1. Topology Optimization Andrés Tovar Process Simulation and Optimization December 2, 2003

2. Content What’s Topology Optimization How does it work How to solve a Topology Optimization Problem Examples

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

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

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

6. How can we do Topology Optimization?

7. 1) Using a structural parameter as a design variable. r

8. 1 1 a b

9. 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]

10. 3) Using microstructural parameters as design variables. 1 1 a b This method is known as homogenization approach. [Bendsøe & Kikuchi, 1988]

11. 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]

12. Solution of a topology optimization problem Using the density approach

18. [O. Sigmund, 2001]

19. Density approach

20. Density approach + filtering

21. Examples From GENESIS (a commercial software)

22. Homogenization approach

23. New biological inspired approach

24. Questions?