Free material optimization: recent progress†

†Dedicated to Bert Jongen on the occasion of his 60th birthday.

Abstract

We present a compact overview of the recent development in free material optimization (FMO), a branch of structural optimization. The goal of FMO is to design the ultimately best material (its mechanical properties and distribution in space) for a given purpose. We show that the current FMO models naturally lead to linear and non-linear semidefinite programming problems (SDP); their numerical tractability is then guaranteed by recently introduced SDP algorithms.

†Dedicated to Bert Jongen on the occasion of his 60th birthday.

Keywords:

• optimization of elastic structures
• material optimization
• topology optimization
• semidefinite programming
• method of augmented Lagrangians

Subject Classification: :

• 74P05
• 90C22
• 90C26

Acknowledgements

This research was supported by the Academy of Sciences of the Czech Republic through grant No. A1075402 and by the Eu Commision in the Sixth Framework Program, Project No. 30717 – PLATO-N. Most of the work was done while M. Kočvara was with the Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic.

Notes

†Dedicated to Bert Jongen on the occasion of his 60th birthday.