Stability under step loading of infinitely long columns with localized imperfections
Authors:
John C. Amazigo and Deborah F. Lockhart
Journal:
Quart. Appl. Math. 34 (1976), 249-256
DOI:
https://doi.org/10.1090/qam/99654
MathSciNet review:
QAM99654
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Abstract: The dynamic buckling of a long column with small dimple imperfections resting on a nonlinear foundation and subjected to axial step-loading is studied using a formal multi-variable perturbation expansion. Simple asymptotic formulas are obtained for the dynamic buckling load and lateral deflection in terms of the Fourier transform of the imperfection. It is found that the static and dynamic buckling loads are equal.
W. T. Koiter, On the stability of elastic equilibrium (in Dutch), Thesis, Delft, Amsterdam (1945); English translation issued as NASA TTF-10, 1967
B. Budiansky and J. W. Hutchinson, Dynamic buckling of imperfection-sensitive structures, in Proceedings of the eleventh international congress of applied mechanics, ed. H. Görtler, Springer-Verlag, 1966, 636–651
J. W. Hutchinson and B. Budiansky, Dynamic buckling estimates, A.I.A.A. Journal 4, 525–530 (1966)
B. Budiansky, Dynamic buckling of elastic structures: criteria and estimates, in Dynamic stability of structures, ed. G. Herrmann, Pergamon, New York, 1966
J. C. Amazigo and D. Frank, Dynamic buckling of an imperfect column on nonlinear foundation, Quart. Appl. Math. 31, 1–9 (1973)
J. C. Amazigo, B. Budiansky and G. F. Carrier, Asymptotic analysis of the buckling of imperfect columns on nonlinear elastic foundations, Int. J. Solids Struct. 6, 1341–1356 (1970)
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. II, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1989. Partial differential equations; Reprint of the 1962 original; A Wiley-Interscience Publication. MR 1013360
W. T. Koiter, On the stability of elastic equilibrium (in Dutch), Thesis, Delft, Amsterdam (1945); English translation issued as NASA TTF-10, 1967
B. Budiansky and J. W. Hutchinson, Dynamic buckling of imperfection-sensitive structures, in Proceedings of the eleventh international congress of applied mechanics, ed. H. Görtler, Springer-Verlag, 1966, 636–651
J. W. Hutchinson and B. Budiansky, Dynamic buckling estimates, A.I.A.A. Journal 4, 525–530 (1966)
B. Budiansky, Dynamic buckling of elastic structures: criteria and estimates, in Dynamic stability of structures, ed. G. Herrmann, Pergamon, New York, 1966
J. C. Amazigo and D. Frank, Dynamic buckling of an imperfect column on nonlinear foundation, Quart. Appl. Math. 31, 1–9 (1973)
J. C. Amazigo, B. Budiansky and G. F. Carrier, Asymptotic analysis of the buckling of imperfect columns on nonlinear elastic foundations, Int. J. Solids Struct. 6, 1341–1356 (1970)
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. II, Wiley (Interscience), New York, 1962, 486–490
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Article copyright:
© Copyright 1976
American Mathematical Society
