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2001 FE-Design GmbH www.fe-design.de
The TOSCA-Topology Optimisation -Mesh Adaption and Manufacturing
Restrictions
© FE-Design GmbH 2002
Peter Allinger
2001 FE-Design GmbH www.fe-design.de
The TOSCA-Topology Optimisation -Mesh Adaption and Manufacturing
Restrictions
• Who is FE-Design?
• What is TOSCA?
• Manufacturing restrictions for topology
optimisation
• Mesh adaption for topology optimisation
• Conclusions
2001 FE-Design GmbH www.fe-design.de
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• FE structural analyses
• Structural optimisation
• CDF calculations• Computation• Consulting• Training
Engineering Service
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Research & Development
Software Development• TOSCA• MSC.Construct...• ASPNational & International research projects• HiPOP• iViP• Elano
Software Products
• TOSCA.topology, TOSCA.shapeTOSCA.smooth
• OEM-Products:MSC.ConstructCATopo visualNastran Desktop FEA
• Support
2001 FE-Design GmbH www.fe-design.de
Automotive industry
Aerospace industry
Universities &Research
Supply industry
ETH ZürichETH Zürich
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2001 FE-Design GmbH www.fe-design.de
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• Structural optimisation system• Stable and fast algorithms• Interfaces to MSC.NASTRAN, ABAQUS, ANSYS, IDEAS• UNIX and NT• Optimisation of nearly every FE-model• Unlimited number of load cases• Efficient handling of very large models (> 4,5 Mio. DOF)
Fields of application
• Domestic appliances • Machine tools • Automotive- and aerospace-industry• …
Basic Technology of
2001 FE-Design GmbH www.fe-design.de
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Topology Optimization with
Optimal design from a given design space
• Shorter development time• Economic use of material
Shape Optimization with
Load homogenization by modification of the component‘s surface• Increase of durability• Reduction of stress concentration
By courtesy of AUDI AG
2001 FE-Design GmbH www.fe-design.de
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Optional: Shape Optimization
Design Space Topology Optimization
Smoothing, Data Reduction, Remeshing,
Remodelling
Transfer to CAD(STL, IGES)
Analysis ModelOptimization and
V�P�R�R�W�K
2001 FE-Design GmbH www.fe-design.de
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„The topology and the shape of a component has to be determined in such a way, that its mechanical behaviour is an optimum for the
specified design criteria. Only the available boundary conditions, the forces and the design area for the component has to be defined. “
[Maute 98]
Design area Iteration loop Design proposal
2001 FE-Design GmbH www.fe-design.de
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Motivation• Bending and torsion load
lead to a hollow body� Results of the topology
optimisation cannot be transferred into real components because of the costs for producing.
� The manual transfer of the results into a castablecomponent needs a lot of time and of leads to sub-optimal components.
2001 FE-Design GmbH www.fe-design.de
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• Pull direction / removable components• No undercuts or hollow structures• Removal angle• No conglomeration of material (problems during cooling
process)• No thin structures or supports• ...
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2001 FE-Design GmbH www.fe-design.de
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2001 FE-Design GmbH www.fe-design.de
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F F F F
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4961 Nodes; 4000 Hexaeder elements
2001 FE-Design GmbH www.fe-design.de
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Side view
Front view
Pull direction sideways
Pull direction backwards
Side view
Front view
2001 FE-Design GmbH www.fe-design.de
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93854 Nodes; 495158 Tetraeder-elements
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By courtesy of AUDI AG
2001 FE-Design GmbH www.fe-design.de
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Advantage:+ more detailed solution + better material distribution
Disadvantage:- increase of design variables- dramatic increase of computational time
Adaptive mesh refinement during topology optimization
-> refinement of result without big influences of disadvantages
Coarse mesh
Fine mesh
2001 FE-Design GmbH www.fe-design.de
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Selective refinement Necessary areas: refined mesh
Unnecessary areas: mesh of start model
When should the refinement be performed? start criteria
Where should the refinement take place? location criteria
How should the refinement been done? refinement algorithms
2001 FE-Design GmbH www.fe-design.de
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2) Coupling of nodal displacement
1) refinement with templates
)(2
1213
iii XXX +∗=
displaced mesh
initial mesh
3
2
1
Multi Point Constraint (MPC)
2001 FE-Design GmbH www.fe-design.de
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2b2a10 43
How to ensure the mesh consistency ?
Templates for QUAD elements
Element to be refined
= Nodes marked for refinement
Select template No. 2aand rotate clockwise 90°
Select template No. 4
2D and 3D refinement is possible
2001 FE-Design GmbH www.fe-design.de
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• Permanent mesh refinement / coarsening
• Error estimator as indicator for the mesh refinement area
• Refinement in areas of high error indicator values
• Coarsening in areas of high error indicator values
• Definition of a limit volume of elements to be refined
• Error criteria enables the system to refine in more than one level (multi level refinement)
2001 FE-Design GmbH www.fe-design.de
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2001 FE-Design GmbH www.fe-design.de
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6 min 15 sec
9 min 48 sec
17 min 50 sec
26 min 1 sec
time
24,0 %
37,6 %
68,5 %
100%
percentage
Without refinement
Refinement with displacement conditions (each element border is divided into two new borders)
Template refinement(each element border is divided intothree new borders)
complete refinement
model
PC 866 MHz with 512 MB RAM
2001 FE-Design GmbH www.fe-design.de
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2001 FE-Design GmbH www.fe-design.de
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Coarse mesh
CPU-Time=9,6%
DOF= 22 000
Fine mesh
CPU-Time=100 %
DOF= 151 000
Adaptive mesh refinement
CPU-Time=60,9%
DOF=100 000
2001 FE-Design GmbH www.fe-design.de
Maximize stiffness
obj. Function:
210000Youngs modul [N/mm2 ]
0,3Poisson ratio
Material: Steel
Mesh type: Pave
9252tetraeder elements(3D)
2924nodes
944shell elements (2D)
Optimization task:
55%constraint volume:
mixed mesh: 2D-3D elementsLocation criteria: errror indicator distribution
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2001 FE-Design GmbH www.fe-design.de
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Without refinement
adaptive mesh refinement
Complete refinement
Results of the tetraeder mesh are smoothed
2001 FE-Design GmbH www.fe-design.de
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• Manufacturing restrictions– Difficult to transfer solutions of non restricted optimization– Manufacturing process has to be included in the early stages of
the product development
• Adaptive refinement during topology optimization – Error indicator distribution is used as location criteria– Permanent mesh refinement and coarsening during iteration
process– Results of the adaptive topology optimization are comparable to
the optimization with the fine mesh
• Optimization system TOSCA– integrated solution for structural optimization of real-world
problems– wide acceptance in industry