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Topology Optimization with Contact Constraints Mikael Thellner, Erik Sunnanbo Scania European HTC 2010 NAC/Mikael Thellner
Topology Optimization with ContactConstraints
Mikael Thellner, Erik Sunnanbo
Scania
European HTC 2010
NAC/Mikael Thellner
Outline
Scania
Introduction
Contact
Topology optimization
Topology optimization with contact constraints
Conclusions
NAC/Mikael Thellner
Provider of transport solutions
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NAC/Mikael Thellner
Modular system
NAC/Mikael Thellner
Premium products and services
NAC/Mikael Thellner
The world of Scania
NAC/Mikael Thellner
Master Thesis Project
How does the contact algorithm in OptiStruct work?
How hard is it to model contact in HyperMesh?
How much higher is the computational cost for using contact?
NAC/Mikael Thellner
Approach
Solve a simple contact problem.
Solve a 2D topology optimization problem with contactconstraints.
Solve a 3D topology optimization problem of a real life structure.
NAC/Mikael Thellner
Contact in OptiStruct
Elements:
node-to-node
node-to-surface
Type of contact:
Slide
Stick
Freeze
Penalty formulation
NAC/Mikael Thellner
Contact in OptiStruct
Elements:
node-to-node
node-to-surface
Type of contact:
Slide
Stick
Freeze
Penalty formulation
NAC/Mikael Thellner
Contact in OptiStruct
Elements:
node-to-node
node-to-surface
Type of contact:
Slide
Stick
Freeze
Penalty formulation
NAC/Mikael Thellner
Simple example - two cylinders in contact
F
R
R
F
NAC/Mikael Thellner
Model
Using symmetry
NAC/Mikael Thellner
Results
Analytical solution compared with OptiStruct.
NAC/Mikael Thellner
Topology optimization
t
Ω
Ω
s
Objective: Determine the stiffest design given a limited amount ofmaterial.
Question: Given a limited design domain Ω and limited amount ofmaterial - where should we put material and where should it bevoid?
NAC/Mikael Thellner
Topology optimization
Parameterization: The design variable ρi represents the densityin each finite element i.
Problem formulation:
maxρ
stiffness
s.t.
∑
i ρi ≤ V0 < ρi ≤ 1Ku = F
where ρ = 1 means material and ρ = 0 means void.
NAC/Mikael Thellner
Topology optimization
Parameterization: The design variable ρi represents the densityin each finite element i.
Problem formulation:
maxρ
stiffness
s.t.
∑
i ρi ≤ V0 < ρi ≤ 1Ku = F
where ρ = 1 means material and ρ = 0 means void.
NAC/Mikael Thellner
Topology optimization in practice
where green represent material and white represent void.
NAC/Mikael Thellner
Topology optimization in practice
where green represent material and white represent void.
NAC/Mikael Thellner
Topology optimization with contact constraints
Problem formulation:
maxρ
stiffness
s.t.
∑
i ρi ≤ V0 < ρi ≤ 1Ku = FSignorini’s contact condition
In each optimization iteration solve contact problem.
NAC/Mikael Thellner
Topology optimization with contact constraints
F = (0,−1)N. Strömberg, A. Klarbring (2010) Topologyoptimization of structures in unilateral contact. StructMultidiscipl Optim 41:57-64.
NAC/Mikael Thellner
Topology optimization with contact constraints
F = (0,−1)N. Strömberg, A. Klarbring (2010) Topologyoptimization of structures in unilateral contact. StructMultidiscipl Optim 41:57-64.
NAC/Mikael Thellner
Topology optimization with contact constraints
F = (0,−1)N. Strömberg, A. Klarbring (2010) Topologyoptimization of structures in unilateral contact. StructMultidiscipl Optim 41:57-64.
NAC/Mikael Thellner
Topology optimization of bearing caps for rear axle
NAC/Mikael Thellner
Topology optimization of bearing caps for rear axle
NAC/Mikael Thellner
NAC/Mikael Thellner
Design domain
NAC/Mikael Thellner
Problem size
DOF:s 844771
Elements 374372
Computational time 6h 30 min onan IBM Power5 with 2 cpus
NAC/Mikael Thellner
Results
NAC/Mikael Thellner
Number of nonlinear iterations
Convergence Tolerance: 5.0000E-03
NAC/Mikael Thellner
Conclusions
Works well
Reasonable increased computational cost with contact constraints.
Matching meshes is not needed for contact modeling.
Areas for improvements
Can not plot contact pressure.
Can not plot area in contact.
Can not divide the analysis into different load steps.
Specify initial gap.
Documentation for contact modeling.
NAC/Mikael Thellner
Conclusions
Works well
Reasonable increased computational cost with contact constraints.
Matching meshes is not needed for contact modeling.
Areas for improvements
Can not plot contact pressure.
Can not plot area in contact.
Can not divide the analysis into different load steps.
Specify initial gap.
Documentation for contact modeling.
NAC/Mikael Thellner
