Topology optimization subject to additive manufacturing constraints

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...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:2190-5983
2190-5983
DOI:10.1186/s13362-021-00115-6