| Shape Optimization by the Homogenization Method Softcover Repri Edition Contributor(s): Allaire, Gregoire (Author) |
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ISBN: 1441929428 ISBN-13: 9781441929426 Publisher: Springer OUR PRICE: $104.49 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Technology & Engineering | Civil - General - Mathematics | Applied - Mathematics | Probability & Statistics - General |
| Dewey: 624.1 |
| Series: Applied Mathematical Sciences (Springer) |
| Physical Information: 0.96" H x 6.14" W x 9.21" (1.46 lbs) 458 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 tar- geted 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 equa- tion (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is al- ways 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 literat ure 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]. |