Topology Optimization

Andrés TovarProcess Simulation and Optimization

December 2, 2003

Content

• What’s Topology Optimization

• How does it work

• How to solve a Topology Optimization Problem

• Examples

What is Topology Optimization?

It is a FE-based method to find an optimum “lay-out” of material in a fuzzy design domain.

What is Topology Optimization?

It is a FE-based method to find an optimum “lay-out” of material in a fuzzy design domain.

What is Topology Optimization?

It is a FE-based method to find an optimum “lay-out” of material in a fuzzy design domain.

How can we do Topology Optimization?

1) Using a structural parameter as a design variable.

r

1) Using a structural parameter as a design variable.

1 1a b

2) Using a material property as a design variable.

or E

When

E E0 p,

the method is called SIMP, power-law or density

approach.

[Bendsøe, 1989]

3) Using microstructural parameters as design variables.

1 1a b

This method is known as homogenization approach.

[Bendsøe & Kikuchi, 1988]

4) Heuristically: removing or adding elements (not necessarily solving an optimization problem).

The most common one is the evolutionary structural

optimization (ESO).

[Xie & Steven, 1993]

Solution of a topology optimization problem

Using the density approach

[O. Sigmund, 2001]

Density approach

Density approach + filtering

Examples

From GENESIS (a commercial software)

Homogenization approach

New biological inspired approach

Questions?