Topology optimization subject to additive manufacturing constraints

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...

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Main Authors:	Moritz Ebeling-Rump, Dietmar Hömberg, Robert Lasarzik, Thomas Petzold
Format:	article
Language:	EN
Published:	SpringerOpen 2021
Subjects:	Additive manufacturing Topology optimization Linear elasticity Phase field method Optimality conditions Numerical simulations Mathematics QA1-939 Industry HD2321-4730.9
Online Access:	https://doaj.org/article/353f35641fa44c95adb93b83d68db430
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spelling	oai:doaj.org-article:353f35641fa44c95adb93b83d68db4302021-11-14T12:15:01ZTopology optimization subject to additive manufacturing constraints10.1186/s13362-021-00115-62190-5983https://doaj.org/article/353f35641fa44c95adb93b83d68db4302021-11-01T00:00:00Zhttps://doi.org/10.1186/s13362-021-00115-6https://doaj.org/toc/2190-5983Abstract 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.Moritz Ebeling-RumpDietmar HömbergRobert LasarzikThomas PetzoldSpringerOpenarticleAdditive manufacturingTopology optimizationLinear elasticityPhase field methodOptimality conditionsNumerical simulationsMathematicsQA1-939IndustryHD2321-4730.9ENJournal of Mathematics in Industry, Vol 11, Iss 1, Pp 1-19 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Additive manufacturing Topology optimization Linear elasticity Phase field method Optimality conditions Numerical simulations Mathematics QA1-939 Industry HD2321-4730.9
spellingShingle	Additive manufacturing Topology optimization Linear elasticity Phase field method Optimality conditions Numerical simulations Mathematics QA1-939 Industry HD2321-4730.9 Moritz Ebeling-Rump Dietmar Hömberg Robert Lasarzik Thomas Petzold Topology optimization subject to additive manufacturing constraints
description	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.
format	article
author	Moritz Ebeling-Rump Dietmar Hömberg Robert Lasarzik Thomas Petzold
author_facet	Moritz Ebeling-Rump Dietmar Hömberg Robert Lasarzik Thomas Petzold
author_sort	Moritz Ebeling-Rump
title	Topology optimization subject to additive manufacturing constraints
title_short	Topology optimization subject to additive manufacturing constraints
title_full	Topology optimization subject to additive manufacturing constraints
title_fullStr	Topology optimization subject to additive manufacturing constraints
title_full_unstemmed	Topology optimization subject to additive manufacturing constraints
title_sort	topology optimization subject to additive manufacturing constraints
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/353f35641fa44c95adb93b83d68db430
work_keys_str_mv	AT moritzebelingrump topologyoptimizationsubjecttoadditivemanufacturingconstraints AT dietmarhomberg topologyoptimizationsubjecttoadditivemanufacturingconstraints AT robertlasarzik topologyoptimizationsubjecttoadditivemanufacturingconstraints AT thomaspetzold topologyoptimizationsubjecttoadditivemanufacturingconstraints
_version_	1718429339475771392

Topology optimization subject to additive manufacturing constraints

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