Abstract
Plastic instability is discussed from the point of view of generic bifurcation theory. We try to get an exhaustive classification of the singularities that can occur for the socalled dissipative systems. This goal is achieved for systems with two degrees of freedom. For continuous systems, we analyse the post-bifurcation behavior of representative beam buckling problems with variable cross-sections.
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References
BENALLAL, A., BILLARDON, R. and GEYMONAT, G.: C.R. Acad. Sci., 308, II, 1989, 893–897.
BUDIANSKY, B.: Theory of buckling and postbuckling behaviour of elastic structures, Advances in Appl. Mech., 14, 1974, 1–65.
CAMOTIM, D.R.: To appear in Dynamics Stability of Systems,1992.
CHOW, S.N., HALE, J.K., MALLET-PARET, J.: Applications of generic bifurcation, I Arch. Rat. Mech. Anal., 59, 1975, 159–188, II id. 62, 1976, 209–235.
CIMETIERE, A.: Modèle incrémental pour la forte flexion des plaques élastoplastiques. C.R. Acad. Sci. Paris, 298, série II, 1984, 99–102.
CIMETIERE, A.: Flambage élastoplastique des plaques: Thèse d’Etat, Université de Poitiers, 1987.
DUVAUT, G. et LIONS, J.-L.: Equations et inéquations en mécanique et en physique, Dunod, Paris, 1972.
ENGESSER, F.: Ueber die Knickfestigkeit Gerader Stäbe, Z. Architektur Ing., vol. 35, 1889, p. 455.
GOLUBITSKY, M., SCHAEFFER, D.G.: A theory for imperfect bifurcation via singularity theory, 32, Comm. Pure Appl. Match, 1979, 21–98.
GOLUBITSKY, M., SCHAEFFER, D.G.: Singularities and Groups in Bifurcation Theory, vol. 1, Springer-Verlag, New York, 1985.
HILL, R.: A general theory of uniqueness and stability in elastic/plastic solids. J. Mech. Phys. Solids, 6, 1958, 236–249.
HUTCHINSON, J.W.: Post-bifurcation behavior in the plastic range, J. Mech. Phys. Solids, 21, 1973, 163–190.
HUTCHINSON, J.W.: Imperfection sensitivity in the plastic range, J. Mech. Phys. Solids, 21, 1973, 191–204.
HUTCHINSON, J.W.: Plastic buckling, Adv. Appl. Mech., 14, 1974, 67–144.
KOITER, W.T.: On the Stability of Elastic Equilibrium, Thesis, Delft, 1945, English translation NASA Techn. Trans. F-10, 833, 1967.
LEGER, A. and POTIER-FERRY, M. Sur le flambage plastique, J. Mécanique Théor. Appl., 7, 1988, 819–857.
LEGER, A. and POTIER-FERRY, M. Elastic-plastic post-buckling from a heterogeneous state, to appear in J. Mech. Phys. Solids,1992.
NGUYEN, Q.S.: Stabilité et bifurcation en rupture et en plasticité, C.R. Acad. Sci. Paris, 292, série II, 1981, 817–821.
NGUYEN, Q.S.: Bifurcation et stabilité des systèmes irréversibles obéissant au principe de dissipation maximale, J. Méc. Théo. Appl., 3, 1984, 41–61.
NGUYEN, Q.S.: Bifurcation and Postbifurcation Analysis in Plasticity and Brittle Fracture, J. Mech. Phys. Solids, 33, 1987, 303–324.
POTIER-FERRY, M.: On the Mathematical Foundations of Elastic Stability Theory, Arch. Rat. Mech. Anal., 78, 1982, 301–320.
POTIER-FERRY, M.: Towards a Catastroph Theory for the Mechanics of Plasticity and Fracture, Int. J. Engng. Sci., 23, 1985, 821–837.
POTIER-FERRY, M.: Buckling and Postbuckling, Lecture Notes in Physics, 288, Springer-Verlag, Heidelberg, 1987, 1–82.
SHANLEY, F.R.: Inelastic Column Theory, J. Aeronaut. Sci., 14, 1947, 261–267.
TRIANTAFYLLIDIS N. On the Bifurcation and Postbifurcation Analysis of Elastic-Plastic Solids under General Prebifurcation Conditions, J. Mech. Phys. Solids, 31, 1983, 499–510.
THOMPSON, J.M.T. and HUNT, G.W.: A General Theory of Elastic Stability, Wiley, London, 1973.
TVERGAARD, V. and NEEDLEMAN, A.: On the buckling of Elastic-Plastic Columns with Asymmetric Cross-Sections, Int. J. Mech. Sci., 17, 1975, 419–424.
VON KARMAN, Th.: Untersuchungen über knickfestigkeit, mitteilungen über forschungsarbeiten, VDI (Ver. Deut. Ing.) Forschungsh. 81, 1910.
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Léger, A., Potier-Ferry, M. (1993). Generic Singularities for Plastic Instability Problems. In: Nguyen, Q.S. (eds) Bifurcation and Stability of Dissipative Systems. International Centre for Mechanical Sciences, vol 327. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2712-4_4
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DOI: https://doi.org/10.1007/978-3-7091-2712-4_4
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