Paper about piezoelectric self-penalization submitted

End of January we submitted a second paper entitled:

Wein, M. Kaltenbacher, Leugering, Bänsch, Schury; Self-Penalizing Topology Optimization of Piezoelectric Composite; 2010

to SMO.

It is devoted to the phenomenon that there is no penalization necessary performing SIMP topology optimization (let's stick to 'SIMP' even if the special feature of SIMP, the P which stands for penalization is omitted ... :) ).  Hence there is also no filtering or other regularization or any other kind of constraint necessary (for the configurations where self-penalization occurs!).

Imagine the optimization strategy: As there is also no volume constraint one can just follow the gradient to add or remove material. I used a simple move limit and after 5 iterations you have a black and white design ... at least for the best working case which is static displacement maximization. Normally I use a 'grown up' optimizer which is SCPIP from Ch. Zillober, a MMA implementation with all the features which make life easier:) (see my frontend C++SCPIP)

At WCSMO-8 I was really surprised to find that Cory Rupp had the same observation (and to some extend als Maria Dühring) but this is the first paper entierely devoted to self-penalization.

Again the cosmos of topology optimizaton is a Danish centric system :) Self-penalization itself has been first (and as far as I know almost limited to) reported by Ole Sigmund and Jakob S. Jensen: Sigmund, Jensen; Systematic design of phononic band-gap materials and structures by topology optimization; 2003. They did not use the term 'self-penalization' yet and actually I could not google any corresponding reference to the term. At WCSMO-8 I talked with Ole Sigmund about my observation and I was told the term 'self-penalization' and the references from him. The best I came up by myself up to then was 'intrinsic avoidance of intermediate material' :( I just want to emphasis that the credits for the term belong to Ole (or maybe Jakob?)!

In the paper a whole range of objective functions is applied to my standard system, by heart I know only of single further objective function meaningful for piezoelectric topology optimization (the one of Maria Dühring but it is quite special). So the paper is also kind of a little review :) The objective functions are:

• mean transduction
• displacement
• sound radiation
• electric potential
• electric energy
• energy conversion
• electric power

There is no pre-print I can link to so just mail me for a draft if you are interested.