Paper on Piezoelectric Self-Penalization Published

Our second paper is published (online):

F. Wein, M. Kaltenbacher, B. Kaltenbacher, G. Leugering, E. Baensch and F. Schury; On the effect of self-penalization of piezoelectric composites in topology optimization; Structural and Multidisciplinary Optimization; DOI: 10.1007/s00158-010-0570-2

springerlink

It covers the effect of self-penalization of many piezoelectric topology optimization problems. That means that no penalization, volume constraint and regularization is applied to gain often mesh independent black and white solutions. It's not a method we describe but a phenomenon, so to report when it does not work is part of the job.
I guess we implemented almost all relevant piezoelectric objective functions and to compare them based on the same model is IMHO also of interest. The objective functions are mean transduction, displacement, sound power, electric potential, electric energy, energy conversion and electric power.

We give an explanation based on the piezoelectric model: stiffness, electrostatic and piezoelectric coupling. More density is bad with respect to stiffness but good for the other fields, opposite for less density. That means that there is balance of the effects and when this balance is outside the feasible design set (0,1], there is no greyness.

Self-penalization has been, to my knowledge, first reported by Ole Sigmund and Jakob S. Jensen 2003 with (elastic) wave guiding. It also appears in other, especially non-elastic problems but has never been investigated. Meanwhile I almost belief that probably most non-compliance problems show some form of self-penalization. I hope I can find a general explanation as this might eventually lead to new method in topology optimization. :) I have at least one idea on how to proceed ... Let's see when I find the time and if I have success.

P.S.: It seems that the term "self-penalization" has not been used before in the context of topology optimization (I actually don't want to know what google finds for self-penalization in other contexts :) ) but I learned the expression from Ole Sigmund, so he deserves the credits.