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!