Sage Journals: Discover world-class research

Abstract

In the first part of the paper, stability analysis of nonlinearly inelastic damaging structures is shown by applying polygonal approximation for the nonlinear material functions. The basis of the nonsmooth stability analysis together with a lot of numerical illustrations has originally been laid down in the papers of M. Kurutz (1989, 1993a, 1993b, 1995). In the first part of this paper, the theoretical bases of the nonsmooth damage and localization instabilities of structures having polygonal stress-strain diagrams are presented. In the second part, the numerical illustrations are shown.

The presented example aims to follow the famous historical example of Shanley (1947), related to the elasto-plastic behaviour of the Euler-column. By using a very simple mechanical model of the problem, the damage behaviour of the plastic hinges of the buckled state can be analysed.

Keywords

polygonal material behaviour strain softening damage localization equilibrium paths stability bifurcation nonsmoothness subdifferential superpotential

Get full access to this article

View all access options for this article.

References

Bazant, Z. P. 1988. "Stable States and Paths of Structures with Plasticity or Damage," J. Eng. Mech. (ASCE), 114(12):2013-2034.

Bazant, Z. P. 1989. "Stable States and Stable Paths of Propagation of Damage Zones and Interactive Fractures," In: Cracking and Damage-Strin Localization and Size Effect, ed. by J. Mazars , Z. P. Bazant , pp. 183-205, Elsevier, London, New York.

Bazant, Z. P. and L. Cedolin . 1991. "Stability of Structures. Elastic, Inelastic, Fracture and Damage Theories," Oxford University Press, New York, Oxford.

Kurutz, M. 1989. "Stability of Simple Structures with Nonsmooth Energy Functionals in the One-Dimensional Case," Acta Technica Sci. Hung. 102(3-4):291-314, Budapest.

Kurutz, M. 1993a. "Stability of Structures with Nonsmooth Nonconvex Energy Functionals, the One-Dimensional Case," Europ. Journ. of Mech. A/Solids, 12(3):347-385.

Kurutz, M. 1993b. "Equilibrium Paths of Polygonally Elastic Structures," Journ. of Mech. of Struct. and Mach., 22(2):181-210.

Kurutz, M. 1995. "Generalization of the Tangent Modulus for Nonsmooth Material Behaviour," Acta Technica Acad. Sci. Hung. (to be published).

Shanley, F. R. 1947. "Inelastic Column Theory," J. Aero. Sci., 14(5):261-268.

Thompson, J. M. T. and G. W. Hunt . 1973. "A General Theory of Elastic Stability, " Wiley, London.

10.

Thompson, J. M. T. and G. W. Hunt . 1984. "Elastic Instability Phenomena:" Wiley, Chichester.

Equilibrium Paths of Polygonally Damaging Structures Part Two: One-Dimensional Example for Nonsmooth Damage and Localization

Abstract

Keywords

Get full access to this article

References