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

Products

Heavy trucks

Heavy buses

Engines

Services

Workshops

Parts

Driver training

24-hour roadsideassistance

Financing

Operational leases

Financial leases

Hire purchase

Insurance solutions

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