Applied Mathematical Sciences

Imperfect Bifurcation in Structures and Materials

Engineering Use of Group-Theoretic Bifurcation Theory

Authors: Ikeda, Kiyohiro, Murota, Kazuo

  • Exercises at the ends of chapters or sections
  • Solutions to selected exercises
  • Detailed illustrations
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About this Textbook

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)

About the authors

Kiyohiro Ikeda is a Professor in the Department of Civil Engineering, Graduate School of Engineering at Tohoku University. Kazuo Murota is a Professor in the Department of Mathematical Informatics, Graduate School of Information Science and Technology at University of Tokyo.

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)

From the reviews of the second edition:

“The book provides a modern theory of imperfect bifurcation phenomena in physical and engineering problems. … the reviewed book can be useful in developing a modern imperfect bifurcation theory. Additionally, the book can also be considered as a reliable bridge between the mathematical theory and engineering practice.” (Boris V. Loginov, Zentralblatt MATH, Vol. 1204, 2011)


Table of contents (16 chapters)

  • Overview of Book

    Ikeda, Kiyohiro (et al.)

    Pages 1-32

  • Critical Points and Local Behavior

    Ikeda, Kiyohiro (et al.)

    Pages 35-68

  • Imperfection Sensitivity Laws

    Ikeda, Kiyohiro (et al.)

    Pages 69-86

  • Worst Imperfection (I)

    Ikeda, Kiyohiro (et al.)

    Pages 87-106

  • Random Imperfection (I)

    Ikeda, Kiyohiro (et al.)

    Pages 107-124

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-1-4419-7296-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $84.95
price for USA
  • ISBN 978-1-4419-7075-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $84.95
price for USA
  • ISBN 978-1-4614-2665-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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
2010
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science and Business Media, LLC
eBook ISBN
978-1-4419-7296-5
DOI
10.1007/978-1-4419-7296-5
Hardcover ISBN
978-1-4419-7075-6
Softcover ISBN
978-1-4614-2665-3
Series ISSN
0066-5452
Edition Number
2
Number of Pages
XX, 520
Additional Information
2nd edition
Topics