| 书目名称 | Optimal Design of Multi-Phase Materials |
| 副标题 | With a Cost Function |
| 编辑 | Juan Casado-Díaz |
| 视频video | |
| 概述 | Provides a comprehensive introduction to the mathematical modeling of material design problems.Shows, in a practical example, the interest of introducing a relaxed formulation in an optimization probl |
| 丛书名称 | SpringerBriefs in Mathematics |
| 图书封面 |  |
| 描述 | .This book aims the optimal design of a material (thermic or electrical) obtained as the mixture of a finite number of original materials, not necessarily isotropic. The problem is to place these materials in such a way that the solution of the corresponding state equation minimizes a certain functional that can depend nonlinearly on the gradient of the state function. This is the main novelty in the book...It is well known that this type of problems has no solution in general and therefore that it is needed to work with a relaxed formulation. The main results in the book refer to how to obtain such formulation, the optimality conditions, and the numerical computation of the solutions. In the case of functionals that do not depend on the gradient of the state equation, it is known that a relaxed formulation consists of replacing the original materials with more general materials obtained via homogenization. This includes materials with different properties of the originals but whose behavior can be approximated by microscopic mixtures of them. In the case of a cost functional depending nonlinearly on the gradient, it is also necessary to extend the cost functional to the set of the |
| 出版日期 | Book 2022 |
| 关键词 | Optimal material; homogenized material; elliptic linear equation; H-convergence; optimality conditions; n |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-98191-4 |
| isbn_softcover | 978-3-030-98190-7 |
| isbn_ebook | 978-3-030-98191-4Series ISSN 2191-8198 Series E-ISSN 2191-8201 |
| issn_series | 2191-8198 |
| copyright | The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 |
发表于 2025-3-21 19:30:08
