Generating Topologically OptimizedCellularStructures forAdditiveManufacturing

SteveOwen,JoshRobbins,BrettClark,TomVoth,BradleyParks,TedBlacker

OverviewWeintroduce anew method forgenerating anSTLdefinition ofa lattice structure thatcanbe3Dprinted using standard Additive Manufacturing technologies. Using a topologyoptimization codedeveloped atSandia, anorganic shape designed toaccommodate specificloads and boundary conditions is first meshed using the Sculptapplication. Thehexelements produced areused as thebasis forgenerating alattice structure that is exportedasanSTL file. Following 3Dprinting, the result isa reduced-weight component usingminimal material tomeet structural strength criteria.

Topology OptimizationBased on various load conditions and material properties, anoptimized shape isproduced.

SculptHexMeshingFromthe STLboundaryrepresentation produced from thetopology optimization, Sandia’s Sculptcode is used togenerate anall-hexmesh atauser defined resolution.

LatticeTemplatesAtemplate geometry tobeused ineachhexof themesh is selected. Templates aredefinedfromBoolean operations on analytic cylinders configured tooptimize strength and densitycharacteristics. Templates are required tobesuper-symmetric, where rotations inu, v, orwdirections yield identical results. To reduce memory requirements, analytic surfaces arereduced toaminimal setof triangles foreachconfiguration.

Octahedron Hexahedron Tetrahedron

96Triangles 232Triangles 468Triangles

TemplateMappingThetriangles in theselected template arecopied andmapped into eachhexof the finiteelement mesh generated with Sculpt. The template, defined onaunit cube is mapped toageneral 3Dspace element using the following.

Transfinite interpolation is used tomapagivenSTLtriangle vertexon theunit cubewithcoordinate u,v,w, toa3Dx,y,z coordinate. Edge and facecoordinates canbecomputed asfollows:

With the 3Dcoordinate computed asa linear combination of the three coordinate directions.

Triangles on the facesofthe template areonly mapped to the 3Dhexelement if it lies ontheexterior boundary ofthe model. This allows fora single continuous water-tight volumecomposed ofSTLfacets.

Lattice networks defined on a mesh of a sphere with 32 hexes

1728 Triangles 12,624 Triangles 5072 Triangles

Paper reference:J. Robbins, S.J. Owen, B.W.Clark, T.E.Voth, “An efficient and scalable approach forgenerating topologically optimized cellular structures foradditive manufacturing, AdditiveManufacturing, Available online 21 July2016http://dx.doi.org/10.101 6/ j.addma.2 016.0 6.013

Sandia National Laboratories is a mul ti -program laboratory managed and operated by Sandia Corporation, a whol ly owned s ubsid iary of Loc kheed Martin Corporation, for the U.S. Department o f Energy ’s National Nuc lear Sec uri ty Admin is tra tion under c ontrac t DE-AC04-94AL85000. SAND No. SAND2016-9193 C

3DPrinting

Topologically optimized geometry with coarsecellular structureprinted in316Lstainless steel using a3DSystems ProX 200.CourtesyofDavidSaiz andBradley Jared, Sandia National Laboratories.

Acantilever beammodeled asa lattice structure was usedtovalidate the characteristics of the latticestructure. Sandia’s Sierra/SMcodewas used foranalysis.

ImageofSTLmodel producedfrommapping procedure.Shaded region on inset showsasingle hexelement where aunit cube tetrahedrontemplate has been mapped.

CUBITReview,25th InternationalMeshingRoundtableWashingtonDC,September26,2016

ValidationModeling

ImageofSTLmodel ofahighresolutiontetrahedron lattice structurewith over 26milliontriangles

To computationally validate thestrength of lattice structures, two different finite elementapproximations wereused: (1)acontinuum model composed of3Dcylinders andconformallymeshed with hexahedral elements, and (2)abeamelement approximation, where eachcylinder isapproximated bya single beam element.

(1)3DContinuummodelcomposedofhexesoftwolatticetemplatesofthetetrahedronconfiguration

(2)3Dbeammodelcomposedofbeamsofthesametetrahedronconfiguration.

Graphs on left illustrate thecomputational approximation

differences between using acontinuum vs.abeammodel fordisplacement andstress values.

Those on the right utilize thecontinuum model andmodify the the latticecell size tocompare values forstress anddisplacement.