Applet visualizing square plate vibrations

I found this very cool applet from Paul Falstad. There are many more technical applets on his homepage.

The applet allows to interactively play with the structural resonance modes of an elastic plate. I also like the transient simulation when the plate is "pinged" by the mouse.

Von Pizeo Blog

Paul made cool applets for several physical problems, worth to have look :)

Acoustic near field topology optimization

Here I share my talk I gave on ECCM 2010. It presents acoustic near field optimization. Last year, at WCSMO-8 I compared acoustic topology optimization where the acoustic field was assumed to be far field/ plane wave type/ constant acoustic impedance at the structure itself (so no acoustic is calculated) and at the boundary of by acoustic domain. Now I did the step further and optimize the acoustic power directly w/o any assumption. Thanks to Michael Stingl who helped with some very useful comments! It turned out, that the same objective function had already been used in Jensen and Sigmund; Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide; 2005. It was disappointing that it had (for other physics) already been done - but it would have been really bad if I had not found it and claimed it as a own result.

For my numerical examples the optimal results where quite close to the acoustic far field optimization. This was quite surprising but before I could for lower frequencies not guarantee any physical validity. So it was definitely worth it.

Acoustic near field topology optimization of a piezoelectric loudspeaker

ECCM 2010 is over

I just came home from ECCM 2010 (European Conference on Computational Mechanics) in Paris. I was invited by Ole Sigmund to the multiphysics topology optimization minisymposium (I'm proud of it, therefore I mention it all the time :)). I gave a talk on Acoustic near field topology optimization of a piezoelectric loudspeaker, see my other blog post about it. I also contributed to the talk my collegue Fabian Schury gave about Design of isotropic lightweight material structures by inverse homogenization and topology optimization. What he actually showed is, that an old regularization method, the slope constraints (Petersson and Sigmund; Slope constrained topology optimization; 1998), is actually quite useful when used with appropriate optimizers. The standard MMA implementations simply cannot handle the many thousand constraint problem (we have up to 400.000!) but e.g. SnOpt can do it and we are working on other optimizers within our group.

Ole Sigmund gave a semi-plenary talk with a variation of the robust optimization presentend last year at WCSMO-8 but now including heaviside type density filters. It seems that this finally really solves the problem of the resolution of hinges in mechanism design (e.g. force inverter). The details of the hinges are a long known problem - yet often ignored. The optimizer abuses the numerics of low order linear elasticity and bends elements ("bricks") only by their momentum free nodal or edge connection. I actually wonder if this could be resolved by stress constraints (I known they have their own problems)? I would say that this special area of length-scale control is one of the few areas where significant contribution to the SIMP method can still be done! It would be very cool if our group (the one of Michael Stingl) could come up with a new approach :)

Again the talks from the Danish guys where advanced and interesting (DTU *and* Aalborg), including a talk on transient optimization to reduce the speed of light with several thousand time steps of "adjoint history" by Rene Matzen. More related to our own work was Optimization of the pressure coupling coefficient in periodic poroelastic materials by Casper Andreasen.

At least at ECCM I noticed no further strong topology optimization group. Apart from the minisymposium I heard not that much interesting talks. A lot turned out in using genetic algorithms or other stochastic methods and one cannot really learn much from it. It's a "This is our interesting problem, we put a black box over it, show some colorful graphs labeled A...H because we do science and now we come to the conclusion." Nice for the guy who solved his existing problem but no new idea I can take home. I wish they would clearly identify this genetic stuff talks - especially as there where about 40-50 talks in parallel!! and I often heard just the wrong one.

Paris is a nice place, I like all the open places where people gather and street artists give performances. We had a really nice little hotel, Hotel Helipolis at a good location and a very nice vibrations for 77 Euro a single room.

I'm looking forward to WCSMO-9 2011 in Japan!

The global village

** Teaser!! ** This is kind of a private post!

When I was a teen and the Internet was only know to a very special circle, the world got interconnected by dial-up modem connections via POT (plain old telephone) -lines and bulletin board systems (Fido, ...) the buzzword was "the global village".

The spirit of that time with "Netiquette", which was a guideline to all newcomers to the global net, was openness. So like google books today, the IMHO most/only philanthropically google service, the credo was global knowledge.

It is impressive to note the equal distribution of drop ins to my blog (according to the statistics) from all over the world. Clearly significant US-Americans and Europeans but also people (students, fellow PH.D students?) from the whole world: China, India, Pakistan, Marocco, Iran, Thailand, Vietnam, Puerto Rico, Columbia, Romania, Finland, ..., ....

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.

ECCM 2010 in Paris

I'll be on ECCM 2010, the IVth European Conference on Computational Mechanics - Solids, Structures and Coupled Problems in Engineering.

I'm accepted for the minisymposium Topology Optimization for Multiphysics Problems by Ole Sigmund and Kurt Maute.

The title for my talk is "Acoustic Near Field Topology Optimization of a Piezoelectric Loudspeaker". I (hope) it is cool stuff - at least it drives the computational costs back to "normal". Having a 3D Helmholtz Equation with a discretization driven by acoustic far field conditions is very expensive - too expensive to do experiments with broad frequency range optimization. It is difficult stuff for the optimizer requiring a hell of iterations and one has to take care to be not only left with colorful pictures ...

I'm very proud that I got invited (by Ole Sigmund) and according to professors its an honour. So I'm simply happy and will do my best! :)

The conference is in Paris from May 16 to 21 in 2010. A lot of colleagues from Erlangen will also come - we are a really big structural optimization group there! I hope it's not too expensive - Lisbon was cool! Tube for 80 cents, a beer in a Cafe 1,10 Euros and probably the most appealing capital in Europe to me. I haven't been to Paris for a very long time - and always camped then.

Blog blogging

A year has passed since I added my blog to feedjit.com to control who's reading my blog (beside google). You can see the data on the right sidebar in the lower region - a world-map and an detailed access list. When people google me I can even see what the googled for.

Well, now I know at least that some people read me - even when they actually searched for something different. Here comes a short list of common stuff people search for:

• "piezo matlab" - sorry I use a complex C++ FEM code


• "math riddle" - I have only a single one.


• "topology optimization" - in some countries I'm quite high in google ?!


• "topology optimization book" - some read my review - and with feedjit I can see which amazon link the followed.
  
• "piezoelectric loudspeaker" - yeah - some new stuff! :)


• paper - a few times people searched for my paper - once from South Korea. Now, please cite me! :)
  

It also seams that some people bookmarked me and I know of at least two scientists who found and read me. So I'll continue blogging - hopefully more regularly :). I know of no other blog within my community - unfortunately, it would be interesting what the Danish and piezo guys do ...

Actually I like to blog but it is time consuming and I blog only at night. I don't write as open as I would like. I would like to share some remarks about my community - but not in public. It's no good style and you never know hows reviewing you. I also have no private blog and I believe there is often a 'private' side in some of my posts. I'll have to do more on my facebook account to 'satisfy' this. :)

I'm happy about comments or mails - even more if you start a own blog - just let me know :)

Happy new year!