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some problems about cantilever under Electrostatic force + contact

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Hi,

When I simulate cantilever bending under electrostatic force with COMSOL, there are some problems and errors I can not fix. Could someone please give me advises? I attach my file.
(1) When the applied voltage is larger than pull in, the cantilever should crash to the substrate. Right now when I apply voltage bigger than pull-in, there is error 'Failed to find a solution: In segregated group 1: Divergence of the linear iterations. Returned solution has not converged.' and warning 'inverted mesh element near ...' .

What to do with this error and warning?

(2) The contact pairs I set up are the bottom of cantilever and the top of glass. Does it matter that which is source and which is destination? What to do with the penalty factor and contact pressure?

(3) I follow "ale_cantilever_beam_2d.mph" to set up the multiphysics relation between solid mechanics and electrostatic by integrating Q. However I am not sure whether I did the right multiphysics set, since the example is from 3.5a version which is quite different from 4.0.

Thanks a lot!


9 Replies Last Post 1 apr 2013, 21:16 GMT-4
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Posted: 1 decade ago 8 feb 2011, 16:35 GMT-5
I have a same question about this. Is there anyone who can help to solve it?
I have a same question about this. Is there anyone who can help to solve it?

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 9 feb 2011, 02:30 GMT-5
Hi

ther are probably many things to say, but after a very quick look, I notice that you restrain your lower electrode (fixed) and leave the upper free except for the left boundary fixed. Great but you calculate the total force on both electrodes, for me this should add up to "0" or therearund. I would only calculate theforce or the upper one separately for the lower one (if you want to check) and apply the force as a body load to the upper canteliever in the structrural part.

Then I would start without contacts, and test contacts separately i.e. applying a pressure on the top of the beam and with no ACDC. Just because tweaking these physcs need some play and tests, and mixing everything in one go is tricky and errr prone. At the end only I would mix everything

--
Good luck
Ivar
Hi ther are probably many things to say, but after a very quick look, I notice that you restrain your lower electrode (fixed) and leave the upper free except for the left boundary fixed. Great but you calculate the total force on both electrodes, for me this should add up to "0" or therearund. I would only calculate theforce or the upper one separately for the lower one (if you want to check) and apply the force as a body load to the upper canteliever in the structrural part. Then I would start without contacts, and test contacts separately i.e. applying a pressure on the top of the beam and with no ACDC. Just because tweaking these physcs need some play and tests, and mixing everything in one go is tricky and errr prone. At the end only I would mix everything -- Good luck Ivar

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Posted: 1 decade ago 13 feb 2011, 11:55 GMT-5
Hi,

I followed your advice and just applied a pressure on the top of the beam and with no ACDC. Please see my attached models. One model tried to use moving mesh to solve the contact problem, but I can not get the solution. Another model did not use the moving mesh and the solution seems good. So the question is that can we use moving mesh to solve the contact problem? If we add the electrostatic model, we need the moving mesh. How to solve this? Thank you very much.
Hi, I followed your advice and just applied a pressure on the top of the beam and with no ACDC. Please see my attached models. One model tried to use moving mesh to solve the contact problem, but I can not get the solution. Another model did not use the moving mesh and the solution seems good. So the question is that can we use moving mesh to solve the contact problem? If we add the electrostatic model, we need the moving mesh. How to solve this? Thank you very much.


Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 13 feb 2011, 16:58 GMT-5
Hi

1) you should update to latest version (patch, see the main Comsol site) there are several minor errors that have been corrected since 4.1.0.88
2) with the ALE it's not converging and there is in my mind several reasons:
- your imposed displacements u,v are not consistent overall in the "air gap" in particular edge "9" is fixed
- your contact means that the mesh dissapears fully in the contact region, but that is a topology change COMSOL cannot survive with => use at elast a small offset contact displacement to allow the ALE mesh to remain defined in between the contact region
- if I disable the ALE mesh your system solves (when setting the loads and contact parameter as for the other file) so the convergence issue is linked to the ALE presence, if the load is small it works also with the ALE, but above -25[N/m] the surfaces overlap.
- then why ALE overall ? you can also use the spatial frame and declaring your "air" as an elastic domain i.e E=1[atm], nu=0, rho =1
- there are also some ALE mesh "spring behaviour" settings to play with (Winslow ...) havent tried that, could be linked
- the material constants of Aluminium (the elastoplastic material) is reporting a warning, but the variable does not seem to be used. Why use elasto-plastic and not just linear ?

Finally something is puzzling me, for both models: the right boundary is not contracting, rotating, there is as a u=0 rule applying on the right boundaries, I would expect the beam right boundary to rotate -Rz. I cannot find out why just now, but it does not look correct.
And I hope you have noted that your small beam is still 1[m] long (default Z depth of Comsol in 2D) not really an issue if you normalise all your absolute values per "[m]"

--
Good luck
Ivar
Hi 1) you should update to latest version (patch, see the main Comsol site) there are several minor errors that have been corrected since 4.1.0.88 2) with the ALE it's not converging and there is in my mind several reasons: - your imposed displacements u,v are not consistent overall in the "air gap" in particular edge "9" is fixed - your contact means that the mesh dissapears fully in the contact region, but that is a topology change COMSOL cannot survive with => use at elast a small offset contact displacement to allow the ALE mesh to remain defined in between the contact region - if I disable the ALE mesh your system solves (when setting the loads and contact parameter as for the other file) so the convergence issue is linked to the ALE presence, if the load is small it works also with the ALE, but above -25[N/m] the surfaces overlap. - then why ALE overall ? you can also use the spatial frame and declaring your "air" as an elastic domain i.e E=1[atm], nu=0, rho =1 - there are also some ALE mesh "spring behaviour" settings to play with (Winslow ...) havent tried that, could be linked - the material constants of Aluminium (the elastoplastic material) is reporting a warning, but the variable does not seem to be used. Why use elasto-plastic and not just linear ? Finally something is puzzling me, for both models: the right boundary is not contracting, rotating, there is as a u=0 rule applying on the right boundaries, I would expect the beam right boundary to rotate -Rz. I cannot find out why just now, but it does not look correct. And I hope you have noted that your small beam is still 1[m] long (default Z depth of Comsol in 2D) not really an issue if you normalise all your absolute values per "[m]" -- Good luck Ivar

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Posted: 1 decade ago 13 feb 2011, 20:54 GMT-5
Hi,

Thank you very much for your reply. I have already updated my version to the latest one. According to your reply, I modified my model a little bit. Actually, what I want to model is a fixed-fixed beam.

In this model, even though I set a contact surface offset(0.5um) in the contact frame, I can still not get a solution if I use ALE. It seems like the beam can not see the substrate with ALE. Changing mesh smoothing types( Laplace, winslow and hyperelastic) can not solve it, either.

"- then why ALE overall ? you can also use the spatial frame and declaring your "air" as an elastic domain i.e E=1[atm], nu=0, rho =1"

I do not quite understand the above statement . The reason I want to use ALE is I need to couple this model with electrostatics to drive the beam later, finally maybe fluid flow will also be added. If the ALE can not be used, can we get the accurate electrical field when the beam is deformed? This is really a big problem for me.

Thanks again.

Hi, Thank you very much for your reply. I have already updated my version to the latest one. According to your reply, I modified my model a little bit. Actually, what I want to model is a fixed-fixed beam. In this model, even though I set a contact surface offset(0.5um) in the contact frame, I can still not get a solution if I use ALE. It seems like the beam can not see the substrate with ALE. Changing mesh smoothing types( Laplace, winslow and hyperelastic) can not solve it, either. "- then why ALE overall ? you can also use the spatial frame and declaring your "air" as an elastic domain i.e E=1[atm], nu=0, rho =1" I do not quite understand the above statement . The reason I want to use ALE is I need to couple this model with electrostatics to drive the beam later, finally maybe fluid flow will also be added. If the ALE can not be used, can we get the accurate electrical field when the beam is deformed? This is really a big problem for me. Thanks again.


Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 14 feb 2011, 03:55 GMT-5
Hi

indeed there is something between the contact and the intermediate ALE.

In anycase, I would keep only domain = 2 for the ALE and remove the "Prescribed deformation 1" and the "Prescribed displacement 2" is not required as there is already the "1"

In the Solver Stationary Solver 1 Advance, you can select Solver log Detailed to get also scaling info out

Then another issue will show up with the pull-in effect when the displacement will go above some 2/3 of the gap (if I remember right)


My only explanation is that you are in union mode, and contacts are normally used in assembly mode, when adding the ALE something mixes up. If I set myself in assembly mode (adding a union + split all before in the geometry as your rectangles overlap) we then have the problem that u,v are not defined on the ALE interiour domain 2 boundaries. Then we need to map the displacement on the boundary. These are issues I usually send to "support"

The other way is to forget ALE, use the structural on all 3 domains, define domain 2 as air with a fictitious Young modulus of some 1 to 100[kPa], nu=0, rho=1. This will deform the air gap more or less like the ALE. You can then apply ES to the air gap too. The only "thing" the standard contact is not working either, you you need to use some non linear spring for the air to simulate the contact, and leave a minimum air gap to not squeeze the mesh to far

--
Good luck
Ivar
Hi indeed there is something between the contact and the intermediate ALE. In anycase, I would keep only domain = 2 for the ALE and remove the "Prescribed deformation 1" and the "Prescribed displacement 2" is not required as there is already the "1" In the Solver Stationary Solver 1 Advance, you can select Solver log Detailed to get also scaling info out Then another issue will show up with the pull-in effect when the displacement will go above some 2/3 of the gap (if I remember right) My only explanation is that you are in union mode, and contacts are normally used in assembly mode, when adding the ALE something mixes up. If I set myself in assembly mode (adding a union + split all before in the geometry as your rectangles overlap) we then have the problem that u,v are not defined on the ALE interiour domain 2 boundaries. Then we need to map the displacement on the boundary. These are issues I usually send to "support" The other way is to forget ALE, use the structural on all 3 domains, define domain 2 as air with a fictitious Young modulus of some 1 to 100[kPa], nu=0, rho=1. This will deform the air gap more or less like the ALE. You can then apply ES to the air gap too. The only "thing" the standard contact is not working either, you you need to use some non linear spring for the air to simulate the contact, and leave a minimum air gap to not squeeze the mesh to far -- Good luck Ivar

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Posted: 1 decade ago 14 feb 2011, 11:25 GMT-5
Hi,

Thank you. Can we set the prescribed displacement in the solid mechanics model. That means when the y displacement of the beam(v) is bigger than some value(such as 0.9*gas gap), v will be set as 0.9*gas gap and will not increase any more. Is that possible?
Hi, Thank you. Can we set the prescribed displacement in the solid mechanics model. That means when the y displacement of the beam(v) is bigger than some value(such as 0.9*gas gap), v will be set as 0.9*gas gap and will not increase any more. Is that possible?

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 14 feb 2011, 15:16 GMT-5
Hi

then I would rather use the "solver continuatiuonparametric sweep" and enforce a displacement in steps until I get to 90% of the gap.

But for electrostatic pull-in effcts, how do you expect to handle the non-linearity and the biffurcation of the solutions ? That is an interesting issue, I have to now, not really found out how to "correctly" handle ina controlled way

--
Good luck
Ivar
Hi then I would rather use the "solver continuatiuonparametric sweep" and enforce a displacement in steps until I get to 90% of the gap. But for electrostatic pull-in effcts, how do you expect to handle the non-linearity and the biffurcation of the solutions ? That is an interesting issue, I have to now, not really found out how to "correctly" handle ina controlled way -- Good luck Ivar

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Posted: 1 decade ago 1 apr 2013, 21:16 GMT-4

Hi

then I would rather use the "solver continuatiuonparametric sweep" and enforce a displacement in steps until I get to 90% of the gap.

But for electrostatic pull-in effcts, how do you expect to handle the non-linearity and the biffurcation of the solutions ? That is an interesting issue, I have to now, not really found out how to "correctly" handle ina controlled way

--
Good luck
Ivar


Hi,
This point is intersting for me. I followed the model name "electrostatically actuated cantilever" in model library to build my own model - an RF MEMS shunt switch with fixed fixed bridge. In the "electrostatically actuated cantilever" model, the author finds the pull in voltage by basing on the divergence of the solver. I did not quite satisfy with that since I am also interested in the final geometry when the beam landing on the bottom electrode. I worked for weeks using contact pair, longing for a converge solution of that electromechanical problem but did not suceeded.
Do you think I should carry on that way, or should I give up?
[QUOTE] Hi then I would rather use the "solver continuatiuonparametric sweep" and enforce a displacement in steps until I get to 90% of the gap. But for electrostatic pull-in effcts, how do you expect to handle the non-linearity and the biffurcation of the solutions ? That is an interesting issue, I have to now, not really found out how to "correctly" handle ina controlled way -- Good luck Ivar [/QUOTE] Hi, This point is intersting for me. I followed the model name "electrostatically actuated cantilever" in model library to build my own model - an RF MEMS shunt switch with fixed fixed bridge. In the "electrostatically actuated cantilever" model, the author finds the pull in voltage by basing on the divergence of the solver. I did not quite satisfy with that since I am also interested in the final geometry when the beam landing on the bottom electrode. I worked for weeks using contact pair, longing for a converge solution of that electromechanical problem but did not suceeded. Do you think I should carry on that way, or should I give up?

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