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Applied Mathematical Sciences

Imperfect Bifurcation in Structures and Materials

Engineering Use of Group-Theoretic Bifurcation Theory

Authors: Ikeda, Kiyohiro, Murota, Kazuo

  • Opens up a variety of methods involving symmetries, and group theory in general, to an entirely new audience
  • For engineers: Introduction to a modern view of bifurcatoin theory by minimizing mathematical formalism
  • For mathematicians: Numerous examples illuminate a static bifurcation theory for infinite dimensional systems and its implications for practical problems
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eBook $74.99
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  • ISBN 978-1-4757-3697-7
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About this Textbook

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.

Reviews

From the reviews:

MATHEMATICAL REVIEWS

"The book is an excellent source of practical applications for mathematicians working in this field. It fulfills its goal of helping close the gap between mathematical and engineering practice in bifurcation analysis, especially of geomaterials such as sand and soil. 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."

"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." (Boris V. Loginov, Zentralblatt MATH, Vol. 1005, 2003)

"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, Issue 2003 f)

"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." (J Petrolito, Applied Mechanics Reviews, Vol. 56 (3), 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." (David Wagg, UK Nonlinear News, November, 2002)


Table of contents (15 chapters)

  • Introduction to Bifurcation Behavior

    Ikeda, Kiyohiro (et al.)

    Pages 1-32

  • Critical Points and Local Behavior

    Ikeda, Kiyohiro (et al.)

    Pages 36-66

  • Imperfection Sensitivity Laws

    Ikeda, Kiyohiro (et al.)

    Pages 67-81

  • Critical Initial Imperfection (I)

    Ikeda, Kiyohiro (et al.)

    Pages 82-100

  • Random Initial Imperfection (I)

    Ikeda, Kiyohiro (et al.)

    Pages 101-121

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4757-3697-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Imperfect Bifurcation in Structures and Materials
Book Subtitle
Engineering Use of Group-Theoretic Bifurcation Theory
Authors
Series Title
Applied Mathematical Sciences
Series Volume
149
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-3697-7
DOI
10.1007/978-1-4757-3697-7
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XVII, 414
Number of Illustrations and Tables
97 b/w illustrations
Topics