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Mobius Strip Geometry

Posted 20.06.2012, 08:37 GMT-4 Geometry Version 4.2a 7 Replies

Shoval Zoran
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Hi everyone,

I am trying to create a geometry that looks like a Mobius strip. I don't know how to do it.

I want to have an ellipse, which spins around some axis for a whole circle - like a torus - but which also spins around its center while spinning around that axis. I want it to complete one full rotation exactly when it gets to the point where it started.

Is there a way to do such a geometrical object in COMSOL? I've asked a friend if he could create that in Solidworks and I'll import it, but so far no good.

Thank you,
Shoval


P.S.
it might be worth mentioning that a mobius strip can easily be made with Parametric Surface, using
x=2*cos(s1)*(1+0.5*s2*cos(s1/2))
y=2*sin(s1)*(1+0.5*s2*cos(s1/2))
and
z=s2*sin(s1/2)

where s1 is form 0..2pi and s2 is from -1..1.

something similar can be done with just a parametric curve, where just substitute s2=1: two parametric curves like that with opposite signs in X-value.
7 Replies Last Post 25.06.2012, 12:14 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 20.06.2012, 15:52 GMT-4
Hi

I'm not sure how to do that in COMSOL, possibly with a twisted sweep of a line, around a circle / ellipse.

But one thing strikes me, a Moebius strip has only 1 boundary it covers "both" sides, that are in fact only 1 side looping twice, no ?
Are you sure this topology is coherent with a carthesian definition and the related physics equations ?
For me, there might be an issue there

--
Good luck
Ivar
Hi I'm not sure how to do that in COMSOL, possibly with a twisted sweep of a line, around a circle / ellipse. But one thing strikes me, a Moebius strip has only 1 boundary it covers "both" sides, that are in fact only 1 side looping twice, no ? Are you sure this topology is coherent with a carthesian definition and the related physics equations ? For me, there might be an issue there -- Good luck Ivar
Shoval Zoran
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Posted: 1 decade ago 20.06.2012, 17:06 GMT-4
Well the whole concept of a Mobius strip *is* that it has only one side. The Parametric Surface way gets us to a domain that indeed is three dimensional and has only one face. It is very interesting in seeing how Comsol treats that, since one of the traits such a strip has is that it is has no direction topologically, if I am not mistaken.

anyway, I managed to import it to comsol with a ".x_t" file eventually; can't attach the file I imported, but attached a picture.

I tried to simulate something very very easy and light with it, and it started getting lengthy already, so I let it run for the night. Tomorrow morning we'll see what's going on.
Well the whole concept of a Mobius strip *is* that it has only one side. The Parametric Surface way gets us to a domain that indeed is three dimensional and has only one face. It is very interesting in seeing how Comsol treats that, since one of the traits such a strip has is that it is has no direction topologically, if I am not mistaken. anyway, I managed to import it to comsol with a ".x_t" file eventually; can't attach the file I imported, but attached a picture. I tried to simulate something very very easy and light with it, and it started getting lengthy already, so I let it run for the night. Tomorrow morning we'll see what's going on.

Attachments:

Shoval Zoran
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Posted: 1 decade ago 24.06.2012, 07:54 GMT-4
So it appears that Comsol is not quite compatible with the Mobius Strip ;)

I attached my model; it seems that solution never converges. I tried Point Charge, I tried Surface Charge Density, and I tried more; The convergence graph looks like noise every time.

I will now try the same with Triangle- and Square-based mobius rings.
So it appears that Comsol is not quite compatible with the Mobius Strip ;) I attached my model; it seems that solution never converges. I tried Point Charge, I tried Surface Charge Density, and I tried more; The convergence graph looks like noise every time. I will now try the same with Triangle- and Square-based mobius rings.

Attachments:

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 24.06.2012, 08:24 GMT-4
Hi

I'm not sure it COMSOL as such, rather that the standard physics equations are not compatible with your topology, you need probably to change the PDE coefficient accordingly, but I'm no math specialist for that kind of unconventional toplogy, I'm far too "down to earth".

But its an interesting approach, how many bio-molecules are skewed like that ?

--
Good luck
Ivar
Hi I'm not sure it COMSOL as such, rather that the standard physics equations are not compatible with your topology, you need probably to change the PDE coefficient accordingly, but I'm no math specialist for that kind of unconventional toplogy, I'm far too "down to earth". But its an interesting approach, how many bio-molecules are skewed like that ? -- Good luck Ivar
Magnus Ringh COMSOL Employee

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Posted: 1 decade ago 25.06.2012, 08:35 GMT-4
Hi,

I don't think this has to do with the specifics of a Möbius-type geometry but with the physics in general: An electrostatics model with one of the suggested point or boundary conditions probably does not have a well-defined electric potential, which is the field variable (dependent variable) that the Electrostatics physics defines. Shouldn't the model be grounded somewhere or in some other way have a well-defined potential?

Best regards,
Magnus Ringh, COMSOL
Hi, I don't think this has to do with the specifics of a Möbius-type geometry but with the physics in general: An electrostatics model with one of the suggested point or boundary conditions probably does not have a well-defined electric potential, which is the field variable (dependent variable) that the Electrostatics physics defines. Shouldn't the model be grounded somewhere or in some other way have a well-defined potential? Best regards, Magnus Ringh, COMSOL
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 25.06.2012, 09:16 GMT-4
Hi

You are right Magnus, now that I'm back in my office and can load the model, for me this is a skewed torus hence still in standard 3D topology, by removing the interiour and charging the torus boundary and setting a GND you get a results.

I had in mind a 2D strip Moebius boundary in the middle of a sphere, hence the up and down are superposed ;) but I do not really see how to make one on those with the COMSOL geometry

--
Good luck
Ivar
Hi You are right Magnus, now that I'm back in my office and can load the model, for me this is a skewed torus hence still in standard 3D topology, by removing the interiour and charging the torus boundary and setting a GND you get a results. I had in mind a 2D strip Moebius boundary in the middle of a sphere, hence the up and down are superposed ;) but I do not really see how to make one on those with the COMSOL geometry -- Good luck Ivar
Shoval Zoran
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Posted: 1 decade ago 25.06.2012, 12:14 GMT-4
you are indeed correct and it works.

and you can make the strip with the superposition of the up-and-down with the parametric curve I mentioned in the first post. Wonder what that'll produce.

Shoval~
you are indeed correct and it works. and you can make the strip with the superposition of the up-and-down with the parametric curve I mentioned in the first post. Wonder what that'll produce. Shoval~

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