High-fidelity Isosurface Extraction of Topology Optimized ... · Sandia National Laboratories is a...

High-fidelity Isosurface Extraction of Topology Optimized Shapes for Additive Manufacturing Fig 1: Marching Cubes generates triangles at ea ch cube/hex using the scalar field at nodes. Fifteen unique cases convert a hex mesh into a coarse triangulation that may contain high- and low-frequency noise. 1. Extract Coarse Isosurface Goal Workflow W. Roshan Quadros 1 ,Salvatore Elder 2 , Josh Robbins 1 ,Brett Clark 1 1 Sandia National Laboratories, PO Box 5800, MS 0897, Albuquerque, NM 87185, USA. 2 School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA. Topology Optimization Additive Manufacturing 2. Refinement Fig 2: N-level refinement gives desired level of high- fidelity with 4 N triangles. O(4 N n) for N=2, O(16n) N=0 N=1 N=2 N=3 0 1 2 3 4 5 6 0 100000 200000 300000 400000 Time (Sec) Number of Triangles Isosurface Extraction Extract high-fidelity smooth isosurfaces from implicit data of topology optimized shapes for additive manufacturing 4. Projection Fig 4: Steepest decent is used to project newly inserted nodes on to isosurface using trilinear shape function 3. Stitching Fig 3: Stitch optimized (pink) and fixed (yellow) blocks

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Transcript of High-fidelity Isosurface Extraction of Topology Optimized ... · Sandia National Laboratories is a...

Page 1: High-fidelity Isosurface Extraction of Topology Optimized ... · Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned

High-fidelity Isosurface Extraction ofTopologyOptimizedShapes forAdditiveManufacturing

Fig 1: Marching Cubes generates triangles at eachcube/hex using the sca lar field at nodes. Fifteen uniquecases convert a hex mesh into a coarse triangulation thatmay contain high- and low-frequency noise.

1.ExtractCoarseIsosurface

Goal

Workflow

W.RoshanQuadros1,SalvatoreElder2,JoshRobbins1,BrettClark11SandiaNationalLaboratories,POBox5800,MS0897,Albuquerque,NM87185,USA.2SchoolofAppliedandEngineeringPhysics,CornellUniversity,Ithaca,NY14853,USA.

TopologyOptimization

AdditiveManufacturing

2.Refinement

Fig2:N-levelrefinement givesdesired levelofhigh-fidelity with4N triangles.O(4Nn)forN=2, O(16n)

N=0 N=1 N=2 N=3

0 100000 200000 300000 400000

Time(Sec)

NumberofTriangles

IsosurfaceExtraction

Extract high-fidelity smooth isosurfaces from implicit data of topology optimized shapes for additive manufacturing

4.Projection

Fig 4: Steepest decent is used toproject newly inserted nodes onto isosurface using trilinearshape function

3.Stitching

Fig3:Stitch optimized (pink)andfixed(yellow)blocks

Page 2: High-fidelity Isosurface Extraction of Topology Optimized ... · Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned

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. 2011-XXXXP

6.Visualization

Results

ExplicitData:STLfile

6.VisualizeIsosurface

5.Smoothing

Thermal StructuralThermal+Structural

Marching Cubes

1-level refinement

2-level refinement 2-level refinement &curvature flattening

M (V, E, T): Surface meshf : V→ℝ3

f(Vi)n+1 = f(Vi)n + λΔf(Vi)n

∇2f= 0