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)
Applied Mathematical Sciences Volume 149 Editors S.S. Antman J.E. Marsden L. Sirovich
Advisors L. Greengard P. Holmes J. Keener J. Keller R. Laubenbacher B.J. Matkowsky A. Mielke C.S. Peskin K.R. Sreenivasan A. Stevens A. Stuart
For further volumes: http://www.springer.com/series/34
Kiyohiro Ikeda • Kazuo Murota
Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory Second Edition
Dr. Kiyohiro Ikeda Department of Civil Engineering Tohoku University Aramaki-aza-Aoba 980-8579 Sendai Aoba-ku Japan
[email protected]
Dr. Kazuo Murota Department of Mathematical Informatics Graduate School of Information Science & Technology University of Tokyo Hongo 7-3-1 113-8656 Tokyo Bunkyo-ku Japan
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ISSN 0066-5452 ISBN 978-1-4419-7075-6 e-ISBN 978-1-4419-7296-5 DOI 10.1007/978-1-4419-7296-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010935020 Mathematics Subject Classification (2010): 74-X, 74Gxx, 74G60, 58-XX, 58D19, 58E09, 58Kxx, 58K70, 20-xx, 20Cxx, 34-XX, 34Fxx © Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be t