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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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
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Abstract	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.
AbstractList	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. 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. Abstract 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.
ArticleNumber	19
Author	Ebeling-Rump, Moritz Hömberg, Dietmar Petzold, Thomas Lasarzik, Robert
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Cites_doi	10.1007/s00158-016-1551-x 10.1007/978-3-642-23099-8 10.1137/05062723X 10.1002/num.21742 10.1007/978-3-0348-0133-1_13 10.1007/s00158-011-0688-x 10.1007/978-1-4614-6034-3 10.1007/s11831-012-9075-z 10.1016/j.cma.2010.04.011 10.1051/cocv/2014006 10.1007/s00158-018-1994-3 10.3390/ma11081333 10.1103/PhysRevE.57.4323 10.1142/9789814415309_0005 10.1017/CBO9780511618635 10.1137/S1052623401383558 10.1016/j.jcp.2003.09.032 10.1016/j.cma.2018.02.003 10.1016/S0045-7825(02)00559-5 10.1063/1.1744102 10.1016/0001-6160(79)90196-2 10.1179/1743284714Y.0000000728 10.1016/0167-2789(93)90189-8 10.1016/j.jcp.2009.12.017 10.1007/BF02163264 10.1137/16M1092301 10.1146/annurev.matsci.32.101901.155803 10.1016/j.bushor.2011.11.003 10.1016/j.jcp.2017.09.041 10.1016/j.crma.2017.04.008 10.1016/0045-7825(88)90086-2
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Snippet	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... Abstract 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...
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SubjectTerms	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
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Title	Topology optimization subject to additive manufacturing constraints
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