Imperfect Bifurcation in Structures and Materials [electronic resource] : Engineering Use of Group-Theoretic Bifurcation Theory / by Kiyohiro Ikeda, Kazuo Murota.
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.
Bibliographic references
Includes bibliographical references and index.
Contents
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.
ISBN
3-030-21473-7
Doi
10.1007/978-3-030-21473-9
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