Imperfection sensitivity laws

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The strength of structures undergoing bifurcation is affected by imperfections. The mechanism of such a dependence of the strength has been conventionally described by “imperfection sensitivity laws.” We follow the Liapunov–Schmidt–Koiter approach and introduce imperfection sensitivity laws for simple critical points of various kinds that are described in Chap. 2, which is a prerequisite of this chapter. This chapter lays a foundation of Chaps. 4 – 6 and is extended to a system with group symmetry in Chap. 9.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages77-99
Number of pages23
DOIs
Publication statusPublished - 2019 Jan 1

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume149
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Bifurcation equation
  • Critical point
  • Hilltop bifurcation
  • Imperfection
  • Imperfection sensitivity
  • Liapunov–Schmidt reduction
  • Limit point
  • Pitchfork bifurcation
  • Transcritical bifurcation
  • Two-thirds power law

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Ikeda, K., & Murota, K. (2019). Imperfection sensitivity laws. In Applied Mathematical Sciences (Switzerland) (pp. 77-99). (Applied Mathematical Sciences (Switzerland); Vol. 149). Springer. https://doi.org/10.1007/978-3-030-21473-9_3