Imperfect Bifurcation in Structures and Materials

Engineering Use of Group-Theoretic Bifurcation Theory
Third Auflage 2019
ISBN: 978-3-030-21472-2
Verlag: Springer International Publishing

Buch, Englisch, Band 149, 590 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1080 g

Reihe: Applied Mathematical Sciences

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

Zielgruppe

Graduate

Autoren/Hrsg.

Murota, Kazuo

Ikeda, Kiyohiro

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik

Inhaltsverzeichnis

Overview of Book.- Imperfect Behavior at Simple Critical Points.- Critical Points and Local Behavior.- Imperfection Sensitivity Laws.- Worst Imperfection (I).- Random Imperfection (I).- Experimentally Observed Bifurcation Diagrams.- Imperfect Bifurcation of Symmetric Systems.- Group-Theoretic Bifurcation Theory.- Bifurcation Behavior of Dn-Equivariant Systems.- Worst Imperfection (II).- Random Imperfection (II).- Description and Computation of Bifurcation Behaviors.- Efficient Transformation for Block-Diagonalization.- Modeling of Bifurcation Phenomena.- Bifurcation of Cylindrical Sand Specimens.- Echelon-Mode Formation.- Bifurcation of Steel Specimens.- Flower Patterns on Honeycomb Structures.- Answers to Problems.

Über Autor(innen)

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.