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Imperfect Bifurcation in Structures and Materials

Engineering Use of Group-Theoretic Bifurcation Theory

  • Kiyohiro Ikeda
  • Kazuo Murota
Textbook

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

Table of contents

  1. Front Matter
    Pages i-xxv
  2. Kiyohiro Ikeda, Kazuo Murota
    Pages 1-32
  3. Part I

    1. Front Matter
      Pages 33-34
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 35-76
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 77-99
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 101-120
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 121-140
    6. Kiyohiro Ikeda, Kazuo Murota
      Pages 141-164
  4. Part II

    1. Front Matter
      Pages 165-166
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 167-200
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 201-235
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 237-295
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 297-316
    6. Kiyohiro Ikeda, Kazuo Murota
      Pages 317-334
    7. Kiyohiro Ikeda, Kazuo Murota
      Pages 335-360
    8. Kiyohiro Ikeda, Kazuo Murota
      Pages 361-402
  5. Part III

    1. Front Matter
      Pages 403-404
    2. Kiyohiro Ikeda, Kazuo Murota
      Pages 405-433
    3. Kiyohiro Ikeda, Kazuo Murota
      Pages 435-448
    4. Kiyohiro Ikeda, Kazuo Murota
      Pages 449-501
    5. Kiyohiro Ikeda, Kazuo Murota
      Pages 503-546
  6. Back Matter
    Pages 547-590

About this book

Introduction

This book provides a modern static imperfect bifurcation theory applicable to bifurcation phenomena of physical and engineering problems and fills the gap between the mathematical theory and engineering practice.

Systematic methods based on asymptotic, probabilistic, and group theoretic standpoints are used to examine experimental and computational data from numerous examples, such as soil, sand, kaolin, honeycomb, and domes. For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its applications for practical problems, is illuminated by numerous examples. Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory.

This third edition strengthens group representation and group-theoretic bifurcation theory. Several large scale applications have been included in association with the progress of computational powers. Problems and answers have been provided.

 Review of First Edition:

"The book is unique in considering the experimental identification of material-dependent bifurcations in structures such as sand, Kaolin (clay), soil and concrete shells. … These are studied statistically. … The book is an excellent source of practical applications for mathematicians working in this field. … A short set of exercises at the end of each chapter makes the book more useful as a text. The book is well organized and quite readable for non-specialists."

 Henry W. Haslach, Jr., Mathematical Reviews, 2003

Keywords

Bifurcation phenomena Bifurcation theory Group-theoretic bifurcation theory Static bifurcation theory Transformation bifurcation linear optimization modeling stability pattern selection probability initial imperfections

Authors and affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Department of Civil EngineeringTohoku UniversitySendaiJapan
  2. 2.Department of Economics and Business AdministrationTokyo Metropolitan UniversityHachiojiJapan

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