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Introduction – Topology optimisation
- Design requirements
– Boundary conditions – Variables: material placement – Objective: maximum stiffness (minimum compliance) – Constraint: limit amount of material used
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Automated and Accurate Geometry Extraction and Shape Optimisation of - - PowerPoint PPT Presentation
Automated and Accurate Geometry Extraction and Shape Optimisation of - - PowerPoint PPT Presentation
Automated and Accurate Geometry Extraction and Shape Optimisation of 3D Topology Optimisation Results London 15 th of October 2019 Femto Engineering Marco Swierstra www.nafems.org Introduction Topology optimisation Design
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Introduction – Topology optimisation
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Optimised design Topology
- ptimisation
Design requirements Post-processing
jagged boundaries intermediate densities
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Introduction – Post-processing
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Stage 1 Stage 3 Stage 2
Optimised design Shape
- ptimisation
Geometry extraction Topology
- ptimisation
Design requirements
post-processing
- Goals
– Automatic – Accurate and optimised – 3D
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Contents
- Structural design optimisation (2D)
Stage 1. Topology optimisation (TO) Stage 2. Geometry extraction Stage 3. Shape optimisation
- Case studies (3D)
- Performance
- Conclusions
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Geometry extraction
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jagged boundaries intermediate densities image processing smooth crisp
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Level Set Function (LSF)
- Radial Basis Function (RBF):
- Sum RBFs to Level Set
Function (LSF):
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Topology optimised result to LSF
- RBF at every element
- LSF equals TO density
value at every element centre location
- LSF is fully positive
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Solve set of linear equations
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LSF to smooth density field (1)
- Heaviside function
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LSF to smooth density field (2)
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Shape optimisation
- Not an optimised design anymore
- Image interpretation – no mechanics
- Variables: weights 𝑥𝑗 of Radial Basis Functions
- Two tools: structural analysis and sensitivity analysis
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Stage 1 Stage 3 Stage 2
Optimised design Shape
- ptimisation
Geometry extraction Topology
- ptimisation
Design requirements
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Structural analysis
- Same mesh as topology optimisation
- p-FEM + quadtree integration = Finite Cell Method
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Sensitivity analysis
- Gradient-based optimisation
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density at integration points
- bjective
weights RBFs are design variables Level Set Function at integration points
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Shape optimisation
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Summary three-staged procedure
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Stage 1 Stage 3 Stage 2
Optimised design Shape
- ptimisation
Geometry extraction Topology
- ptimisation
Design requirements
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Case studies (1)
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Case studies (2)
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Performance – computation time (1)
- Post-processing takes more time on average
- Prototype Python implementation
- Similar quality using TO alone is less efficient
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Case study Grid size Stage 1 Stage 2 Stage 3 Stage 2 + 3 2D MBB 64 x 32 20 1 22 53% 2D Cantilever 180 x 120 371 6 167 32% 3D MBB 64 x 10 x 32 1,203 53 3,108 72% 3D Cantilever 30 x 30 x 30 1,454 80 2,369 63% Computation times (s) for the case studies.
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Performance computation time (2)
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3-staged process took 23 seconds 20 extra TO iterations took 25 seconds 20 extra TO iterations took 262 seconds
64 x 32 grid 128 x 64 grid 256 x 128 grid 64 x 32 RBFs
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Performance – accuracy
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Conclusions
- Automatically smooth and optimised designs
- Almost no intermediate densities
- Computation times are high (or low?)
- No remeshing, still sufficient analysis accuracy
- Easily extendable to other types of optimisation problems
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Thank you very much!
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