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结构和材料中的不完全分岔:群论分岔理论的工程应用-Imperfect Bifurcation in Structures and Materials: Engineering Use of Group

上传于 2020-03-02 8次下载 3281次围观
标题(title):Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory
作者(author):Kiyohiro Ikeda, Kazuo Murota
出版社(publisher):Springer International Publishing
大小(size):18 MB (18959981 bytes)

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

Table of contents :
Front Matter ....Pages i-xxv
Overview of Book (Kiyohiro Ikeda, Kazuo Murota)....Pages 1-32
Front Matter ....Pages 33-34
Local Behavior Around Simple Critical Points (Kiyohiro Ikeda, Kazuo Murota)....Pages 35-76
Imperfection Sensitivity Laws (Kiyohiro Ikeda, Kazuo Murota)....Pages 77-99
Worst Imperfection (I) (Kiyohiro Ikeda, Kazuo Murota)....Pages 101-120
Random Imperfection (I) (Kiyohiro Ikeda, Kazuo Murota)....Pages 121-140
Experimentally Observed Bifurcation Diagrams (Kiyohiro Ikeda, Kazuo Murota)....Pages 141-164
Front Matter ....Pages 165-166
Group and Group Representation (Kiyohiro Ikeda, Kazuo Murota)....Pages 167-200
Group-Theoretic Bifurcation Theory (Kiyohiro Ikeda, Kazuo Murota)....Pages 201-235
Bifurcation Behavior of Dn-Equivariant Systems (Kiyohiro Ikeda, Kazuo Murota)....Pages 237-295
Worst Imperfection (II) (Kiyohiro Ikeda, Kazuo Murota)....Pages 297-316
Random Imperfection (II) (Kiyohiro Ikeda, Kazuo Murota)....Pages 317-334
Numerical Analysis of Symmetric Systems (Kiyohiro Ikeda, Kazuo Murota)....Pages 335-360
Efficient Transformation for Block-Diagonalization (Kiyohiro Ikeda, Kazuo Murota)....Pages 361-402
Front Matter ....Pages 403-404
Bifurcation Behaviors of Cylindrical Soils (Kiyohiro Ikeda, Kazuo Murota)....Pages 405-433
Bifurcation of Steel Specimens (Kiyohiro Ikeda, Kazuo Murota)....Pages 435-448
Echelon-Mode Formation (Kiyohiro Ikeda, Kazuo Murota)....Pages 449-501
Flower Patterns on Honeycomb Structures (Kiyohiro Ikeda, Kazuo Murota)....Pages 503-546
Back Matter ....Pages 547-590
结构和材料中的不完全分岔:群论分岔理论的工程应用-Imperfect Bifurcation in Structures and Materials: Engineering Use of Group
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