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DDC: 510 × Type: article × search.filters.applied.f.series: Journal of mathematics in industry 11 (2021) × Subject: Optimality conditions ×

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    Topology optimization subject to additive manufacturing constraints
    (Berlin ; Heidelberg : Springer, 2021) Ebeling-Rump, Moritz; Hömberg, Dietmar; Lasarzik, Robert; Petzold, Thomas
    In topology optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg–Landau term. During 3D printing overhangs lead to instabilities. As a remedy an additive manufacturing constraint is added to the cost functional. First order optimality conditions are derived using a formal Lagrangian approach. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the additive manufacturing constraint brings about support structures, which can be fine tuned according to demands and increase stability during the printing process.