Help Needed: Modeling Beam Bending with Electrostatic Forces

[evelyncanarvon]

Hey--
I'm trying to model the bending of a beam due to electrostatic forces. (Femlab does offer this model on their website, but the module I'd need to run it costs $600!)

I have no problem modeling a beam bending, and I have no problem creating a parallel plate capacitor, but when I combine the two in multiphysics, I don't get a reasonable result.

Any femlab gurus out there who might be able to help? Thanks a lot!

 

[PerennialII]

More Femlab users ... cool ! Have you gotten the coupling to produce anything reasonable and how've you done the actual coupling of the mechanical and electrostatical problems ?

(btw I might have that model somewhere ... have collected quite a bit of stuff from them)

 

[krab]

Show us what you have, and what you call uneasonable. To help you I also need more information. Is the deflection angle small? I.e., do the deflection plates curve to follow the particle trajectory?

 

[evelyncanarvon]

I basically just set up a beam (a rectangle) with the left side fixed into place, and a plate (a fixed line) underneath it, and I set up a voltage difference between the two. This produces an electric field between them, but that field does not bend down the beam. I don't know why this is: in the structural mechanics module, I just had to apply a load to a beam fixed at one end to get it to bend. Isn't that what I'm doing when I apply a field to it? Thanks!

 

[krab]

Terminology problem here: By beam, I automatically assumed a charged particle beam. Sorry.

 

[PerennialII]

A safe bet there is something in the coupling of the application modes . What route have you taken in coupling the electrostatic and static elastic problems, i.e. building, say, in linear coupling :

$$T_{p}=c^{E}_{pq}S_{q}-e_{kp}E_{k}$$
$$D_{i}=e_{iq}S_{q}+\epsilon^{S}_{ik}E_{k}$$

?

 

[evelyncanarvon]

Woah--sorry, I'm afraid I don't know what you mean. I haven't ever fiddled with any of the equations they gave me. Should I have? I am quite new at this--up to this point I've just been creating the objects and choosing properties for them from a list of options in the subdomain and boundary physics categories. I never had to input any equations into the single-physics mode, and I assumed it would all be taken care of in the multiphysics mode. Is this incorrect? Thanks!

 

[PerennialII]

If your elasticity solution displays all zeros (only the coupling induced loading?) then it's likely the coupling is not active at all (it solves both multiphysics problems totally independent). I've been running piezoelectric problems in 3.1 using the same coupling scheme and at least in this version the coupling for the electric and mechanical multiphysics problems needs to "implemented" by hand ... i.e. you need to modify the subdomain equation system settings ... and naturally introducing the related material property matrices. If you've the structural mechanics module in its basic model library reference there are a couple of piezoelectricity models which you can use as a reference in doing this ... following the cases given there makes it pretty simple, some work although.

Some of the couplings in Femlab can be taken to use inherently (like thermal - mechanical etc.) but in many cases you need to modify the subdomains etc. to introduce the coupling equations. Gives you the lots of 'leeway' but takes some effort ... and makes use of those examples a way to get things done quickly.

 

[evelyncanarvon]

Oh ok. I think that might be it. I'll look at connecting them manually. Thanks a lot!

 

[PerennialII]

... if the thing doesn't seem to comply I can hook you up with some models which have the coupling done - have fun !