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G. Allaire (1)
E. Bonnetier (2)
G. Francfort (3)
F. Jouve (4)
| (1) | Commissariat a l'Energie Atomique DRN/DMT/SERMA, C.E. Saclay 91191 Gif sur Yvette, France Laboratoire d'Analyse Numérique, Université Paris 6 |
| (2) | CMAP |
| (3) | Institut Galilee Universite Paris-Nord 93430 Villetaneuse, France |
| (4) | CMAP |
Abstract : In the context of shape optimization, we seek minimizers of the elastic compliance and of the weight of a solid structure under loading. This problem is known not to be well-posed, and a rela formulation is introduced. Its effect is to allow for microperf composites as admissible designs. In a two-dimensional setting 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 contri is twofold; first, we prove a relaxation theorem, valid in any secondly, we introduce a new numerical algorithm for computing complemented with a penalization technique which permits to rem designs in the final shape. Since it places no assumption on th holes cut within the domain, it can be seen as a topology optim algorithm. Numerical results are presented for various two and dimensional problems.
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