Topology Optimization Andrés Tovar Process 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 1 a b

2) Using a material property as a design variable.  or E When E  E 0  p, the method is called SIMP, power-law or density approach. [Bendsøe, 1989]

3) Using microstructural parameters as design variables. 1 1 a 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?