cross-sectional structural analysis for 3d printing ...€¦ · cross-sectional structural analysis...
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Cross-sectional Structural Analysis for 3D Printing Optimization
Nobuyuki Umetani Ryan Schmidt
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Shape Design for 3D Printing is Difficult
Beginners cannot design structurally sound shape
3D printing
(1-2 hours)
(1-3 weeks)
[source: DBrager14@Thingiverse]
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Goal: Real-time Weakness Detection During Design
Design with interactive trial & error
3D printing
The user thicken leg This part is too fragile Here we go !
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Related Works
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Related Works: Simulation during Interactive Design
Structural analysis for solid 3D shape had been extremely difficult
[Umetani et al. Siggraph 2012] [Umetani et al. Siggraph 2011]
[Umetani et al. NIME 2010]
[Furuta et al. Eurographics 2010]
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Related Works: Structural Weakness Detection
All previous works are based on Finite Element Method
[Luo et al. Siggraph Asia 2012] [Stava et al. Siggraph 2012] [Zhou et al. Siggraph 2013]
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Drawbacks of Finite Element Method
• Slow • Mesh construction • Linear solver
• FEM requires fair mesh • Without hole & intersection (only less than 25% meshes are closed manifold, 90% are self-intersecting [Gilbert 2013]) • Well-shaped triangle
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Solution: Cross Sectional Structural Analysis
Key idea: bending momentum conservation
Force
Fixed boundary
Stress ? Stress!
Cross-section
Bending moment
Bending moment
Moment arm
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Problem is simplified very much
Force Fixed boundary
Stress Fixed boundary
Fixed boundary
• Location of fixed boundaries We don’t care
• Object’s in-between 3D shape
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How the structure break ?
How a beam bends?
Structure breaks at slender parts
Structure breaks by bending
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History of the Beam Theory
[Galileo 1638]
[source:The Stillman Drake Collection]
[Euler 1750]
[source: wikipedia]
2nd industrial revolution
[ source:wikipedia]
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Euler-Bernoulli Assumption
" Neutral axis
" Neutral axis does not stretch
" Cross sections do not deform
" Cross sections remain orthogonal to neutral axis
Deformation
centroid
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Stress on a Cross-Section
Deformation
Second moment of area
neutral axis
cross-section
Fracture condition
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How we can extend beam theory into 3D shape?
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Extension to 3D Shape
" Topology analysis of cross sections
Fixed boundary
Force
Cutting plane
Force
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Neutral Axis Detection
" Stress computation from arbitrary cross section
neutral axis
centroid
cross section to compute stress
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Comparison with FEM
External Force
FEM
Linear solid material analysis with 2nd–order finite element method
Ours
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Structural Weakness is Both Local and Global Strong Strong
Shorter
Weak Strong
Wider
Smaller
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Weakness of a Cross-Section
Fixed boundary
Minimum breaking force
Bending moment
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Acceleration of Weakness Computation
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Weak Cross Sections Performance
|T| = 17k n-sample=60k time = 0.18sec
|T| = 34k n-sample=200k time = 0.31sec
|T| = 600k n-sample=414k time = 3.8sec
" 13 directions of cross section, 32 slices in each direction
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Live Demo with
http://www.meshmixer.com/
Please download and check it out !
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Application: 3D printing optimization
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strong weak
Printed Objects Have Large An-isotropy
printing direction
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Printing Direction Determines Strength
printing direction
printing direction
max load: 0.22kg
max load: 3.51kg
weak
strong
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Printing Optimization
" Filament should goes through weak cross section
" Printing direction should be perpendicular to weak cross sections
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Results
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Experiment #1
printing direction
max load: 0.21kg
max load: 1.43kg
weak
printing direction
strong
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Experiment #2
max load: 0.51kg
max load: 1.5kg
printing direction
weak
printing direction
strong
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Experiment #2
printing direction
max load: 0.41kg
max load: 3.91kg
weak
printing direction
strong
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Discussion
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Analysis on Skinny Triangle Mesh
" Desirable for industrial design
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Analysis on Holey Mesh
" Skip the cross sections on the hole
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Comparison with a Typical Procedure of FEM
Input mesh
+Mesh simplificaIon +Hole filling +Embedded mesh
Tetrahedral mesh generaIon
Linear system construcIon
Solving linear system
FEM Input mesh
Cross-‐secIon generaIon
Beam equaIon (closed form)
Ours
manual intervention
not robust
slow & memory intensive
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Limitations
" Complex fracture is difficult (e.g. Buckling)
" Round object is difficult
" Some boundary conditions are hard
F F
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Future Work: Direct Stress Analysis on CSG
" Real-time stress analysis for interactive CAD system
[source: IRIT user’s manual]
Cross section
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Cross-sectional Structural Analysis for 3D Printing Optimization
Nobuyuki Umetani Ryan Schmidt