[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.
Accepté le :
Publié le :
@article{CRMATH_2017__355_6_699_0,
author = {Gr\'egoire Allaire and Charles Dapogny and Alexis Faure and Georgios Michailidis},
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},
}
TY - JOUR AU - Grégoire Allaire AU - Charles Dapogny AU - Alexis Faure AU - Georgios Michailidis 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 DO - 10.1016/j.crma.2017.04.008 LA - en ID - CRMATH_2017__355_6_699_0 ER -
%0 Journal Article %A Grégoire Allaire %A Charles Dapogny %A Alexis Faure %A Georgios Michailidis %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 %R 10.1016/j.crma.2017.04.008 %G en %F CRMATH_2017__355_6_699_0
Grégoire Allaire; Charles Dapogny; Alexis Faure; Georgios Michailidis. Shape optimization of a layer by layer mechanical constraint for additive manufacturing. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 699-717. doi : 10.1016/j.crma.2017.04.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.008/
[1] Conception optimale de structures, Math. Appl., vol. 58, Springer-Verlag, Berlin, 2007
[2] G. Allaire, L. Jakabcin, Taking into account thermal residual stresses in topology optimization of structures built by additive manufacturing (in preparation).
[3] Structural optimization using shape sensitivity analysis and a level-set method, J. Comput. Phys., Volume 194 (2004), pp. 363-393
[4] G. Allaire, C. Dapogny, R. Estevez, A. Faure, G. Michailidis, Structural optimization under overhang constraints imposed by additive manufacturing technologies (in preparation).
[5] Design optimization of supports for overhanging structures in aluminum and titanium alloys by selective laser melting, Mater. Des., Volume 64 (2014), pp. 203-213
[6] Modeling and Simulation in Scilab/Scicos, Springer, New York, 2006
[7] Topology Optimization for Additive Manufacturing, Technical University of Denmark, 2016 (Ph.D. Thesis)
[8] Bridging the gap: automated steady scaffoldings for 3D printing, ACM Trans. Graph., Volume 33 (2014) no. 4, pp. 1-10
[9] Introducing the sequential linear programming level-set method for topology optimization, Struct. Multidiscip. Optim., Volume 51 (2015), pp. 631-643
[10] Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, FL, USA, 1992
[11] Topology optimization considering overhang constraints: eliminating sacrificial support material in additive manufacturing through design, Struct. Multidiscip. Optim. (2016) | DOI
[12] Additive Manufacturing Technology: Rapid Prototyping to Direct Digital Manufacturing, Springer Science Business Media, Inc., 2010
[13] Elliptic Problems in Nonsmooth Domains, Pitman Publishing, Inc., Boston, MA, USA, 1985
[14] New development in FreeFem++, J. Numer. Math., Volume 20 (2012) no. 3–4, pp. 251-265
[15] Variation et optimisation de formes, une analyse géométrique, Math. Appl., vol. 48, Springer, Berlin, 2005
[16] Fundamentals of Differential Geometry, Springer, 1991
[17] Topology optimization of 3D self-supporting structures for additive manufacturing, Addit. Manuf., Volume 12 (2016), pp. 60-70
[18] Support structure constrained topology optimization for additive manufacturing, Comput. Aided Des. (2016) | DOI
[19] A method to eliminate anchors/supports from directly laser melted metal powder bed processes, Sheffield, UK (2011), pp. 55-64
[20] Sur le contrôle par un domaine géométrique, Laboratoire d'analyse numérique, Paris, 1976 (Technical report RR-76015)
[21] Topological Derivatives in Shape Optimization, Springer, Heidelberg, Germany, 2012
[22] Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York, 1984
[23] A Semi Derivation Lemma on BV Functions, ArXiv Mathematics, 2008 (Technical report)
[24] Introduction to Shape Optimization: Shape Sensitivity Analysis, Springer Ser. Comput. Math., vol. 10, Springer, Berlin, 1992
[25] Stereolithography Interface Specification, July 1988
[26] Hamiltonian Approach to Geodesic Image Matching, ArXiv Mathematics, 2008 (Technical report)
Cité par Sources :
Commentaires - Politique