I started to work with stress constraints. It's pretty interesting and up to now more stuff seems unclear to me that being clarified.
I read a bunch of papers, but need to read the original Duysinx and Bendsoe; Topology optimization of continuum structures with local stress constraints; 1998 paper again (maybe there are the answers to my questions hidden :)). Our results are in good agreement with the standard solutions, so our approach seems to work. However, the results of Le; Stress-based topology optimization for continua; 2010 are really extraordinary good, unmatched by any other publication I read and far better that our results.
I still wonder, why
min vol
s.th. stress constraint
works. At least for qp-regularization (Bruggi; On an alternative approach to stress constraints relaxation in topology optimization; 2008) rho_min should be the global optimum. But the results are all similar to the compliance solution. I cannot imagine, that the regularization just hides this global optimum as we use a second order optimizer ... well, I hope I'll find out.
The next thing is, that beside Le, all (of what I read up to now) published results show some grayness embedded in full material. What happens if we have to map to manufacturable black and white topologies? I have not found any discussion of this grayness yet.
Thursday 4 November 2010
Wednesday 13 October 2010
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.
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.
Wednesday 6 October 2010
Mean Transduction
In 1999, Silva et al. introduced in
Silva, Nishiwaki, Kikuchi; Design of piezocomposite materials and piezoelectric transducers using topology optimization—Part II; Archives of Computational Methods in Engineering; 1999
the objective function mean transduction. It describes the piezoelectric coupling, and it is quite intuitive to maximize that coupling. The mean transduction was applied quite often by Silva. To my knowledge there are no recent publications, where it is used, but I might be wrong.
I don't use the function but as I started 4 years ago with it, it is still in my mind and somehow I still try to actually understand it properly.
I make currently good progress in writing my thesis and just work on a section about mean transduction. I finally found the link between mean transduction and classical adjoint based sensitivy analysis - which clearly helps in understanding the nature of the mean transduction. Just, I don't know if this is of interest, as I don't know, if the mean transduction is used any more. For sensor applications, maximizing the electric power as done by Cory Rupp is IMHO more practical - and for actor applications the physics might be necessary, e.g. acoustic formulations to prevent acoustic short circuits as I have shown.
This piezo stuff is really heavy (optimization) stuff :)
Silva, Nishiwaki, Kikuchi; Design of piezocomposite materials and piezoelectric transducers using topology optimization—Part II; Archives of Computational Methods in Engineering; 1999
the objective function mean transduction. It describes the piezoelectric coupling, and it is quite intuitive to maximize that coupling. The mean transduction was applied quite often by Silva. To my knowledge there are no recent publications, where it is used, but I might be wrong.
I don't use the function but as I started 4 years ago with it, it is still in my mind and somehow I still try to actually understand it properly.
I make currently good progress in writing my thesis and just work on a section about mean transduction. I finally found the link between mean transduction and classical adjoint based sensitivy analysis - which clearly helps in understanding the nature of the mean transduction. Just, I don't know if this is of interest, as I don't know, if the mean transduction is used any more. For sensor applications, maximizing the electric power as done by Cory Rupp is IMHO more practical - and for actor applications the physics might be necessary, e.g. acoustic formulations to prevent acoustic short circuits as I have shown.
This piezo stuff is really heavy (optimization) stuff :)
Sunday 30 May 2010
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.
Paul made cool applets for several physical problems, worth to have look :)
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 :)
Sunday 23 May 2010
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.
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.
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!
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!
Sunday 14 February 2010
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, ..., ....
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, ..., ....
Friday 12 February 2010
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:
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
Monday 4 January 2010
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.
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:
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!
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! :)
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!
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