Topology Optimization for Additive Manufacturing

168 Pages·2016·23.22 MB·English

Topology Optimization for Additive Manufacturing
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Anders Clausen
DCAMM Special Report No. S214
September 2016

P D
H THESIS
TOPOLOGY OPTIMIZATION FOR ADDITIVE MANUFACTURING
PhDthesisbyAndersClausen
Supervisor: ProfessorOleSigmund
Co-supervisors: AssociateProfessorNielsAage
ProfessorHansNørgaardHansen
Titleofthethesis:
Topologyoptimizationforadditivemanufacturing
PhDstudent:
AndersClausen
E-mail: [email protected]
Supervisors:
OleSigmund
E-mail: [email protected]
NielsAage
E-mail: [email protected]
HansNørgaardHansen
E-mail: [email protected]
Address:
DepartmentofMechanicalEngineering,SolidMechanics
TechnicalUniversityofDenmark
NilsKoppelsAllé,Building404,2800Kgs. Lyngby,Denmark
Copyright c 2016AndersClausen
(cid:13)
DCAMMSpecialReportno. S214
ISBN:978-87-7475-466-4
Preface
This thesis is submitted as part of the requirements for obtaining the degree of PhD in
mechanicalengineeringattheTechnicalUniversityofDenmark(DTU).ThePhDproject
was funded by the Villum Foundation (the NextTop project) and DTU Mechanical En-
gineering, andwascarriedoutattheDepartmentofMechanicalEngineering, Sectionof
SolidMechanicsatDTUduringtheperiodfromMarch1st,2013,toSeptember16th,2016,
at a capacity corresponding to a total of three years of full time employment. The main
supervisor was Professor Ole Sigmund. Associate Professor Niels Aage and Professor
HansNørgaardHansenactedasco-supervisors.
A number of people have contributed to this work, either directly or by providing
greatsupport. ForthisIamverygrateful.
First of all, I want to thank my supervisors Ole and Niels for excellent guidance and
for always being very supportive, accessible and responsive, and Hans for sharing his
manufacturingexpertiseandforsupportingandco-fundingtheprojectinthefirstplace.
I want to thank my colleagues in 404 for creating a pleasant working environment,
andtheTopOptgroupandmyofficematesinthePhDroomformanygooddiscussions.
Special thanks to Joe Alexandersen for help and input on a range of topics, and to Erik
Andreassenformuchhelp,input,discussionsandgreatcollaboration.
IwanttothankKlausLoftHøjbjerreforsharinghisexpertisewithinAMandprovid-
ingfeedbackonideas. ThankstoAsbjørnSøndergaard,DanaMaierandOdedAmirfor
aninterestingcollaborationonarchitecturalapplicationsoftopologyoptimization.
PartoftheworkwascarriedoutduringaresearchstayattheLewisGroupatHarvard
SEAS, the Wyss Institute, Cambridge, MA, USA. I want to thank Professor Jennifer A.
Lewis for accepting me as a visiting scholar allowing me this great experience, and the
entiregroupforbeingextremelyhelpfulandforwelcomingmeduringmystay. Special
thanks to Joseph Muth and Jordan Raney for both their scientific and social support.
Also,IwanttothankFengwenWang,mycollaboratorfromDTU,forherhardworkand
impressiveefficiencyingeneratingnewsetsofdesignsasexperimentsprogressed.
Moreover, I want to thank former Head of Department, Professor Emeritus Henrik
Carlsen,andagainmysupervisorOleforagreeingtotheparttimesetupallowingmeto
pursuemystartupambitionsinparalleltothePhD.
Finally, I want to thank my girlfriend Ditte for being extremely supportive and our
sonsAkselandLauritsforguaranteeingthatmymindhasbeeneffectivelyclearedevery
dayafterwork.
Kgs. Lyngby,September16th,2016
AndersClausen
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Dansk resumé (in Danish)
Denneph.d.-afhandlingomhandlerkombinationenaftopologioptimeringogadditivfrem-
stilling(AM,ogsåkendtsom3D-print). Forudenmitegetarbejdeindeholderafhandlin-
genenbrederegennemgangogvurderingafdenøvrigelitteraturindenforfeltet.
Afhandlingen indledes med en klassificering af de forskellige AM-teknologier, en
gennemgang af relevante produktionsmaterialer, disses egenskaber i det additivt frem-
stilledeemne,samtproduktionsbegrænsningermedpotentialefordesignoptimering.
Herefter gennemgås specifikke formuleringer inden for topologioptimering som er
relevante for de væsentligste AM-relaterede produktionsbegrænsninger. Disse begræn-
sningerinddelesiretningsbestemteogikke-retningsbestemtebegrænsninger.
Ikke-retningsbestemtebegrænsningeromhandlerminimum/uniformlængdeskalaog
hulrumsbegrænsning. Detvises,atmodificeredefilterrandbetingelserernødvendigefor
at den såkaldt robuste optimeringsmetode sikrer overholdelse af mindste længdeskala i
nærhedenafdomæneranden.
Den vigtigste retningsbestemte begrænsning er en såkaldt overhængsbegrænsning
(overhangconstraint),hvorprimærttoformuleringerfralitteraturendiskuteres.
Mit eget arbejde har hovedsageligt omhandlet en bedre udnyttelse af de nye pro-
duktionsmuligheder, som AM har bidraget med. Disse behandles under kategorierne
multi-materiale-ogmulti-skala-design, samtinterface-problemersomberørerbeggekat-
egorier. Det vises, hvordan mikrostrukuren for et materiale med foreskrevet, næsten
konstant Poisson’s forhold for store tøjninger kan designes og fremstilles ved hjælp af
direct ink writing. Strukturer opnås for et Poisson’s forhold i hele intervallet [-0.8, 0.8],
alle med uniform detaljestørrelse og sikring af en kontinuert værktøjsbane, således at
strukturerneharpotentialeforskalerbarfremstilling.
Under interface-problemer vises det, hvordan et fleksibelt tomt område kan inklud-
eresietsædvanligttopologioptimeringsproblemvedhjælpafetekstradesignvariabelfelt
og brug af et sensitivitetsfilter. Det vises endvidere hvordan design af coatede struk-
turer kan modelleres som et differentiabelt topologioptimeringsproblem. Dette gøres
ved dels at benytte rumlige gradienter af densitetsvariablen i interpolationsfunktionen
mellem designvaribel og fysiske variable, dels ved at anvende et to-skridtsfilter til at
styre gradientfeltet. Metoden eftervises for både to- og tredimensionelle problemer. Et
specialtilfælde af denne type problemer er porøse skalstrukturer, som ofte anvendes in-
den for 3D-print. Baseret på såvel numeriske som eksperimentelle studier vises det, at
sådannestrukturerharlaverestivhedendfuldtmassivestrukturer,mentilgengældud-
viser markant forbedrede bulingsegenskaber og bedre modstår uforudsete lasttilfælde.
Disse egenskaber opnås implicit med den givne formulering, det vil sige uden eksplicit
definitionafyderligerebegrænsninger.
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Abstract
ThisPhDthesisdealswiththecombinationoftopologyoptimizationandadditiveman-
ufacturing (AM, also known as 3D-printing). In addition to my own works, the thesis
containsabroaderreviewandassessmentoftheliteraturewithinthefield.
The thesis first presents a classification of the various AM technologies, a review of
relevantmanufacturingmaterials,thepropertiesofthesematerialsintheadditivelyman-
ufacturedpart,aswellasmanufacturingconstraintswithapotentialfordesignoptimiza-
tion.
Subsequently, specific topology optimization formulations relevant for the most im-
portant AM-related manufacturing constraints are presented. These constraints are di-
videdintodirectionalandnon-directionalconstraints.
Non-directionalconstraintsincludeminimum/uniformlengthscaleandacavitycon-
straint. Itisshownthatmodifiedfilterboundaryconditionsarerequiredinorderforthe
so-called robust formulation to ensure satisfaction of the minimum feature size in the
vicinityofthedesigndomainboundary.
Themostimportantdirectionalconstraintisaso-calledoverhangconstraint. Inrela-
tiontothis,mainlytwoformulationsfromtheliteraturearediscussed.
My own work has mainly been focused on better exploiting the new opportunities
provided by AM. These are treated under the categories of multi-material applications,
multi-scale approaches, and interface problems which incorporates elements from both
of the preceding categories. It is shown how the material microstructure for a mate-
rial with programmable, nearly constant Poisson’s ratio for large deformations may be
designed and fabricated using direct ink writing. Structures are generated for the full
interval [ 0.8,0.8], all with uniform feature size and a continuous print path, ensuring
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thepotentialforscalablemanufacturing.
Inrelationtointerfaceproblemsitisshownhowaflexiblevoidareamaybeincluded
into a standard minimum compliance problem by employing an additional design vari-
ablefieldandasensitivityfilter. Furthermore,itisshownhowthedesignofcoatedstruc-
tures may be modeled as a differentiable topology optimization problem. This is done
partlybyusingspatialgradientsofthedensityvariableintheinterpolationfunctionbe-
tween the design variable field and physical variables, partly by employing a two-step
filtering scheme in order to control the gradient field. The approach is implemented for
both 2D and 3D problems. A special case of this type of design problem is porous shell
structureswhichareoftenusedwithinAM.Basedonnumericalaswellasexperimental
studiesitisshownthatsuchstructureshavealowerstiffnessthanfullysolidstructures,
however, they possess significantly improved buckling properties and are less sensitive
towardsloadperturbations. Thesepropertiesareinherentlyensured,thatis,withoutthe
explicitdefinitionofadditionalconstraints.
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Publications
Thefollowingjournalpublicationsarepartofthethesis:
[P1] Clausen, A., Wang, F., Jensen, J. S., Sigmund, O., and Lewis, J. A. (2015c). “Topol-
ogy optimized architectures with programmable Poisson’s ratio over large defor-
mations”. AdvancedMaterials27(37),pp.5523–5527
[P2] Clausen, A., Aage, N., andSigmund, O.(2014). “Topologyoptimizationwithflexi-
blevoidarea”. StructuralandMultidisciplinaryOptimization50(6),pp.927–943
[P3] Clausen,A.,Aage,N.,andSigmund,O.(2015b). “Topologyoptimizationofcoated
structuresandmaterialinterfaceproblems”. ComputerMethodsinAppliedMechanics
andEngineering290,pp.524–541
[P4] Clausen, A., Aage, N., and Sigmund, O. (2016). “Exploiting additive manufactur-
ing infill in topology optimization for improved buckling load”. Engineering 2 (2),
pp.250–257
[P5] Clausen, A. and Andreassen, E. “On filter boundary conditions in topology opti-
mization”. Inreview
[P6] Clausen, A., Andreassen, E., and Sigmund, O. “Topology optimization of 3D shell
structureswithporousinfill”. Inpreparation
The following conference proceedings publications were published during the PhD
project(notincludedintheappendix):
[P7] Aage, N., Amir, O., Clausen, A., Hadar, L., Maier, D., and Søndergaard, A.(2015a).
“AdvancedTopologyOptimizationMethodsforConceptualArchitecturalDesign”.
AdvancesinArchitecturalGeometry2014. Springer,pp.159–179
[P8] Clausen, A., Andreassen, E., and Sigmund, O. (2015a). “Topology optimization for
coated structures”. In: Q. Li, G. P. Steven, Z. Zhang, eds. Proceedings of WCSMO-11.
Sydney: ISSMO,pp.25–30
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Contents
Preface i
Publications iv
Contents v
1 Introduction 1
1.1 Projectbackground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Thesisstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Thecontributionsofthiswork . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Additivemanufacturing 5
2.1 Additivevs. conventional,subtractivemanufacturing . . . . . . . . . . . . 5
2.2 AMtechnologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Materialoptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Partqualityandmaterialproperties . . . . . . . . . . . . . . . . . . 9
2.2.3 Supportstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.4 Infill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Newcostdrivers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Combiningtopologyoptimizationandadditivemanufacturing 15
3.1 Briefintroductiontotopologyoptimization . . . . . . . . . . . . . . . . . . 15
3.2 TopologyoptimizationandAM-theidealmarriage . . . . . . . . . . . . . 17
3.3 Datastructuresandtransmission . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Manufacturingconstraints 19
4.1 Non-directionalconstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1.1 Featuresizecontrol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.1.2 Cavityconstraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Directionalconstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 Overhangsupport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.2 Warping—theneedforadequateprocesssimulation. . . . . . . . . 27
4.2.3 Layer-inducedanisotropy . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3 Relevanceofconstraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
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vi Contents
5 Newdesignopportunities 31
5.1 Multi-materialapplications . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.2 Multi-scaleapproachesanddesignwithmicrostructure . . . . . . . . . . . 32
5.2.1 Parameterizedmicrostructure . . . . . . . . . . . . . . . . . . . . . . 33
5.2.2 Architectedmaterials. . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.2.3 Fullyresolvedmulti-scale . . . . . . . . . . . . . . . . . . . . . . . . 39
5.3 Materialinterfaceproblems . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3.1 Flexiblevoidarea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.3.2 Coatingapproach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3.3 Shellstructureswithlocallyoptimizedmicrostructure . . . . . . . 54
5.3.4 Otherapplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6 Concludingremarks 57
References 59
A ListofcommoncommercialAMtechnologies 67
[P1]TopologyoptimizedarchitectureswithprogrammablePoisson’sratiooverlarge
deformations 68
[P2]Topologyoptimizationwithflexiblevoidarea 80
[P3]Topologyoptimizationofcoatedstructuresandmaterialinterfaceproblems 98
[P4]Exploitingadditivemanufacturinginfillintopologyoptimizationforimproved
bucklingload 117
[P5]Onfilterboundaryconditionsintopologyoptimization 127
[P6] Topology optimization of 3D shell structures with porous infill (in prepara-
tion) 137