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＜E-Book＞
Imperfect Bifurcation in Structures and Materials : Engineering Use of Group-Theoretic Bifurcation Theory / by Kiyohiro Ikeda, Kazuo Murota
(Applied Mathematical Sciences. ISSN:2196968X ; 149)

Edition	3rd ed. 2019.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2019
Language	English
Size	XXV, 590 p. 239 illus., 33 illus. in color : online resource
Authors	*Ikeda, Kiyohiro author Murota, Kazuo author SpringerLink (Online service)
Subjects	LCSH:System theory LCSH:Control theory LCSH:Control engineering LCSH:Engineering mathematics LCSH:Engineering -- Data processing  All Subject Search LCSH:Dynamical systems LCSH:Mechanics, Applied LCSH:Solids FREE:Systems Theory, Control FREE:Control and Systems Theory FREE:Mathematical and Computational Engineering Applications FREE:Dynamical Systems FREE:Solid Mechanics
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-030-21473-9

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