Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



The swallowtail and butterfly cuspoids and their application in the initial post-buckling of single-mode structural systems

Authors: David Hui and Jorn S. Hansen
Journal: Quart. Appl. Math. 38 (1980), 17-36
MSC: Primary 58C28; Secondary 73H99, 73K99
DOI: https://doi.org/10.1090/qam/575830
MathSciNet review: 575830
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Abstract: This paper investigates the swallowtail and butterfly catastrophes from the point of view which is applicable in the theory of elastic stability. Thus, the results are concerned with the various forms of these instabilities as well as the determination of the critical load surfaces which are of engineering significance. It is demonstrated that the results are applicable to an axially loaded beam resting on a nonlinear elastic foundation.

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  • [1] René Thom, Structural stability and morphogenesis, W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1976. An outline of a general theory of models; Translated from the French by D. H. Fowler; With a foreword by C. H. Waddington; Second printing. MR 0488156
  • [2] W. T. Koiter, On the stability of an elastic equilibrium, doctoral thesis, Delft, The Netherlands, 1945 (NASA Tech. Trans. F10,833,1967 and AFFDL-TR-70-25. 1970)
  • [3] J. M. T. Thompson and G. W. Hunt, A general theory of elastic stability, Wiley-Interscience [John Wiley & Sons], London-New York-Sydney, 1973. MR 0400868
  • [4] B. Budiansky and J. W. Hutchinson, Dynamic buckling of imperfection-sensitive structures, in Proc. 11th Int. Cong, of App. Mech., Munich, 1964, edited by H. Gortler, Springer-Verlag (1966), pp. 636-651
  • [5] John M. T. Thompson and Giles W. Hunt, Towards a unified bifurcation theory, Z. Angew. Math. Phys. 26 (1975), no. 5, 581–603 (English, with German summary). MR 0388441, https://doi.org/10.1007/BF01594031
  • [6] D. Hui, The parabolic umbilic catastrophe and its application in the theory of elastic stability, M.A. Sc. thesis, Univ. of Toronto, 1977
  • [7] D. Hui and J. S. Hansen, Buckling and initial post-buckling of a two-mode infinite plate on a non-linear elastic foundation: an application of catastrophe theory, to be published
  • [8] V. Tvergaard, Imperfection-sensitivity of a wide integrally stiffened panel under compression, Int. J. Solids Struct. 9, 177-192 (1973)
  • [9] W. T. Koiter, Buckling and post-buckling behavior of a cylindrical panel under axial compression, Trans. Nat. Aero. Res. Inst., Amsterdam, NLL-TR-S476 (1956)
  • [10] W. Stephens, Imperfection sensitivity of axially compressed stringer reinforced cylindrical panels under internal pressure, AIAA J. 9, 1713-1719 (1971)
  • [11] J. W. Hutchinson and J. C. Amazigo, Imperfection-sensitivity of eccentrically stiffened cylindrical shells, AIAA J. 5, 392-401 (1967)
  • [12] J. W. Hutchinson, Buckling and initial post-buckling behavior of oval cylindrical shells under axial compression, J. App. Mech. 35, 66-72 (1968)
  • [13] N. R. Bauld, Jr., Imperfection sensitivity of axially compressed stringer reinforced cylindrical sandwich panels, Int. J. Solids Struct. 10, 833-902 (1974)
  • [14] J. R. Fitch, The buckling and post-buckling behavior of spherical caps under concentrated load, Int. J. Solids Struct. 4, 421-446 (1968)
  • [15] J. R. Fitch and B. Budiansky, The buckling and post-buckling of spherical caps under axisymmetric load, AIAA J. 8, 686-692 (1970)
  • [16] A. E. R. Woodcock and T. Poston, A geometric study of the elementary catastrophes, Springer-Verlag (1974)
  • [17] E. C. Zeeman, Catastrophe theory, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1977. Selected papers, 1972–1977. MR 0474383
  • [18] Tim Poston and Ian N. Stewart, Taylor expansions and catastrophes, Pitman, London-San Francisco, Calif.-Melbourne, 1976. Research Notes in Mathematics, Vol. 7. MR 0494231

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DOI: https://doi.org/10.1090/qam/575830
Article copyright: © Copyright 1980 American Mathematical Society

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