Mechanical Models for the Subclasses of Catastrophes

  • Zsolt Gaspar
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 470)


First some concepts of the structural stability and the elementary catastrophe theory are shown. A short chapter explains which types of the catastrophes are typical at elastic structures. Hence the load parameter has a special role among the parameters, a subclassification is needed in the stability analysis. The main part of the paper shows this subclassification and illustrates almost every type by simple elastic models.


Critical Load Potential Energy Function Equilibrium Path Perfect Structure Catastrophe Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Arnol’d, V. U. (1972). Normal forms for functions near degenerate critical points, the Weyl groups of A k,D k and E k, and Lagrangian singularities. Functional Anal. Appl., 6, 254–272.CrossRefGoogle Scholar
  2. Augusti, G. (1964). Stabilita’ di strutture elastiche elementari in prezenza di grandi spostamenti. Atti Accad. Sci.fls. mat., Napoli, Serie 3a, 4, No. 5.Google Scholar
  3. Domokos, G. (1991). An elastic model with continuous spectrum. Int. Series of Numerical Mathematics, 97, 99–103.MathSciNetGoogle Scholar
  4. Domokos, G. (1994). Global description of elastic bars. ZAMM, 74(4), T289–T291.MathSciNetGoogle Scholar
  5. Gaspar, Z. (1977). Buckling models for higher catastrophes. J. Struct. Mech., 5, 375–368.Google Scholar
  6. Gaspar, Z. (1982). Critical imperfection territory. J. Struct. Mech., 11, 297–325.MathSciNetGoogle Scholar
  7. Gaspar, Z. (1985). Imperfection-sensitivity at near-coincidence of two critical points. J. Struct. Mech., 13, 45–65.MathSciNetGoogle Scholar
  8. Gaspar, Z. (1999). Stability of elastic structures with the aid of catastrophe theory. In Kollar, L., ed., Structural Stability in Engineering Practice. London: Spon. 88–128.Google Scholar
  9. Gaspar, Z., Domokos, G. (1991) Global description of the equilibrium paths of a simple mechanical model. In Ivanyi, M., ed., Stability of Steel Structures. Budapest: Akademiai Kiado. 79–86.Google Scholar
  10. Gaspar, Z., Lengyel, A. (2002). Critical points of compatibility paths. In Ivanyi, M., ed., Stability and Ductility of Steel Structures, SDSS 2002, Budapest: Akademiai Kiado, 779–785.Google Scholar
  11. Gaspar, Z., Mladenov, K. (1996). Post-critical behavior of a column loaded by a polar force. In Ivanyi, M., ed., Stability of Steel Structures, 1995 Budapest, Further Directions in Stability Research and Design. Budapest: Akademiai Kiadó, Vol. II., 897–903.Google Scholar
  12. Gaspar, Z., Nemeth, R. (2002). Models to illustrate special bifurcations. (in Hungarian) In Tassi, G., Hegedus, I., Kovacs, T., eds, Scientific Publ. of Department of Struct. Eng., Faculty of Civ. Eng., Budapest Univ. of Technology and Economics. Budapest: Muegyetemi Kiado. 81–92.Google Scholar
  13. Gioncu, V., Ivan, M. (1984). Theory of Critical and Post-critical Behaviour of Elastic Structures. (in Rumanian) Bucuresti: Editura Acad. Resp. Soc. Rom..Google Scholar
  14. Hackl, K. (1990). Ausbreitung von Instabilitäten in einem Knickmodell von Thompson und Gaspar. ZAMM, 70, T189–T192.CrossRefMathSciNetGoogle Scholar
  15. Hegedus, I. (1986). Contribution to Gaspar’s paper: Buckling model for a degenerated case. News Letter, Techn. Univ. of Budapest, 4(1), 8–9.Google Scholar
  16. Hegedus, I. (1988). The stability of a hinged bar fixed by weightless chords. News Letter, Techn. Univ. of Budapest, 6(3), 15–22.MathSciNetGoogle Scholar
  17. Hunt, G. W. (1978). Imperfections and near-coincidence for semi-symmetric bifurcations. Annals of the New York Academy of Sciences, 316, 572–589.CrossRefGoogle Scholar
  18. Hunt, G. W., Reay, N. A., Yoshimura, T. (1979). Local diffeomorphism in the bifurcational manifestations of the umbilic catastrophes. Proc. Roy. Soc. Lond. A, 369, 47–65.MATHMathSciNetGoogle Scholar
  19. Koiter, W. T. (1945). On the Stability of Elastic Equilibrium. (in Holland) Dissertation, Delft, Holland, (English translation: NASA, Techn. Trans., F10, 833, 1967)Google Scholar
  20. Kollar, L. P. (1990). Postbuckling behavior of structures having infinitely great critical loads. Mech. Struct. Machines, 18, 17–31.CrossRefGoogle Scholar
  21. Pajunen, S., Gaspar, Z. (1996). Study of an interactive buckling model — From local to global approach. In Rondal, J., Dubina, D., Gioncu, V., eds, Proc. 2 nd Int. Conf. on Coupled Instabilities in Metal Struct. CIMS’96. London: Imperial College Press. 35–42.Google Scholar
  22. Poston, T., Stewart, I. N. (1976). Taylor Expansions and Catastrophes. Research Notes in Mathematics, 7, London: Pitman.MATHGoogle Scholar
  23. Poston, T., Stewart, I. N. (1978). Catastrophe Theory and its Applications. London: Pitman.MATHGoogle Scholar
  24. Shanley, F. R. (1947). Inelastic column theory. J. Aero Sci., 14, 261–268.Google Scholar
  25. Tarnai, T. (2001). Kinematic bifurcation. In Pellegrino, S., ed., Deployable structures, CISM Courses and Lectures No. 412, Wien: Springer, 143–169.Google Scholar
  26. Tarnai, T. (2003). Zero stiffness elastic structures. Int. J. of Mechanical Sciences, 45, 425–431.MATHCrossRefGoogle Scholar
  27. Thorn, R. (1972). Stabilité Structurelle et Morphogenése. New York: Benjamin.Google Scholar
  28. Thompson, J. M. T., Gaspar, Z. (1977). A buckling model for the set of umbilic catastrophes. Math. Proc. Camb. Phil. Soc., 82, 497–507.MATHCrossRefMathSciNetGoogle Scholar
  29. Thompson, J. M. T., Hunt, G. W. (1973). A General Theory of Elastic Stability. London: Wiley.MATHGoogle Scholar
  30. Thompson, J. M. T., Hunt, G. W. (1984). Elastic Instability Phenomena. Chichester: Wiley.MATHGoogle Scholar
  31. Zeeman, E. C. (1977). Catastrophe Theory: Selected Papers (1972–1977). Reading: Addison-Wesley.MATHGoogle Scholar

Copyright information

© CISM, Udine 2005

Authors and Affiliations

  • Zsolt Gaspar
    • 1
    • 2
  1. 1.Department of Structural MechanicsBudapest University of Technology and EconomicsHungary
  2. 2.Research Group for Computational Structural MechanicsHungarian Academy of SciencesBudapestHungary

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