[Une méthode de lignes de niveaux pour l'optimisation de forme]
Nous proposons une méthode de lignes de niveaux pour l'optimisation de la forme de structures élastiques. Notre approche combine la méthode des lignes de niveaux d'Osher et Sethian et la dérivée classique de formes. Bien que cette méthode ne soit pas spécifiquement conçue pour faire de l'optimisation topologique, elle permet très facilement les changements de topologie de la forme d'une structure pour des fonctions objectifs très générales. Son coût en temps de calcul est modéré puisqu'il s'agit d'une méthode numérique de capture de formes sur un maillage eulérien fixe.
We study a level-set method for numerical shape optimization of elastic structures. Our approach combines the level-set algorithm of Osher and Sethian with the classical shape gradient. Although this method is not specifically designed for topology optimization, it can easily handle topology changes for a very large class of objective functions. Its cost is moderate since the shape is captured on a fixed Eulerian mesh.
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@article{CRMATH_2002__334_12_1125_0,
author = {Allaire, Gr\'egoire and Jouve, Fran\c{c}ois and Toader, Anca-Maria},
title = {A level-set method for shape optimization},
journal = {Comptes Rendus. Math\'ematique},
pages = {1125--1130},
publisher = {Elsevier},
volume = {334},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02412-3},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02412-3/}
}
TY - JOUR AU - Allaire, Grégoire AU - Jouve, François AU - Toader, Anca-Maria TI - A level-set method for shape optimization JO - Comptes Rendus. Mathématique PY - 2002 SP - 1125 EP - 1130 VL - 334 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02412-3/ DO - 10.1016/S1631-073X(02)02412-3 LA - en ID - CRMATH_2002__334_12_1125_0 ER -
%0 Journal Article %A Allaire, Grégoire %A Jouve, François %A Toader, Anca-Maria %T A level-set method for shape optimization %J Comptes Rendus. Mathématique %D 2002 %P 1125-1130 %V 334 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02412-3/ %R 10.1016/S1631-073X(02)02412-3 %G en %F CRMATH_2002__334_12_1125_0
Allaire, Grégoire; Jouve, François; Toader, Anca-Maria. A level-set method for shape optimization. Comptes Rendus. Mathématique, Tome 334 (2002) no. 12, pp. 1125-1130. doi : 10.1016/S1631-073X(02)02412-3. http://www.numdam.org/articles/10.1016/S1631-073X(02)02412-3/
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