Shape Optimization by the Homogenization Method:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2002
|
| Schriftenreihe: | Applied Mathematical Sciences
146 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account of homogenization theory and explain how it applies to solving optimal design problems, from both a theoretical and a numerical point of view. The application of greatest practical interest targeted by this book is shape and topology optimization in structural design, where this approach is known as the homogenization method. Shape optimization amounts to finding the optimal shape of a domain that, for example, would be of maximal conductivity or rigidity under some specified loading conditions (possibly with a volume or weight constraint). Such a criterion is embodied by an objective function and is computed through the solution of astate equation that is a partial differential equation (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is always assumed to support Neumann boundary conditions (i. e. , isolating or traction-free conditions). In such a setting, shape optimization has a long history and has been studied by many different methods. There is, therefore, a vast literature in this field, and we refer the reader to the following short list of books, and references therein [39], [42], [130], [135], [149], [203], [220], [225], [237], [245], [258] |
| Beschreibung: | 1 Online-Ressource (XVI, 458 p) |
| ISBN: | 9781468492866 9781441929426 |
| DOI: | 10.1007/978-1-4684-9286-6 |
Internformat
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Datensatz im Suchindex
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| author | Allaire, Grégoire |
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| discipline | Mathematik |
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| spelling | Allaire, Grégoire Verfasser (DE-588)123414849 aut Shape Optimization by the Homogenization Method by Grégoire Allaire New York, NY Springer New York 2002 1 Online-Ressource (XVI, 458 p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 146 The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account of homogenization theory and explain how it applies to solving optimal design problems, from both a theoretical and a numerical point of view. The application of greatest practical interest targeted by this book is shape and topology optimization in structural design, where this approach is known as the homogenization method. Shape optimization amounts to finding the optimal shape of a domain that, for example, would be of maximal conductivity or rigidity under some specified loading conditions (possibly with a volume or weight constraint). Such a criterion is embodied by an objective function and is computed through the solution of astate equation that is a partial differential equation (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is always assumed to support Neumann boundary conditions (i. e. , isolating or traction-free conditions). In such a setting, shape optimization has a long history and has been studied by many different methods. There is, therefore, a vast literature in this field, and we refer the reader to the following short list of books, and references therein [39], [42], [130], [135], [149], [203], [220], [225], [237], [245], [258] Mathematics Global analysis (Mathematics) Mechanics Engineering design Civil engineering Analysis Engineering Design Civil Engineering Mathematik Homogenisierung Mathematik (DE-588)4403079-4 gnd rswk-swf Gestaltoptimierung (DE-588)4329076-0 gnd rswk-swf Gestaltoptimierung (DE-588)4329076-0 s Homogenisierung Mathematik (DE-588)4403079-4 s 1\p DE-604 Applied Mathematical Sciences 146 (DE-604)BV040244599 146 https://doi.org/10.1007/978-1-4684-9286-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Allaire, Grégoire Shape Optimization by the Homogenization Method Applied Mathematical Sciences Mathematics Global analysis (Mathematics) Mechanics Engineering design Civil engineering Analysis Engineering Design Civil Engineering Mathematik Homogenisierung Mathematik (DE-588)4403079-4 gnd Gestaltoptimierung (DE-588)4329076-0 gnd |
| subject_GND | (DE-588)4403079-4 (DE-588)4329076-0 |
| title | Shape Optimization by the Homogenization Method |
| title_auth | Shape Optimization by the Homogenization Method |
| title_exact_search | Shape Optimization by the Homogenization Method |
| title_full | Shape Optimization by the Homogenization Method by Grégoire Allaire |
| title_fullStr | Shape Optimization by the Homogenization Method by Grégoire Allaire |
| title_full_unstemmed | Shape Optimization by the Homogenization Method by Grégoire Allaire |
| title_short | Shape Optimization by the Homogenization Method |
| title_sort | shape optimization by the homogenization method |
| topic | Mathematics Global analysis (Mathematics) Mechanics Engineering design Civil engineering Analysis Engineering Design Civil Engineering Mathematik Homogenisierung Mathematik (DE-588)4403079-4 gnd Gestaltoptimierung (DE-588)4329076-0 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Mechanics Engineering design Civil engineering Analysis Engineering Design Civil Engineering Mathematik Homogenisierung Mathematik Gestaltoptimierung |
| url | https://doi.org/10.1007/978-1-4684-9286-6 |
| volume_link | (DE-604)BV040244599 |
| work_keys_str_mv | AT allairegregoire shapeoptimizationbythehomogenizationmethod |