Imperfect Bifurcation in Structures and Materials (eBook)

Engineering Use of Group-Theoretic Bifurcation Theory

Kiyohiro Ikeda, Kazuo Murota (Autoren)

eBook Download: PDF

2010 | 2. Auflage
537 Seiten
Springer New York (Verlag)
978-1-4419-7296-5 (ISBN)

Infos

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).

Engineers may find this book, with its minimized mathematical formalism, to be a useful introduction to modern bifurcation theory. For mathematicians, static bifurcation theory for finite-dimensional systems, as well as its implications for practical problems, is illuminated by the numerous examples.

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.

From the 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 [...]. A short set of exercises at the end of each chapter makes the book more useful as a text.' Mathematical Reviews

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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.

Produkt-Details

• Erscheint lt. Verlag: 5.9.2010
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4419-7296-X / 144197296X
• ISBN-13: 978-1-4419-7296-5 / 9781441972965