Mechanical Models for the Subclasses of Catastrophes

CISM International Centre for Mechanical Sciences, Courses and Lectures

Volumn 470, Issue , 2005, Pages 277-336

  Gaspar, Zsolt ^a,b  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

Catastrophe Theory; Critical Load; Equilibrium Path; Perfect Structure; Potential Energy Function

Indexed keywords

EID: 39449089272     PISSN: 02541971     EISSN: 23093706     Source Type: Book Series    
DOI: 10.1007/3-211-38028-0_5     Document Type: Chapter

References (31)

1. Arnol'd, V. U. (1972). Normal forms for functions near degenerate critical points, the Weyl groups of A~, D k and Ek, and Lagrangian singularities. Functional Anal. Appl., 6, 254-272.
2. R. Benito and S. Sridharan. Mode interaction in thin-walled st r uct ur al members. J. Struct. Mech., 12:517-542, 1984.
3. Domokos, G. (1991). An elastic model with continuous spectrum. Int. Series of Numerical Mathematics, 97, 99-103.
4. Domokos, G. (1994). Global description of elastic bars. ZAMM, 74(4), T289-T291.
5. Gaspar, Z. (1977). Buckling models for higher catastrophes. J. Struct. Mech., 5, 375-368.
6. Gaspar, Z. (1982). Critical imperfection territory. J. Struct. Mech., 11,297-325.
7. Gaspar, Z. (1985). Imperfection-sensitivity at near-coincidence of two critical points. J. Struct. Mech., 13, 45-65.
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.
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: Akad6miai Kiad6.79-86.
10. Gaspar, Z., Lengyel, A. (2002). Critical points of compatibility paths. In Ivanyi, M., ed., Stability and Ductility of Steel Structures, SDSS 2002, Budapest: Akad6miai Kiad6, 779-785.
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: Akad6miai Kiad6, Vol. II., 897-903.
12. R. Benito and S. Sridharan. Mode interaction in thin-walled st r uct ur al members. J. Struct. Mech., 12:517-542, 1984.
13. R. Benito and S. Sridharan. Mode interaction in thin-walled st r uct ur al members. J. Struct. Mech., 12:517-542, 1984..
14. Hackl, K. (1990). Ausbreitung von Instabilitfiten in einem Knickmodell von Thompson und Gaspar. ZAMM, 70, T 189-T 192.
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.
16. Hegedus, I. (1988). The stability of a hinged bar fixed by weightless chords. News Letter, Techn. Univ. of Budapest, 6(3), 15-22.
17. Hunt, G. W. (1978). Imperfections and near-coincidence for semi-symmetric bifurcations. Annal s of the New York Academy of Sciences, 316, 572-589.
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.
19. Koiter, W. T. (1945). On the Stability of Elastic Equilibrium. (in Holland) Dissertation, Delft, Holland, (English translation: NASA, Techn. Trans., F10, 833, 1967)
20. Kollar, L. P. (1990). Postbuckling behavior of structures having infinitely great critical loads. Mech. Struct. Machines, 18, 17-31.
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 "d Int. Conf. on Coupled Instabilities in Metal Struct. CIMS'96. London: Imperial College Press. 35-42.
22. Poston, T., Stewart, I. N. (1976). Taylor Expansions and Catastrophes. Research Notes in Mathematics, 7, London: Pitman.
23. Poston, T., Stewart, I. N. (1978). Catastrophe Theory and its Applications. London: Pitman.
24. Shanley, F. R. (1947). Inelastic column theory. J. Aero Sci., 14, 261-268.
25. Tarnai, T. (2001). Kinematic bifurcation. In Pellegrino, S., ed., Deployable structures, CISM Courses and Lectures No. 412, Wien: Springer, 143-169.
26. Tamai, Y. (2003). Zero stiffness elastic structures. Int. J. of Mechanical Sciences, 45, 425-431.
27. Thorn, R. (1972). StabilitO Structurelle et MorphogenOse. New York: Benjamin.
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.
29. Thompson, J. M. T., Hunt, G. W. (1973). A General Theory of Elastic Stability. London: Wiley.
30. Thompson, J. M. T., Hunt, G. W. (1984). Elastic Instability Phenomena. Chichester: Wiley.
31. Zeeman, E. C. (1977). Catastrophe Theory: Selected Papers (1972-1977). Reading: Addison-Wesley.