Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Buckling under axial compression of long cylindrical shells with random axisymmetric imperfections

Author: John C. Amazigo
Journal: Quart. Appl. Math. 26 (1969), 537-566
DOI: https://doi.org/10.1090/qam/99838
MathSciNet review: QAM99838
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: The buckling of long cylinders with homogeneous random axisymmetric geometric imperfections under uniform axial compression is studied by means of a modified truncated hierarchy technique. It is found that the buckling load of the cylinder depends only on the spectral density of the random imperfections. In particular, for small values of the standard deviation of the axisymmetric imperfection the buckling load depends only on the value of the spectral density at a specific wave number.

References [Enhancements On Off] (What's this?)

  • [1] V. V. Bolotin, Statistical methods in the nonlinear theory of elastic shells, NASA TT F-85, 1962
  • [2] W. B. Fraser, Buckling of a structure with random imperfections, Ph.D. Thesis, Harvard University, 1965
  • [3] Joseph B. Keller, Stochastic equations and wave propagation in random media, Proc. Sympos. Appl. Math., Vol. XVI, Amer. Math. Soc., Providence, R.I., 1964, pp. 145–170. MR 0178638
  • [4] R. C. Bourret, Stochastically perturbed fields, with applications to wave propagation in random media, Nuovo Cimento (10) 26 (1962), 1–31 (English, with Italian summary). MR 0144735
  • [5] J. M. Richardson, The application of truncated hierarchy techniques in the solution of a stochastic linear differential equation, Proc. Sympos. Appl. Math., Vol. XVI, Amer. Math. Soc., Providence, R.I., 1964, pp. 290–302. MR 0193684
  • [6] C. W. Haines, Hierarchy methods for random vibrations of elastic strings and beams, J. Eng. Math. 1, 293-305 (1967)
  • [7] Julius S. Bendat, Principles and applications of random noise theory, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1958. MR 0105753
  • [8] David Middleton, An introduction to statistical communication theory, International Series in Pure and Applied Physics, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1960. MR 0118561
  • [9] W. T. Koiter, The effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression, Kon. Nederl. Akad. Wetensch., Amsterdam, Serie3 B, 66 (1963), No. 5
  • [10] B. O. Almroth, Influence of imperfections and edge restraint on the buckling of axially compressed cylinders, Lockheed Missiles and Space Company, 6-75-65-57
  • [11] W. T. Koiter, Elastic stability and post-buckling behavior, Nonlinear Problems (Proc. Sympos., Madison, Wis., 1962) Univ. of Wisconsin Press, Madison, Wis., 1962, pp. 257–275. MR 0148292

Additional Information

DOI: https://doi.org/10.1090/qam/99838
Article copyright: © Copyright 1969 American Mathematical Society

Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website