<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The purpose of this note is to report on the recent work [<xref ref-type="bibr" rid="j_AMNS.2017.2.00031_ref_002_w2aab3b7b5b1b6b1ab1b7b2Aa">2</xref>, <xref ref-type="bibr" rid="j_AMNS.2017.2.00031_ref_003_w2aab3b7b5b1b6b1ab1b7b3Aa">3</xref>], where new structural optimization strategies are proposed so that the optimized designs are free of <italic>overhang</italic> regions, which jeopardize their constructibility by additive manufacturing technologies. After showing numerical evidence that the intuitive angle-based criteria alone are insufficient to overcome this difficulty, a new constraint functional of the domain is introduced, which aggregates the self-weights of all the intermediate structures appearing in the course of the layer by layer assembly of the total structure. The mathematical analysis of this constraint is outlined and an algorithm is proposed to accelerate the significant computational effort entailed by the implementation of these ideas. Eventually, a numerical validation and several concrete examples are discussed.</p></abstract>

The purpose of this note is to report on the recent work [2, 3], where new structural optimization strategies are proposed so that the optimized designs are free of overhang regions, which jeopardize their constructibility by additive manufacturing technologies. After showing numerical evidence that the intuitive angle-based criteria alone are insufficient to overcome this difficulty, a new constraint functional of the domain is introduced, which aggregates the self-weights of all the intermediate structures appearing in the course of the layer by layer assembly of the total structure. The mathematical analysis of this constraint is outlined and an algorithm is proposed to accelerate the significant computational effort entailed by the implementation of these ideas. Eventually, a numerical validation and several concrete examples are discussed.

Structural optimization under overhang constraints imposed by additive manufacturing processes: an overview of some recent results

Centre de Mathématiques Appliquées, Ecole Polytechnique, CNRS

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The purpose of this note is to report on the recent work [2, 3], where new structural optimization strategies are proposed so that the optimized designs are...

Structural optimization under overhang constraints imposed by additive manufacturing processes: an overview of some recent results

Published Online: Sep 19, 2017

Page range: 385 - 402

Received: Apr 06, 2017

Accepted: Sep 19, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00031

Keywords
Shape optimization, additive manufacturing, level set method, shape derivative

© 2017 Grégoire Allaire, Charles Dapogny, Rafael Estevez, Alexis Faure and Georgios Michailidis, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Structural optimization under overhang constraints imposed by additive manufacturing processes: an overview of some recent results

Published Online: Sep 19, 2017

Page range: 385 - 402

Received: Apr 06, 2017

Accepted: Sep 19, 2017

DOI: https://doi.org/10.21042/AMNS.2017.2.00031

KeywordsShape optimization, additive manufacturing, level set method, shape derivative

© 2017 Grégoire Allaire, Charles Dapogny, Rafael Estevez, Alexis Faure and Georgios Michailidis, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Shape optimization, additive manufacturing, level set method, shape derivative