Imperfection sensitive variation of critical loads at hilltop bifurcation point

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13 Citations (Scopus)

Abstract

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
Volume40
Issue number7
DOIs
Publication statusPublished - 2002 Apr 1

Keywords

  • Hilltop bifurcation
  • Imperfection sensitivity
  • Probabilistic variation

ASJC Scopus subject areas

  • Materials Science(all)
  • Engineering(all)
  • Mechanics of Materials
  • Mechanical Engineering

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