Imperfect Bifurcation in Structures and Materials

Engineering Use of Group-Theoretic Bifurcation Theory

  • Kiyohiro Ikeda
  • Kazuo Murota

Part of the Applied Mathematical Sciences book series (AMS, volume 149)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Introduction to Bifurcation Behavior

    1. Kiyohiro Ikeda, Kazuo Murota
      Pages 1-32
  3. Imperfect Behavior at Simple Critical Points

    1. Front Matter
      Pages 33-35
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 36-66
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 67-81
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 82-100
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 101-121
    6. Kiyohiro Ikeda, Kazuo Murota
      Pages 122-149
  4. Imperfect Bifurcation of Symmetric Systems

    1. Front Matter
      Pages 151-154
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 155-181
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 182-232
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 233-249
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 250-265
    6. Kiyohiro Ikeda, Kazuo Murota
      Pages 266-275
  5. Modeling of Bifurcation Phenomena

    1. Front Matter
      Pages 277-280
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 281-307
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 308-357
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 358-377
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 378-391
  6. Back Matter
    Pages 392-414

About this book

Introduction

Many physical systems lose or gain stability and pattern through bifurca­ tion behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation be­ havior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of im­ perfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as im­ perfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statis­ tical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection.

Keywords

Bifurcation phenomena Group-theoretic bifurcation theory Static bifurcation theory bifurcation bifurcation theory stability

Authors and affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Department of Civil EngineeringTohoku UniversityAoba SendaiJapan
  2. 2.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3697-7
  • Copyright Information Springer-Verlag New York 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2989-1
  • Online ISBN 978-1-4757-3697-7
  • Series Print ISSN 0066-5452
  • About this book
Industry Sectors
Automotive
Chemical Manufacturing
Electronics
Energy, Utilities & Environment
Aerospace
Oil, Gas & Geosciences
Engineering