[Optimisation de forme pour une contrainte mécanique associée aux procédés de fabrication additive]
Nous introduisons dans cet article une nouvelle fonctionnelle dépendant du domaine qui, utilisée comme contrainte dans un problème d'optimisation de forme, impose la constructibilité par les procédés de fabrication additive. Cette fonctionnelle agrège les poids propres de toutes les structures intermédiaires de la forme mises en jeu au cours du processus d'assemblage par strates. Après son analyse mathématique, nous proposons un algorithme pour accélérer significativement les calculs coûteux entraînés par l'implémentation de ces idées. Une validation numérique ainsi qu'un exemple concret sont enfin présentés.
The purpose of this article is to introduce a new functional of the domain, to be used in shape optimization problems as a means to enforce the constructibility of shapes by additive manufacturing processes. This functional aggregates the self-weights of all the intermediate structures of the shape appearing in the course of its layer-by-layer assembly. Its mathematical analysis is performed and an algorithm is proposed to accelerate the significant computational effort entailed by the implementation of these ideas. Eventually, a numerical validation and a concrete example are discussed.
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@article{CRMATH_2017__355_6_699_0,
author = {Allaire, Gr\'egoire and Dapogny, Charles and Faure, Alexis and Michailidis, Georgios},
title = {Shape optimization of a layer by layer mechanical constraint for additive manufacturing},
journal = {Comptes Rendus. Math\'ematique},
pages = {699--717},
publisher = {Elsevier},
volume = {355},
number = {6},
year = {2017},
doi = {10.1016/j.crma.2017.04.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.04.008/}
}
TY - JOUR AU - Allaire, Grégoire AU - Dapogny, Charles AU - Faure, Alexis AU - Michailidis, Georgios TI - Shape optimization of a layer by layer mechanical constraint for additive manufacturing JO - Comptes Rendus. Mathématique PY - 2017 SP - 699 EP - 717 VL - 355 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.04.008/ DO - 10.1016/j.crma.2017.04.008 LA - en ID - CRMATH_2017__355_6_699_0 ER -
%0 Journal Article %A Allaire, Grégoire %A Dapogny, Charles %A Faure, Alexis %A Michailidis, Georgios %T Shape optimization of a layer by layer mechanical constraint for additive manufacturing %J Comptes Rendus. Mathématique %D 2017 %P 699-717 %V 355 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.04.008/ %R 10.1016/j.crma.2017.04.008 %G en %F CRMATH_2017__355_6_699_0
Allaire, Grégoire; Dapogny, Charles; Faure, Alexis; Michailidis, Georgios. Shape optimization of a layer by layer mechanical constraint for additive manufacturing. Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 699-717. doi : 10.1016/j.crma.2017.04.008. http://www.numdam.org/articles/10.1016/j.crma.2017.04.008/
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