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## Calculating Electrostatic Force without MEMS Module

Posted May 6, 2010, 9:46 PM EDT MEMS & Nanotechnology, MEMS & Nanotechnology Version 3.5a 49 Replies

However, I do not have the MEMS Module application in my COMSOL 3.5a license, so I am currently unable to compile a 3D Cantilever Beam. The problem I have is that my Basic Electrostatics application doesn't have a force tab, while the MEMS Module Electrostatics app. does, and this electrostatic force is critical in solving the model.

I was told by COMSOL support desk that I can mimic the MEMS 3D Cantilever beam with my basic COMSOL Multiphysics package by properly setting similar boundary and subdomain settings.

How do I define these boundary/subdomain settings without a force tab in my Electrostatics application?

How can I define an electrostatic force and implement it without the MEMS Module?

Basically, how can I construct the 3D Cantilever beam without the MEMS Module?

Thank you for your time and help.

Kevin Myhro

Can you share on how you are able to achive this. I am trying to do the same and unable to find a suitable solution for it.

--

Syamsul

I would be glad to help. The model I created was similar to the 2D MEMS Cantilever beam, except I specified a slightly different geometry with different boundary constraints. That is to say, I created a device which had a top-gate grounded conductor, separated by an air gap, a substrate, then finally used a back gate conductor with applied voltage. In this model, I successfully coupled the three physics applications:

Version 3.5a

Struct. Mech> Plane Strain (smpn)

COMSOL Multiphysics> Moving Mesh (ALE)

COMSOL Multiphysics> Electrostatics (es)

I assume you have the same dilemna I had: you wish to model the 2D MEMS Cantilever beam, but you don't have the MEMS module, correct?

The trick to follow is thus: Follow all steps in described in the 2D MEMS Cantilever beam pdf file tutorial [add Plane Strain as first application, then add Moving Mesh to the Multiphysics tab (under automatically-created frame: Frame (ale) ), then make sure to add Electrostatics to frame: Frame (ale), and continue to follow the steps in tutorial accordingly].

Now, if you're using version 3.5a and do not have MEMS Module, you probably have noticed that there is no force tab under your Physics boundary settings (indeed, only the MEMS module has a force tab in Physics boundary settings for electrostatics). There is one simple step to circumvent this problem: use Maxwell's (electromagnetic) Stress tensor.

So, simply click Plane Strain application from your Multiphysics tab, and go to boundary settings and apply Maxwell's stress tensor to the appropriate boundaries that you wish to feel the Electromagnetic force, namely:

Plane Strain:

Physics>Boundary Settings>Load tab

and apply the following loads to the appropriate boundaries under the load tab:

Fx = dnTEx_es

Fy = dnTEy_es

or

Fx = unTEx_es

Fy = unTEy_es

Use dn or un if you wish for the stress tensor to point in the downward normal direction or upward normal direction, respectively.

And make sure to click the check box: Edge load is defined as Force/area.

This should be the single trick you need to circumvent the need for MEMS Module.

-------

-------

Use the above technique, and first try to get your 2D MEMS Cantilever Beam model working using Maxwell's Stress tensor. After that, try making your own specific model (where you may need to specify appropriate meshes).

When creating your own specific model, your most likely problem will be either properly specifying your Moving Mesh boundary settings, or properly specifying your mesh itself. If you're having problems with your mesh (Ex. inverted mesh elements error), then you may need to either:

Use Mapped Mesh parameters

or

Try using a swept mesh.

-------

-------

If you are interested, I've actually created a hand-written tutorial explaining Step-by-Step instructions how to compile the specific model I created [a thin membrane (graphene, for example) top gate grounded conductor, separated by air gap and substrate, then bottom gate induced voltage]. There are a few pages in there that are probably meaningless to you (I used it to present to my research group), but the tutorial will nonetheless allow you to create the model and observe deflection caused by electromagnetic forces using Maxwell's Stress tensor and coupling the aforementioned 3 physics applications.

Let me know if you're interested in this tutorial, and I will be able to probably upload it tomorrow (it is saved at student office at my University).

Good luck!

Best regards,

Kevin

am trying to model a cantilever beam in COMSOL 4.0

i supply the potential to the substrate, and ground to the cantilever membrane

i used electrostatics and solid mechanics,

am not able to perform study,

the cantilever does not bend...

What should i do....can u help me....r upload ur file for my reference...

I managed to solve the Cantilever Beam with 3.5a without the MEMS module. Attached, are 2D and 3D Cantilever beams for 3.5a as well as a self-made Tutorial documentation with model describing explicitly how to create a similar model (different geometries and boundary constraints) for version 3.5a. As I do not have version 4.0a, I will not be able to answer any explicit questions regarding that version.

Firstly, I can tell you that the Cantilever beam requires three physics applications:

Structural Mechanics

Moving Mesh (ALE)

Electrostatics

So, by not applying Moving Mesh, that would probably explain why your model is not deflecting, or bending, due to Electrostatic force. You may wish to review the online COMSOL pdf documentation explaining how to create the 2D and 3D cantilever beams, however, they only apply for verison 3.5a. You will need to make any necessary modifications for the model to solve with version 4.0a, and contact COMSOL tech support for advice, accordingly.

Basically, the key details in order to solve the Cantilever beam are (as far as version 3.5a goes):

1) Electrostatics app. must be in the frame containing Moving Mesh (ALE)

2) All app.s (Struct. Mech., moving mesh, electrostatics) must have proper Physics Properties settings

3) Boundary and subdomain settings must be properly specified in all 3 app.s.

The Moving Mesh constraints may sometimes be the hardest to specify, in general, use predefined quantities: u,v, w defining x,y, z variable deformations.

Best regards,

Kevin

Attachments:

it appears that my self-composed tutorial (as well as the model it creates, with different geometries, boundaries, etc.) are each individually too large to be attatched to this forum.

Good luck with your COMSOL modeling!

Why not zip it or send it in parts on the "Community Model Exchange" then, tutorials (also from the users) are often nice courses to learn from :)

--

Good luck

Ivar

im new user in comsol multiphisics and i want to do my project with comsol

i want to read capacity after imposing an external force whit notic to effect of electrostatic force in 3D

for this i used solid stress strain- electrostatic - moving mesh

and i did the boundry setting and subdomain setting for all then meshing . when i want to run this problem

solving stops whit " a nonsymmetric matrix found" in log page

and i dont have any idea for solving this program

do you know where im wrong??

Firstly, as it's been 2 1/2 days since your post, have you solved this error yet?

It seems your model compiles and begins to solve, yet it gets stuck midway.

I do not know what the nonsymmetric matrix error corresponds to, but I would guess it might have something to do with the Mesh or the physics properties. Properly specifying the mesh may be difficult at times...

Ivar, the COMSOL moderator, might be able to help you with the nonsymmetric matrix error, or you could use the 4 digit error code and punch it into the COMSOL Knowledge Base under the Support tab on the website to diagnose this error.

A couple of things:

Are you using version 3.5a or 4.0a?

Are you modeling the cantilever beam itself or a similar model with different geometries/boundary conditions?

Did you follow the cantilever beam tutorial to best accuracy, adding Electrostatics application to Frame (ALE) and applying proper Physics properties to all 3 applications?

Let me know how it goes.

Good luck!

Kevin

sorry but I do not have any good idea what the non symmetric matrice error can be in your case just now, for the rest Kevin has given the same comments that I would have given.

And by the way, I'm a COMSOL user just as you, no specific links to the company Comsol, and I reply in my free time, as my boss asks me to USE COMSOL for him, at work ;)

--

Good luck

Ivar

in that case, thanks for all your help, Ivar.

Your efforts are appreciated on this Discussion forum.

Best regards,

Kevin

your last advices was very usefull and this time i have three problems in previous work

as i said i couple solid stress strain / electrostatic /moving mesh modules

1) i want to read the all of capacity while nD_emes gives me the charge dencity on a plane ?

2)my sestem properties are 2.66(core 2 dual) 4G 6M and when my mesh element numbers exceeds from 5000 i face with memory err what can i do?

3)in all of problems which i solved from the help element type was lagrangian-quadratic and i dont know whether this element is satisfactoriness or not?

your last advices was very usefull and this time i have three problems in previous work

as i said i couple solid stress strain / electrostatic /moving mesh modules

1) i want to read the all of capacity while nD_emes gives me the charge dencity on a plane ?

2)my sestem properties are 2.66(core 2 dual) 4G 6M and when my mesh element numbers exceeds from 5000 i face with memory err what can i do?

3)in all of problems which i solved from the help element type was lagrangian-quadratic and i dont know whether this element is satisfactoriness or not?

Firstly, it appears that you have the MEMS module so it is more sophisticated than the Structural Mechanics and Multiphysics modules that I have for version 3.5a. You should be able to solve for both capacity and charge density, but only after you compile a success solved model. It appears that you must first fix your mesh problem before you will be able to successfully solve your model.

The software fails to solve when your mesh is overly complicated with too many elements (clearly 5,000 mesh elements is too complicated for most models, especially models with electrostatics, plane strain and moving mesh applications all coupled together). The program can be very sensitive to available memory usage and complicated meshes (high number of mesh elements) robs the program of its available memory.

In order to reduce the number of mesh elements (to a reasonable size, say 200-800 mesh elements) you must choose one of a few different techniques (which you may need to combine together depending on your model geometries and sensitivities):

Technique 1)

Mesh>Free Mesh Parameters>Global>Predefined mesh sizes: Extremely coarse

[by choosing extremely coarse, extra coarse, coarser or coarse mesh sizes you effectively reduce the number of mesh elements and free up memory]

Technique 2)

Apply technique 1, but instead of simply selecting "generate mesh," choose one subdomain from the subdomain view on the main screen and then access the menu:

Mesh>Interactive Meshing>Mesh Selected (Free)

This allows you to choose a first subdomain to mesh, then you can complete the mesh by selecting:

Mesh>Interactive Meshing>Mesh Remaining (Swept)

Once you generate a proper mesh without a large number of elements, and assuming that all of your electrostatic, structural, and moving mesh subdomains, boundaries, and physics properties are properly specified, your model should solve.

Lagrangian-Quadratic should be standard element type for electrostatics mode and should work for your model (I'm guessing, that is, assuming that your model is overly complicated).

Good luck!

Best,

Kevin

thanks a lot for all helps

i could mesh with around 5000 element and solve it but i want to get the capacity after it

how can i read the total capacity of the valium?

i entered the voltage as electric potentiol in electrical boundry setting

I would say that capacity is defined as:

C = QV = (rho)vol*V

where rho is the space charge density.

Solve for rho:

Postprocessing>Cross-Section Plot Parameters>Line/Extrusion>Predefined Quantities>Electrostatics>Space charge density

and then multiply by volume*Voltage to get Capacitance.

I believe that's correct.

Hope that helps.

Best regards,

Kevin

"and then multiply by volume" what do you mean?

i inserted V as electric potential in electrostatic boundry setting

also i did what you said the consiquence was zero in a plot for all of the line

can you give me your email address to connect or chat easily?

by the way thanks a lot

I fear that I may not be giving you adequate help. Please understand that I am just a fellow COMSOL user so I should be considered an amateur advisor at best.

The relation C = QV

should give you the capacitance you're looking for, so it's a matter of solving for the net charge.

I was stating that if you solved for volume charge density, you could multiply by volume to get net charge. However, the solver may not work that way exactly. In fact, a line/extrusion plot will only give you data along boundary (or along a line), so indeed it doesn't sound like a simple solution. The space charge density should be different at different locations, so it is a very complex situation (maybe) to calculate the net charge in this manner.

So you may need to search in the other postprocessing options (I don't have the COMSOL program in front of me right now to look at) for something that will help you find net charge, or, more conviently capacitance.

Considering that Ivar (see previous posts) has probably read our conversations and not responded, he is likely unable to help you with your situation. In that case, I would strongly recommend for you to ask COMSOL tech support [contact support] for help on your situation, including a file attachment of your simulation model with your request (of course, you must have an active subscription to do this).

Otherwise, the best way to move forward would be for you to attach your model to this thread so I can take a look at it and (hopefully) give you some advice.

I don't have Instant Messenger programs, so I prefer correspondence over comsol.com as opposed to my private email account.

Best regards,

Kevin

there's a subdomain integration or boundry integration in postproccessing and from there i can integration of surface charge or subdomain charge

thanks for all helps

this problem has solved

your notes were so useful.

i'm working on a project which is about RF MEMS and I want to design a mems varactor.

i have some problem that i think your experiences and knowledge would be useful for me.

1. when i simulate varactors of other thesis ( such as to plate that one of them is fixed and another can move freely by electrostatic force ) , my simulation results very lower spring constant than original thesis. i think my simulation doesn't contribute Residual Stress. how can i import residual stress of a beam in my simulation in COMSOL? or for calculation of "spring constant" of a beam is there any way in comsol?

2. i want to plot and see electrical force on varactor's plate ( i have applied different potential to plates) and i used this way:

postprocessing / boundary integration / Exterior electric Maxwell tensor (for predefined quantities ) Fes_nTEz_emes

is that true? and does that show electrostatic force on plate?

Thank you for your time and help.

Thanks a million.

Mehrdad

I must warn you that I am an amateur COMSOL user and I struggle day by day to understand the program. With that said, take my advice with a grain of salt and cross-check it with COMSOL tech advice, etc.

It seems that you are using the MEMS application mode, presumably with Version 4.0a or 4.1. I have been using ver. 3.5a without the MEMS application mode and have been using the Maxwell Stress tensor in my Solid, Stress-Strain Physics boundary settings in order to simulate an electrostatic force, convienently circumventing my need for the MEMS application mode.

1.1 You are concerned whether Residual stress is properly being applied in your model.

1.2 You're wondering if COMSOL can calculate a spring constant.

Well, honestly I don't know the answer to either of those inquiries. I would guess that 1.1 depends on the specific solver that you are using, I assume you are solving a Parametric-valued solution. Is your solution time dependent? Regarding the spring constant, I've done a cursory inspection and cannot see how it would be calculated, you might consider the following paper discussing a MEMS device and calcluating a spring constant (although they did not explicitly mention "how" they calculated it):

cds.comsol.com/access/dl/papers/6285/Mathur.pdf

2 You're wondering if: Exterior electric Maxwell tensor (for predefined quantities ) Fes_nTEz_emes gives the electric force on a plane.

I know that the diagonal components of the Maxwell stress tensor (T_xx, T_yy, T_zz) give the pressure, or stress on a surface, while the off-diagonal components give the in-plane shear. As I mentioned previously, in my 3D models [which use the applications: solid, stress-strain (smsld); moving mesh (ale) and electrostatics (es)], I specify a downward Maxwell stress tensor (say in the x-direction) dnTEx_es on the proper boundary in the smsld application, this value has units of Pascals, or N/m^2.

So I would assume, although I'm not certain, that Fes_nTEz_emes [a solution postplot parameter for the MEMS application which I don't have] also gives units of pressure as well, and that the F which alludes to Force would be misleading. You should be able to tell by checking the units, if the solution you're given is in Newtons then you know it's a force. Have you tried using the Cross-Section Plot Parameters? Sometimes there are more variables to solve for in there than there is in just the Plot Parameters dialog box alone.

I fear that I may not have been as helpful as I wanted to be. It might help to know which COMSOL version you have, which Physics applications you are using, which solvers you use and which post plot parameters you are using (you might consider trying Cross-Section Plot Parameters or Domain Plot Parameters).

You may have no choice but to ask COMSOL tech support these questions and wait the associated 2-3 business days that follow, and hopefully 1/3 or 2/3 of your questions will be answered (or addressed in a general sense).

Good Luck!

Best regards,

Kevin

in v3.5a if you want to load a model with residual stress as inital conditions for a eigenvalue solving you must go through matlab to store your first stationary stress case and use it as a starting point for the linearisation of the eigenmode solver. In v4.1 you just store the solution and continue from there with the eigenmode solver (these are some of the reasons I have dropped v3.5a now for the newer and in my view better/more structured v4.1 (apply latest patch) that fits better my physics approach. V4 introduces the physics one by one and no longer applications with predefined mixes of physics (in fact the differences are not that many it's a question of methodology)

Finally be aware that the maxwell tensor is very mesh dependent (use a symmetricmesh along the material-air interface where you integrate the maxwell stress tensor

--

Good luck

Ivar

I have a question to you. I am simulating a particle in a micro channel and there is AC electric field in the channel. I want to calculate the forces acting on the particle. The problem is my Potential is AC and it depends on frequency . I use the coupling variables and integrate

unTEyav_emqvw+dnTEyav_emqvw

to find the force acting on it however this formulation doesnt depend on the frequency . Do you know about the frequency effect?

Thanks

Unfortunately, I am unfamiliar with the AC Power Electromagnetics Module.

Your electric potential is AC so it depends on frequency and is time dependent, but you claim that the force is not frequency-dependent:

unTEyav_emqvw+dnTEyav_emqvw

I would ask:

1) Is your frequency constant, or do you vary it in time?

2) If your simulation is time dependent, can you solve for your electric force expression as a function of time? If this is the case and if your frequency doesn't vary in time, then you can infer what the force is at different potentials as a function of time with known frequency.

That is to say, it seems that this model should be time dependent and if you can plot the electric force as a function of time then it doesn't need to be frequency-dependent. If your freqeuncy varies as a function of time, maybe you could plot the frequency vs. time and force vs. time and infer how the force varies with frequency.

Best regards,

Kevin

check also the version there were some sign errors in the first v4.0 and 4.0a "mef" but it might not be your case, repaired in last patched 4.1.0.112

--

Good luck

Ivar

First of all thanks for your reply. My problem is time dependent and i am using quasai statics time harmonic module.

I checked the equations from equation systems but i didnt see any equation related with frequency therefore; i expect to see the particle move upward when frequency is 100Mhz and move downward when 10Khz as i see from the experimental results.

However in the simulation when i change frequency nothing changes it always move upwards. I thing COMSOL is not able to solve this problem. I am using integreation of coupling variables with boundary variables I calculate

unTEyav_emqvw+dnTEyav_emqvw through the bondary and it calculates the force acting on the boundary but it doesnt change with the frequency . I appreciate if you or anybody can help me.

Thanks

and i cheked the equation system there are no relation between the frequency and maxwell stress tensor equations

Thanks

In 3D the expression of force with tensor Maxwell is :

Fx= -0.5*(Ex_es_down*Dx_es_down+Ey_es_down*Dy_es_down+Ez_es_down*Dz_es_down)*unx+ (unx*Dx_es_down+uny*Dy_es_down+unz*Dz_es_down)*Ex_es_down

Fy= -0.5*(Ex_es_down*Dx_es_down+Ey_es_down*Dy_es_down+Ez_es_down*Dz_es_down)*uny+(unx*Dx_es_down+uny*Dy_es_down+unz*Dz_es_down)*Ey_es_down

Fz= -0.5*(Ex_es_down*Dx_es_down+Ey_es_down*Dy_es_down+Ez_es_down*Dz_es_down)*unz+(unx*Dx_es_down+uny*Dy_es_down+unz*Dz_es_down)*Ez_es_down

You have to create a subdomain expression on boundary who acting forces.

You have to adapted these expressions for 4.1 version.

Good luck

Jean-Marc

do not forget that variables names and content are physics dependent, so it's not "just" to copy, but its a good starting point

--

Good luck

Ivar

I am using

Quasai-statics/In plane electric currents/time harmonic module. I need to define a electrical force acting on the boudary and the force needs to be frequecy dependent. I have a particle in the domain and this force is named as dielectrophoretic force. I am using

unTEyav_emqvw+dnTEyav_emqvw

integrated over boundary however these forces are not frequency dependent but they should be. This is the problem could you please help me.

in frequency sweep or time harmonic, normally the forces are the amplitudes & phases and not the full oscillation detail. The latter is the output of a transient time simulation. That could be the confusion. In Time harmonic COMSOL gives mostly the average values "...ave..."

--

Good luck

Ivar

am dng my proj in nanotechnology specifically in electrospinning. i would like to find out the electric field distribution between a grounded Al foil collector plate and a charged needle,dist between these two being around 20 cm..the voltage is in the range of 25kV

How do i start? am new to comsol..i was told about the electrostatics module available in comsol and that it would help me. is tat so?

thank you

that looks as a capacitor, no ?, then you ave models in the COMSOL internal model library, and on the community model exchange and elsewhere in on the website of COMSOL. Start simple and you will soon manage to make a more complex case as you want

--

Good luck

Ivar

hi,

am dng my proj in nanotechnology specifically in electrospinning. i would like to find out the electric field distribution between a grounded Al foil collector plate and a charged needle,dist between these two being around 20 cm..the voltage is in the range of 25kV

How do i start? am new to comsol..i was told about the electrostatics module available in comsol and that it would help me. is tat so?

thank you

Hi..

COMSOL do has a electrostatic module. first is u ve to design ur structure(usually keep them inside air), apply your boundary conditions like where u apply ur potential, ground. and simulate....

Try to do the example models available.. then u ll get to know how to perform...

Ranjana..

I would like to see the tutorial ....I think it will be very helpful for me...how can I access it...????

i will use same physics

Moving mesh

Electrostatic

Solid mechanics

i sure that mt structure is correct as when i calculate electrostatic analytically and put it as body load i get true results

but when calculate force and put it as body load i get very far results

so i understand that i have a certain problem in electrostatic force calculation >>> as i think that i have a mistake in setup Moving mesh section

see this topic for full problem description

www.comsol.com/community/forums/general/thread/20298/

thanks

I am facing the same problem that u faced , so kindly help me

I am doing the same thing with you, simulating the movable plate of a capacitor.

However I ve got this error message:

" Failed to find a solution.

In segregated group 2:

Very ill-conditioned preconditioner.

The relative residual is more than 1000 times larger than the relative tolerance.

Returned solution has not converged."

I dont know what this means

Could you have a look at my simulation and tell me to over come this problem?

Thank you in advance

--

^_^

Problem has just been solved

--

^_^

it would be more interesting for us to know why, so we can learn to ;)

--

Good luck

Ivar

At first , I applied very high voltage (200V), then I got that error ( I think the deformation of the plate is too much)

But I applied lower voltage ( about 30V) I dont get the error :))

I am not quite sure that the deformation of the plate relates to the preconditioner ( relative residual or relative tolerance)

--

^_^

sir, please let me know how to solve the electro static proble ,,, here is my problem

A micromachined polysilicon cantilever of length 150Âµm and a rectangular cross section of 5 Âµm width and 2 Âµm height ,with a charge 8.0*10^-15 C attached at its free end. If there is another charge of -1.0*10^-14 Cbelow the first one at a distance of 1 Âµm fixed to the substrare,as shown in fig .calculate the deflection of beam due to electrostatic attraction.

In V4 check the COMSOL equation (sub node equation, turn on in the preferences). But you can also get the list of variables in the Result section with the CNTRL - Space in the expression field, use use the <> or + icons to replace, respectively add any predefined variable name to pull from a list

--

Good luck

Ivar

I am doing most of my work in 3.5a for now since I understand it a little better.

I've attached my model, where I'm applying a voltage to a pzt_nbp material (it's the built in pzt material that i've modified just minutely).

I just want to see the mechanical properties change (displacement, etc) of the material.

I haven't included the constitutive relations yet because what i've tried to do input isn't working.

i am using a DC voltage on the entire boundary since it is easier, for now.

I am using plane strain (pn), electrostatics (es) and moving mesh (ale)

update:

i've figured out the force error only to learn that i don't have a converging solution.

Attachments:

Hello Shourie,

I managed to solve the Cantilever Beam with 3.5a without the MEMS module. Attached, are 2D and 3D Cantilever beams for 3.5a as well as a self-made Tutorial documentation with model describing explicitly how to create a similar model (different geometries and boundary constraints) for version 3.5a. As I do not have version 4.0a, I will not be able to answer any explicit questions regarding that version.

Firstly, I can tell you that the Cantilever beam requires three physics applications:

Structural Mechanics

Moving Mesh (ALE)

Electrostatics

So, by not applying Moving Mesh, that would probably explain why your model is not deflecting, or bending, due to Electrostatic force. You may wish to review the online COMSOL pdf documentation explaining how to create the 2D and 3D cantilever beams, however, they only apply for verison 3.5a. You will need to make any necessary modifications for the model to solve with version 4.0a, and contact COMSOL tech support for advice, accordingly.

Basically, the key details in order to solve the Cantilever beam are (as far as version 3.5a goes):

1) Electrostatics app. must be in the frame containing Moving Mesh (ALE)

2) All app.s (Struct. Mech., moving mesh, electrostatics) must have proper Physics Properties settings

3) Boundary and subdomain settings must be properly specified in all 3 app.s.

The Moving Mesh constraints may sometimes be the hardest to specify, in general, use predefined quantities: u,v, w defining x,y, z variable deformations.

Best regards,

Kevin

Hi all,

I would like to revive this thread.

I successfully executed Kevin's model 3DCantileverBeam.mph on COMSOL 4.1. I only had to modify the force variables. In 4.1 they are called es.unTx, es.unTy, es.unTz. The stationary study works fine.

Now I would like to calculate the eigenfrequencies of the beam under bias (i.e. electrostatic interaction between the beam and the ground electrode). In Solid Mechanics the electrostatic forces are defined as a Boundary Load. I hope this provides the coupling between the two interfaces?

But the Eigenfrequency Study fails ("Undefined value found. - Detail: Undefined value found in the stiffness matrix.").

Does anybody has a clue where my mistake may be?

Thanks!

rapidshare.com/files/1449448277/3DCantileverBeam_mod.mph

(Unfortunately I couldn't upload the file in the forum because of the size limitation.)

Note that while COMSOL employees may participate in the discussion forum, COMSOL^{®} software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team.

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