Imperfection sensitive variation of critical loads at hilltop bifurcation point

Kiyohiro Ikeda, Kai Oide, Kenjiro Terada

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


Variation of critical loads due to initial imperfections at the hilltop bifurcation point is described by elastic stability theory. We derive a system of bifurcation equations for a potential system expressing local behavior at this bifurcation point, which is a double critical point occurring as a coincidence of a simple pitchfork bifurcation point and a limit point. The piecewise linear law of imperfection sensitivity of critical loads in Thompson and Schorrock [J. Mech. Phys. Solids 23 (1975) 21] is revised by extending initial imperfections to be considered in the bifurcation equations. Based on this sensitivity law, a procedure to determine the most influential (worst or optimum) initial imperfection is formulated. As the most essential development of this paper, under the assumption that initial imperfections are subject to a multi-variate normal distribution, we derive the probability density function of critical loads that follows a Weibull-like distribution. The validity of theoretical developments is assessed through its application to elastic truss structures.

Original languageEnglish
Pages (from-to)743-772
Number of pages30
JournalInternational Journal of Engineering Science
Issue number7
Publication statusPublished - 2002 Apr


  • Hilltop bifurcation
  • Imperfection sensitivity
  • Probabilistic variation


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