Homogenization of Reticulated Structures:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1999
|
| Schriftenreihe: | Applied Mathematical Sciences
136 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book presents recent works on lattice type structure. Some of the results discussed here have already been published in mathematical journals, but we give here a comprehensive and unified presentation. We have also added some new topics such as those contained in Chapter 4 treating elastic problems for gridworks. The aim of this book is to give continuous simple models for thin reticulated structures (which may have a very complex pattern). This means that we have to treat partial differential equations depending on several small parameters and give the asymptotic behavior with respect to these parameters (which can be the period, the thickness of the material, or the thickness of a plate or of a beam). This book is written from the point of view of the applied mathematician, attention being paid to the mathematical rigor, convergence results, and error estimates. It consists of six chapters and more than a hundred figures. The basic ideas are presented in the first two chapters, while the four last ones study some particular models, using the ideas of Chapters 1 and 2. Chapter 1 is an introduction to homogenization methods in perforated domains. Here the parameter to be taken into consideration is the period. After describing the multiple-scale method (which consists in asymptotic expansions), we focus our attention on the variational method introduced by Tartar, whose main idea is the construction of rapidly oscillating test functions |
| Beschreibung: | 1 Online-Ressource (XX, 346p. 114 illus) |
| ISBN: | 9781461221586 9781461274377 |
| DOI: | 10.1007/978-1-4612-2158-6 |
Internformat
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| 500 | |a This book presents recent works on lattice type structure. Some of the results discussed here have already been published in mathematical journals, but we give here a comprehensive and unified presentation. We have also added some new topics such as those contained in Chapter 4 treating elastic problems for gridworks. The aim of this book is to give continuous simple models for thin reticulated structures (which may have a very complex pattern). This means that we have to treat partial differential equations depending on several small parameters and give the asymptotic behavior with respect to these parameters (which can be the period, the thickness of the material, or the thickness of a plate or of a beam). This book is written from the point of view of the applied mathematician, attention being paid to the mathematical rigor, convergence results, and error estimates. It consists of six chapters and more than a hundred figures. The basic ideas are presented in the first two chapters, while the four last ones study some particular models, using the ideas of Chapters 1 and 2. Chapter 1 is an introduction to homogenization methods in perforated domains. Here the parameter to be taken into consideration is the period. After describing the multiple-scale method (which consists in asymptotic expansions), we focus our attention on the variational method introduced by Tartar, whose main idea is the construction of rapidly oscillating test functions | ||
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Datensatz im Suchindex
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| institution | BVB |
| isbn | 9781461221586 9781461274377 |
| language | English |
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| series | Applied Mathematical Sciences |
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| spelling | Cioranescu, Doina ca. 20./21. Jh. Verfasser (DE-588)1089308787 aut Homogenization of Reticulated Structures by Doina Cioranescu, Jeannine Saint Jean Paulin New York, NY Springer New York 1999 1 Online-Ressource (XX, 346p. 114 illus) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 136 This book presents recent works on lattice type structure. Some of the results discussed here have already been published in mathematical journals, but we give here a comprehensive and unified presentation. We have also added some new topics such as those contained in Chapter 4 treating elastic problems for gridworks. The aim of this book is to give continuous simple models for thin reticulated structures (which may have a very complex pattern). This means that we have to treat partial differential equations depending on several small parameters and give the asymptotic behavior with respect to these parameters (which can be the period, the thickness of the material, or the thickness of a plate or of a beam). This book is written from the point of view of the applied mathematician, attention being paid to the mathematical rigor, convergence results, and error estimates. It consists of six chapters and more than a hundred figures. The basic ideas are presented in the first two chapters, while the four last ones study some particular models, using the ideas of Chapters 1 and 2. Chapter 1 is an introduction to homogenization methods in perforated domains. Here the parameter to be taken into consideration is the period. After describing the multiple-scale method (which consists in asymptotic expansions), we focus our attention on the variational method introduced by Tartar, whose main idea is the construction of rapidly oscillating test functions Mathematics Chemistry / Mathematics Global analysis (Mathematics) Engineering Analysis Computational Intelligence Math. Applications in Chemistry Chemie Ingenieurwissenschaften Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Homogenisierungsmethode (DE-588)4257770-6 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Homogenisierungsmethode (DE-588)4257770-6 s 1\p DE-604 Saint Jean Paulin, Jeannine Sonstige (DE-588)1089278454 oth Applied Mathematical Sciences 136 (DE-604)BV040244599 136 https://doi.org/10.1007/978-1-4612-2158-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cioranescu, Doina ca. 20./21. Jh Homogenization of Reticulated Structures Applied Mathematical Sciences Mathematics Chemistry / Mathematics Global analysis (Mathematics) Engineering Analysis Computational Intelligence Math. Applications in Chemistry Chemie Ingenieurwissenschaften Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Homogenisierungsmethode (DE-588)4257770-6 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4257770-6 |
| title | Homogenization of Reticulated Structures |
| title_auth | Homogenization of Reticulated Structures |
| title_exact_search | Homogenization of Reticulated Structures |
| title_full | Homogenization of Reticulated Structures by Doina Cioranescu, Jeannine Saint Jean Paulin |
| title_fullStr | Homogenization of Reticulated Structures by Doina Cioranescu, Jeannine Saint Jean Paulin |
| title_full_unstemmed | Homogenization of Reticulated Structures by Doina Cioranescu, Jeannine Saint Jean Paulin |
| title_short | Homogenization of Reticulated Structures |
| title_sort | homogenization of reticulated structures |
| topic | Mathematics Chemistry / Mathematics Global analysis (Mathematics) Engineering Analysis Computational Intelligence Math. Applications in Chemistry Chemie Ingenieurwissenschaften Mathematik Partielle Differentialgleichung (DE-588)4044779-0 gnd Homogenisierungsmethode (DE-588)4257770-6 gnd |
| topic_facet | Mathematics Chemistry / Mathematics Global analysis (Mathematics) Engineering Analysis Computational Intelligence Math. Applications in Chemistry Chemie Ingenieurwissenschaften Mathematik Partielle Differentialgleichung Homogenisierungsmethode |
| url | https://doi.org/10.1007/978-1-4612-2158-6 |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT cioranescudoina homogenizationofreticulatedstructures AT saintjeanpaulinjeannine homogenizationofreticulatedstructures |