Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2002
|
| Schriftenreihe: | Applied Mathematical Sciences
149 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Many physical systems lose or gain stability and pattern through bifurcation behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation behavior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of imperfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as imperfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statistical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection |
| Beschreibung: | 1 Online-Ressource (XVII, 414 p) |
| ISBN: | 9781475736977 9781441929891 |
| DOI: | 10.1007/978-1-4757-3697-7 |
Internformat
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| 245 | 1 | 0 | |a Imperfect Bifurcation in Structures and Materials |b Engineering Use of Group-Theoretic Bifurcation Theory |c by Kiyohiro Ikeda, Kazuo Murota |
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| 490 | 1 | |a Applied Mathematical Sciences |v 149 | |
| 500 | |a Many physical systems lose or gain stability and pattern through bifurcation behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation behavior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of imperfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as imperfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statistical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Ikeda, Kiyohiro |
| author_GND | (DE-588)121432424 |
| author_facet | Ikeda, Kiyohiro |
| author_role | aut |
| author_sort | Ikeda, Kiyohiro |
| author_variant | k i ki |
| building | Verbundindex |
| bvnumber | BV042421512 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.1 |
| dewey-search | 620.1 |
| dewey-sort | 3620.1 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-3697-7 |
| format | Electronic eBook |
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| id | DE-604.BV042421512 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475736977 9781441929891 |
| language | English |
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| physical | 1 Online-Ressource (XVII, 414 p) |
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| publisher | Springer New York |
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| series | Applied Mathematical Sciences |
| series2 | Applied Mathematical Sciences |
| spelling | Ikeda, Kiyohiro Verfasser aut Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory by Kiyohiro Ikeda, Kazuo Murota New York, NY Springer New York 2002 1 Online-Ressource (XVII, 414 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 149 Many physical systems lose or gain stability and pattern through bifurcation behavior. Extensive research of this behavior is carried out in many fields of science and engineering. The study of dynamic bifurcation behavior, for example, has made clear the mechanism of dynamic instability and chaos. The group-theoretic bifurcation theory is an established means to deal with the formation and selection of patterns in association with symmetry-breaking bifurcation. Since all physical systems are "imperfect," in that they inevitably involve some initial imperfections, the study of imperfect bifurcation (bifurcation of imperfect systems) has drawn a keen mathematical interest to yield a series of important results, such as the universal unfolding. In structural mechanics, bifurcation behavior has been studied to model the buckling and failure of structural systems. The sharp reduction of the strength of structural systems by initial imperfections is formulated as imperfection sensitivity laws. A series of statistical studies has been conducted to make clear the dependence of the strength of structures on the statistical variation of initial imperfections. A difficulty in these studies arises from the presence of a large number of initial imperfections. At this state, most of these studies are carried out based on the Monte Carlo simulation for a number of initial imperfections, or, on an imperfection sensitivity law against a single initial imperfection Engineering Differentiable dynamical systems Mechanical engineering Structural Mechanics Dynamical Systems and Ergodic Theory Ingenieurwissenschaften Technisches System (DE-588)4126276-1 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Unvollkommenheit (DE-588)4220265-6 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 s Technisches System (DE-588)4126276-1 s Unvollkommenheit (DE-588)4220265-6 s 1\p DE-604 Technische Mathematik (DE-588)4827059-3 s 2\p DE-604 Murota, Kazuo 1955- Sonstige (DE-588)121432424 oth Applied Mathematical Sciences 149 (DE-604)BV040244599 149 https://doi.org/10.1007/978-1-4757-3697-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ikeda, Kiyohiro Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory Applied Mathematical Sciences Engineering Differentiable dynamical systems Mechanical engineering Structural Mechanics Dynamical Systems and Ergodic Theory Ingenieurwissenschaften Technisches System (DE-588)4126276-1 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Unvollkommenheit (DE-588)4220265-6 gnd Technische Mathematik (DE-588)4827059-3 gnd |
| subject_GND | (DE-588)4126276-1 (DE-588)4078889-1 (DE-588)4220265-6 (DE-588)4827059-3 |
| title | Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory |
| title_auth | Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory |
| title_exact_search | Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory |
| title_full | Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory by Kiyohiro Ikeda, Kazuo Murota |
| title_fullStr | Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory by Kiyohiro Ikeda, Kazuo Murota |
| title_full_unstemmed | Imperfect Bifurcation in Structures and Materials Engineering Use of Group-Theoretic Bifurcation Theory by Kiyohiro Ikeda, Kazuo Murota |
| title_short | Imperfect Bifurcation in Structures and Materials |
| title_sort | imperfect bifurcation in structures and materials engineering use of group theoretic bifurcation theory |
| title_sub | Engineering Use of Group-Theoretic Bifurcation Theory |
| topic | Engineering Differentiable dynamical systems Mechanical engineering Structural Mechanics Dynamical Systems and Ergodic Theory Ingenieurwissenschaften Technisches System (DE-588)4126276-1 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Unvollkommenheit (DE-588)4220265-6 gnd Technische Mathematik (DE-588)4827059-3 gnd |
| topic_facet | Engineering Differentiable dynamical systems Mechanical engineering Structural Mechanics Dynamical Systems and Ergodic Theory Ingenieurwissenschaften Technisches System Verzweigung Mathematik Unvollkommenheit Technische Mathematik |
| url | https://doi.org/10.1007/978-1-4757-3697-7 |
| volume_link | (DE-604)BV040244599 |
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