Shape optimization of a layer by layer mechanical constraint for additive manufacturing

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. (C) 2017 Academie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license.