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Optimization of support structures in additive manufacturing

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DNMW04 - New trends and challenges in the mathematics of optimal design

Support structures are often necessary in additive manufacturing in order to ensure the quality of the final built part. These additional structures are removed at the end of the fabrication process, therefore their size should be reduced to a minimum in order to reduce the material consumption and impression time, while still preserving their requested properties.   The optimization of support structures is formulated as a shape and topology optimization problem. Support structures need to hold all overhanging parts in order to assure their manufacturability, they should be as rigid as possible in order to prevent the deformations of the structure part/support and they should not contain overhanging parts themselves. In processes where melting metal powder is involved, high temperature gradients are present and support structures need to prevent eventual deformations which are a consequence of these thermal stresses.   We show how to enforce the support of overhanging parts and to maximize the rigidity of the supports using linearized elasticity systems. In a second step we show how a functional depending on the gradient of the signed distance function allows us to efficiently prevent overhang regions in the support structures. The optimization is done by computing the corresponding shape derivatives with the Hadamard method. In order to simulate the build process we also consider models in which multiple layers of the part and of the support are taken into account.   The models presented are illustrated with numerical simulations in dimension two and three. The goal is to obtain algorithms which are computationally cheap, while still being physically relevant. The numerical framework used is the level-set method and the numerical results are obtained with the freeware software FreeFem++ and other freely available software like Advect and Mshdist from the ISCD Toolbox.This work was done in the project SOFIA in collaboration with Grégoire Allaire.

This talk is part of the Isaac Newton Institute Seminar Series series.

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