FREEDOM (MECHANICS); DYNAMIC LOADS; DYNAMICS; ELASTICITY; STEEL STRUCTURES;

LARGE DISPLACEMENTS; SEISMIC DESIGN; SOFTENING; STABILITY OF INELASTIC SYSTEMS;

OSCILLATORS (MECHANICAL);

EID: 33746303521     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2005.09.005     Document Type: Article

References (55)

1. Aschheim M., and Montes E.H. The representation of p-delta effects using yield point spectra. Eng. Struct. 25 (2003) 1387-1396
2. Aydinoglu M.N., and Fahjan Y.M. A unified formulation of the piecewise exact method for inelastic seismic demand analysis including P-delta effect. Earthquake Eng. Struct. Dyn. 32 (2003) 871-890
3. Ballio G. Elastic-plastic dynamic behavior of a beam-column model. Meccanica 3 (1968) 177-186
4. Ballio G. On the dynamic behavior of an elastoplastic oscillator (experimental investigations and theoretical developments). Meccanica 5 (1970) 85-97
5. Bazant Z.P. Instability, ductility and size effect in strain-softening concrete. J. Eng. Mech. 102 (1976) 331-344
6. Bazant Z.P. Stable states and paths of structures with plasticity or damage. J. Eng. Mech. 114 12 (1988) 2013-2034
7. Bazant Z.P., and Cedolin L. Stability of Structures-Elastic, Inelastic, Fracture and Damage Theories (2003), Dover Publications, Inc., New York
8. Bazant Z.P., and Jirasek M. Softening-induced dynamic localization instability: seismic damage in frames. J. Eng. Mech. 122 12 (1996) 1149-1158
9. Bazant Z.P., Pan J., and Pijaudier-Cabot G. Softening in reinforced concrete beams and frames. J. Struct. Eng. 113 (1987) 2333-2347
10. Belytschko T., and Fish J. Embedded hinge lines for plate elements. Comput. Meth. Appl. Mech. Eng. 76 (1989) 67-86
11. Bernal D. Amplification factors for inelastic dynamic p-delta effects in earthquake analysis. Earthquake Eng. Struct. Dyn. 15 (1987) 635-651
12. Bolotin V.V. Nonconservative Problems of the Theory of Elastic Stability (1963), Pergamon Press, New York
13. Capecchi D. Asymptotic motions and stability of the elastoplastic oscillator studied via maps. Int. J. Solids Struct. 30 23 (1993) 3303-3314
14. Caughey T.K. Sinusoidal excitation of a system with bilinear hysteresis. J. Appl. Mech. 27 4 (1960) 649-652
15. Challamel, N., 2003a. Contribution of Liapounov stability theory to geomechanics. In: 16th Eng. Mech. Conf., Seattle.
16. Challamel N. Une approche de plasticité au gradient en construction métallique. C. R. Acad. Sci. 331 9 (2003) 647-654
17. Challamel N. Dynamic analysis of elastoplastic shakedown of structures. Int. J. Struct. Stability Dyn. 5 2 (2005) 259-278
18. Challamel N., and Hjiaj M. Non-local behaviour of plastic softening beams. Acta Mech. 178 (2005) 125-146
19. Challamel N., and Pijaudier-Cabot G. Stabilité et dynamique d'un oscillateur endommageable. Revue Française de Génie Civil 8 4 (2004) 483-505
20. Cocchetti G., and Maier G. Elastic-plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming. Int. J. Solids Struct. 40 (2003) 7219-7244
21. Como M., and Grimaldi A. Theory of Stability of Continuous Elastic Structures (1995), CRC Press 138 p
22. Davies M.A., and Moon F.C. Transition from soliton to chaotic motion following sudden excitation of a nonlinear structure. J. Appl. Mech. 63 (1996) 445-449
23. De Borst R., and Mühlhaus H.B. Gradient-dependent plasticity: formulation and algorithmic aspects. Int. J. Numer. Meth. Eng. 35 (1992) 521-539
24. Guckenheimer J.A., and Holmes P.J. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (1987), Springer, Berlin
25. Hagedorn P. Non-linear Oscillations (1978), Oxford Science Publications p. 283
26. Hill R. A general theory of uniqueness and stability in elastic-plastic solids. J. Mech. Phys. Solids 6 (1958) 236-249
27. Hjelmstad K.D., and Williamson E.B. Dynamic stability of structural systems subjected to base excitation. Eng. Struct. 20 4-6 (1998) 425-432
28. Holmes P.J. A nonlinear oscillator with a strange attractor. Phil. Trans. R. Soc. Lond., Ser. A 292 (1979) 419-448
29. Holmes P.J., and Marsden J. A partial differential equation with infinitely many periodic orbits: chaotic oscillations of a forced beam. Arch. Rat. Mech. Anal. 76 (1981) 135-166
30. Jennings P.C., and Husid R. Collapse of yielding structures under earthquakes. J. Eng. Mech. Div., ASCE 94 (1968) 1045-1065
31. Jirasek M., and Bazant Z.P. Inelastic Analysis of Structures (2002), Wiley 758 p
32. Knops R.J., and Wilkes E.W. Theory of elastic stability. Handbuch der Physik Band Via/3 (1973), Springer-Verlag, New York pp. 125-289
33. La Salle J., and Lefschetz S. Stability by Liapunov's Direct Method with Applications (1961), Academic Press, New York 134 p
34. MacRae G.A. P-Δ effects on single-degree-of-freedom structures in earthquakes. Earthquake Spectra 10 3 (1994) 539-568
35. Maier G., and Perego U. Effects of softening in elastic-plastic structural dynamics. Int. J. Numer. Meth. Eng. 34 (1992) 319-347
36. Maier G., and Zavelani A. Sul comportamento di aste metaliche compresse eccentricamente. Indagine sperimentale e considerazioni teoriche. Costruzioni Metalliche 22 4 (1970) 282-297
37. Mazzolani F.M., and Gioncu V. Ductility of Seismic-resistant Steel Structures (2002), Spon Press 720 p
38. Mazzolani F.M., and Piluso V. Theory and Design of Seismic Resistant Steel Frames (1996), Chapman & Hall 497 p
39. McLaughlin J.B. Period-doubling bifurcations and chaotic motion for a parametrically forced pendulum. J. Statist. Phys. 24 2 (1981) 375-388
40. Minorsky N. Non-linear Mechanics (1947), Edward Brothers, Michigan
41. Mond M., Cederbaum G., Khan P., and Zarmi Y. Stability analysis of the non-linear Mathieu equation. J. Sound Vibrat. 167 1 (1993) 77-89
42. Nayfeh A.H., and Mook D.T. Non linear Oscillations. Pure & Applied Mathematics, A (1979), Wiley, Interscience Series of Texts
43. Nguyen Q.S. Stabilité et mécanique non linéaire (2000), Hermes 461 p
44. Petryk H. Second-order work and dissipation on indirect paths. C. R. Mécanique 330 (2002) 121-126
45. Pijaudier-Cabot G., and Bazant Z.P. Non local damage theory. J. Eng. Mech., ASCE 113 10 (1987) 1512-1533
46. Pratap R., and Holmes P.J. Chaos in a mapping describing elastoplastic oscillations. Nonlinear Dyn. 8 (1995) 111-139
47. Pratap R., Mukherjee S., and Moon F.C. Dynamic behavior of a bilinear hysteretic elasto-plastic oscillator, Part I: free oscillations. J. Sound Vibrat. 172 3 (1994) 321-337
48. Pratap R., Mukherjee S., and Moon F.C. Dynamic behavior of a bilinear hysteretic elasto-plastic oscillator, Part II: oscillations under periodic impulse forcing. J. Sound Vibrat. 172 3 (1994) 339-358
49. Savi M.A., and Pacheco P.M.C.L. Non-linear dynamics of an elasto-plastic oscillator with kinematic and isotropic hardening. J. Sound Vibrat. 207 2 (1997) 207-226
50. Sun C.K., Berg G.V., and Hanson R.D. Gravity effect on single-degree inelastic system. J. Eng. Mech. Div. 99 (1973) 183-200
51. Szemplinska-Stupnicka W. Bifurcations of harmonic solution leading to chaotic motion in the softening type Duffing's oscillator. Int. J. Non-Linear Mech. 23 4 (1988) 257-277
52. Vardoulakis I., and Sulem J. Bifurcation Analysis in Geomechanics (1995), Chapman and Hall 462 p
53. Williamson E.B. Evaluation of damage and P-Δ effects for systems under earthquake excitation. J. Struct. Eng. 129 8 (2003) 1036-1046
54. Williamson E.B., and Hjelmstad K.D. Nonlinear dynamics of a harmonically-excited inelastic inverted pendulum. J. Eng. Mech. 127 1 (2001) 52-57
55. Yu Y., and Zheng J. Dynamic elastic-plastic buckling behavior illustrated by simple model. J. Eng. Mech. 118 10 (1992) 2005-2016