Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory

by Kiyohiro Ikeda, Kazuo Murota

Overview

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

Product Details

ISBN-13:	9783030214753
Publisher:	Springer International Publishing
Publication date:	09/26/2019
Series:	Applied Mathematical Sciences , #149
Edition description:	Third Edition 2019
Pages:	590
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

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.

Table of Contents

1 Introduction to Bifurcation Behavior*2 Critical Point and Local Behavior*3 Imperfection Sensitivity Laws*4 Critical Initial Imperfections (I)*5 Stochasticity of Initial Imperfections (I)*6 Experimentally-observed Bifurcation Diagrams*7 Group-theoretic Bifurcation Theory*8 Bifurcation Behavior of Dn-equivariant Systems*9 Critical Initial Imperfections (II)*10 Stochasticity of Initial Imperfections (II)*11 Description of Bifurcation Behaviors*12 Bifurcation of Cylindrical Sand Specimens*13 Echelon-mode Formation*14 Bifurcation of Steel Specimens*15 Miscellaneous Aspects of Bifurcation Phenomena*References*Index

Editorial 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)

From the Publisher