Bifurcation hierarchy of symmetric structures

Ikeda Kiyohiro, Murota Kazuo, Fujii Hiroshi

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)

Abstract

A group-theoretic method for the analysis of bifurcation behavior of regular-polygonal symmetric structures is described. Possible bifurcation paths and points of these structures are categorized in terms of dihedral and cyclic groups, which express the symmetry. In particular, we offer a complete description of those double bifurcation points which occur due to group symmetry. The type, the number, and the stability of bifurcation paths branching at these points are determined by deriving bifurcation equations. The existence of a potential function plays a substantial role for the existence of bifurcation paths. As a result of these, all possible bifurcation process can be known a Priori as a natural consequence of bifurcation hierarchy before actual numerical analysis. An implementation of this method in numerical analysis shows its validity and usability.

Original languageEnglish
Pages (from-to)1551-1573
Number of pages23
JournalInternational Journal of Solids and Structures
Volume27
Issue number12
DOIs
Publication statusPublished - 1991
Externally publishedYes

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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