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

    1. Front Matter
      Pages 33-34
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 35-68
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 69-86
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 87-106
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 107-124
    6. Kiyohiro Ikeda, Kazuo Murota
      Pages 125-148
  4. Imperfect Bifurcation of Symmetric Systems

    1. Front Matter
      Pages 149-150
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 151-198
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 199-252
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 253-270
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 271-286
    6. Kiyohiro Ikeda, Kazuo Murota
      Pages 287-322
    7. Kiyohiro Ikeda, Kazuo Murota
      Pages 323-364
  5. Modeling of Bifurcation Phenomena

    1. Front Matter
      Pages 365-366
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 367-394
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 395-450
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 451-470
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 471-500

About this book

Introduction

This book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods - based on asymptotic, probabilistic, and group-theoretic standpoints - are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes).
For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples. Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.

This second edition strengthens the theoretical backgrounds of group representation theory and its application, uses of block-diagonalization in bifurcation analysis, and includes up-to-date topics of the bifurcation analysis of diverse materials from rectangular parallelepiped sand specimens to honeycomb cellular solids.

Reviews of first edition: "The present book gives a wide and deep description of imperfect bifurcation behaviour in engineering problems. … the book offers a number of systematic methods based on contemporary mathematics. … On balance, the reviewed book is very useful as it develops a modern static imperfect bifurcation theory and fills the gap between mathematical theory and engineering practice." (Zentralblatt MATH, 2003) "The current book is a graduate-level text that presents an overview of imperfections and the prediction of the initial post-buckling response of a system. ... Imperfect Bifurcation in Structures and Materials provides an extensive range of material on the role of imperfections in stability theory. It would be suitable for a graduate-level course on the subject or as a reference to research workers in the field." ( Applied Mechanics Reviews, 2003) "This book is a comprehensive treatment of the static bifurcation problems found in (mainly civil/structural) engineering applications.... The text is well written and regularly interspersed with illustrative examples. The mathematical formalism is kept to a minimum and the 194 figures break up the text and make this a highly readable and informative book. ... In summary a comprehensive treatment of the subject which is very well put together and of interest to all researchers working in this area: recommended." (UK Nonlinear News, 2002)

Keywords

Bifurcation phenomena Bifurcation theory Group-theoretic bifurcation theory Static bifurcation theory Transformation bifurcation linear optimization modeling stability

Authors and affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Dept. Civil EngineeringTohoku UniversitySendaiJapan
  2. 2.Graduate School of Information, Science & TechnologyUniversity of TokyoTokyoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7296-5
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7075-6
  • Online ISBN 978-1-4419-7296-5
  • Series Print ISSN 0066-5452
  • About this book