Overview

The ?rst edition of this book was published in 2002 for an audience of applied mathematicians and engineers. The response to the ?rst edition, represented by sev eral book reviews, has been most heartening. Accordingly, the second edition of this book maintains its major framework and serves as an expanded revision of our previous work. In the second edition, the theoretical backgrounds of group representation the ory are strengthened and made self contained, in response to a request of a book reviewer and students of the authors. Based on these strengthened backgrounds, a theory and a numerical procedure on block diagonalization are presented. Among a number of methodologies, block diagonalization analysis has come to be acknowl edged as a systematic and rigorous procedure for symmetry exploitation for the following two purposes: • Gain better insight into bifurcation behaviors via blockwise singularity detection. • Enhance the computational e?ciency and accuracy of the numerical analysis.

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9781461426653

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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: 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: 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)

Author Information

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.

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