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Shape optimization by the homogenization method

yhhuang 添加于 2010-3-8 07:54 | 1554 次阅读 | 0 个评论

作者
Allaire G&#x000E9, goire, Bonnetier E, Francfort G, Jouve F
摘要
Summary. In the context of shape optimization, we seek minimizers of the sum of the elastic compliance and of the weight of a solid structure under specified loading. This problem is known not to be well-posed, and a relaxed formulation is introduced. Its effect is to allow for microperforated composites as admissible designs. In a two-dimensional setting the relaxed formulation was obtained in [6] with the help of the theory of homogenization and optimal bounds for composite materials. We generalize the result to the three dimensional case. Our contribution is twofold; first, we prove a relaxation theorem, valid in any dimensions; secondly, we introduce a new numerical algorithm for computing optimal designs, complemented with a penalization technique which permits to remove composite designs in the final shape. Since it places no assumption on the number of holes cut within the domain, it can be seen as a topology optimization algorithm. Numerical results are presented for various two and three dimensional problems.
详细资料
- 文献种类:期刊
- 期刊名称: Numerische Mathematik
- 期刊缩写: Numerische Mathematik
- 期卷页: 1997年第76卷第1期 27-68页
- ISBN: 0029-599X
标签

homogenization shape optimization
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