Applied Mathematics and Mechanics

, Volume 20, Issue 10, pp 1108–1115 | Cite as

The influence of imperfections upon the critical load of structures

  • Zhu Zhengyou
  • Cong Yuhao


By means of the theory of universal unfolding, the influence of multiimperfections upon the critical load of structure in engineering is analysed in this paper. For the pitchfork problem, a lower bound of increments of the critical loads caused by imperfections of the structures is given. A simple and available numerical method for computing the lower bound is described.

Key words

imperfections critical load pitchfork universal unfolding 

CLC number



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Thomson J M T, Hunt G W.A General Theory of Elastic Stability[M]. New York: John Wiley, 1973.Google Scholar
  2. [2]
    Hunt G W. Imperfection sensitivity of semi-symmetric branching[J].Proc Royal Soc London, Ser A 1977,357(2):193–211.zbMATHGoogle Scholar
  3. [3]
    Koiter W T. On the stability of elastic equilibrium [D]. Ph D dissertation. English translation, Delft Holland: NASA Technical translation, 1967,F10:833.Google Scholar
  4. [4]
    Niwa Y, Watanabe E, Nakagawa N. Catastrophe and imperfection sensitivity of two-degree-of freedom systems[J].Proc Japan Soc Civil Engineers, 1981,307(1):99–111.Google Scholar
  5. [5]
    Kirkpatrick S W, Holmen B S. Effects of initial imperfections on dynamic buckling of shells[J].J Engrg Mech Div, 1988,115(5):1025–1093.Google Scholar
  6. [6]
    Elishakoff I. Stochastic simulation of an initial imperfection data bank for isotropic shell with general inperfections[A]. In: I Elishakoff et al eds.Buckling of Structures[C]. Amsterdam: Elsevier, 1988,195–209.Google Scholar
  7. [7]
    Lindberg H E. Random imperfections for dynamic pulse buckling[J].J Engrg Mech Div, 1988,114(6):1144–1165.CrossRefGoogle Scholar
  8. [8]
    Murota K, Ikada K. Critical initial imperfection of structures[J].Int J Solid Struct, 1990,26(8):865–886.zbMATHCrossRefGoogle Scholar
  9. [9]
    Murota K, Ikada K. Critical imperfection of symmetric structures[J].SIAM Appl Math, 1991,51(5):1222–1254.zbMATHCrossRefGoogle Scholar
  10. [10]
    Golubitsky M, Schaeffer D G.Singularities and Groups in Bifurcation Theory[M]. Vol.1, Berlin Heidelberg, New York, Tokyo: Springer-Verlag, 1984.Google Scholar
  11. [11]
    Arnold V I. Singularity theory [J].London Math Soc Lecture Note Series,51, Berlin Heidelberg, New York, Tokyo: Springer-Verlag, 1981.Google Scholar
  12. [12]
    Chow S N, Hale J K, Mallet-Paret J. Application of generic bifurcations[J].Arch Rat Mech Anal, 1975,59(2):159–188.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Zhu Zhengyou
    • 1
    • 2
  • Cong Yuhao
    • 3
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP R China
  2. 2.Department of MathematicsShanghai UniversityShanghaiP R China
  3. 3.College of Mathematical SciencesShanghai Normal UniversityShanghaiP R China

Personalised recommendations