Topology optimization subject to additive manufacturing constraints

• Published in: Journal of mathematics in industry Vol. 11; no. 1; pp. 1 - 19
• Main Authors: Ebeling-Rump, Moritz, Hömberg, Dietmar, Lasarzik, Robert, Petzold, Thomas
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 07.11.2021; Springer Nature B.V; SpringerOpen
• Subjects: Additive manufacturing; Applications of Mathematics; Computing costs; Linear elasticity; Manufacturing; Math. Appl. in Environmental Science; Mathematical and Computational Biology; Mathematical and Computational Engineering; Mathematical Methods in Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Numerical simulations; Optimality conditions; Optimization; Phase field method; Stiffness; Three dimensional printing; Topology optimization; Optimality conditions; Numerical simulations; Linear elasticity; 74P05; Topology optimization; 65M60; Additive manufacturing; Phase field method; 49Q10; 49Q20; 74P10
• ISSN: 2190-5983; 2190-5983
• DOI: 10.1186/s13362-021-00115-6

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.