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3.5a>Struct. Mech.>Shell Mode>Rigid Boundaries with displacement

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Hello,

Model:
I'm attempting to model biaxial compression using version 3.5a on a thin sheet with a large aspect ratio:

X = 3 microns
Y = 5 microns
Z = 0.34 nanometers

And apply inward stress of 50 GigaPascals on both X-Z and Y-Z surfaces (namely, the 4 edges of the rectangular sheet plane).

Using the Shell Mode, I created a surface plane (X-Y) and embed it into 3D and coerced to a face.

At this point, I need to apply the following constraints:

X-edges free to deform and displace (inward)
Y-edges rigid/flat, yet free to displace inward
Z-edges free to deform and displace

The subdomain (or boundary) of the sheet itself must also be free to deform in any way.

I wish to solve for displacement of the thin sheet as a function of x,y and z (and I expect to see ripples in the z-direction).
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Question:
How can I specify rigid Y-edges that are still free to displace inward from compression?

Note: Straight Edge Constraint by Equations example on page 83 of Structural Mech. Module User's Guide does not seem to help because:

1) It maintains a rigid/straight and fixed edge in space which does not displace (I need rigid surfaces/edges which displace inward).

2) The equations use Eigenfrequency analysis and do not specify a specific, quantitative stress or pressure to be implemented to the various sides (I need to implement 50 GigaPascals inward on all 4 sides).
----

Now that I've embedded a plane into 3D Shell Mode, is there any way I can both specify rigid Y-edges and implement stress on all 4 boundaries which then displace inward?

Thanks.

~Kevin


5 Replies Last Post 8 ago 2010, 03:25 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 4 ago 2010, 03:33 GMT-4
Hi

First as you case is very symmetric you could work on only 1/4 and use symmetry conditions along the x=0 - y=0 lines, but if you do eigenmode analysis then you must combine all symmtry/antisymmetry cases something easy to get wrong, this would reduce drastically the number of degrees of freedom hence the time to calculate, and allow a denser mesh

2) I would rather use mapped mesh, but that is somewhat a question of habits, "color and taste ". Apart that shell do not accep mapped (so you need to convert them to tets, forget this one ;)

3) restraining your edges (because now they are all free) I would propose on the two parallel edges to the Y axis to state z=0 (perhaps you want all 4 with z=0 ? But this is not enough.
With shells you also have the rotation DoF's so perhaps using a prescribed displacement z=0 and thz=0 would do, it depends on your desire for your model
Another way is to divide your plate into 4 items (with interiour boundaries) along the symmetry line, and add some restrictions to the additional points you get along the lines at x=0 and y=0. Then you can restrain the central point x=0y=0 to Rx=0 Ry=0 s your centre is not moving

--
Good luck
Ivar
Hi First as you case is very symmetric you could work on only 1/4 and use symmetry conditions along the x=0 - y=0 lines, but if you do eigenmode analysis then you must combine all symmtry/antisymmetry cases something easy to get wrong, this would reduce drastically the number of degrees of freedom hence the time to calculate, and allow a denser mesh 2) I would rather use mapped mesh, but that is somewhat a question of habits, "color and taste ". Apart that shell do not accep mapped (so you need to convert them to tets, forget this one ;) 3) restraining your edges (because now they are all free) I would propose on the two parallel edges to the Y axis to state z=0 (perhaps you want all 4 with z=0 ? But this is not enough. With shells you also have the rotation DoF's so perhaps using a prescribed displacement z=0 and thz=0 would do, it depends on your desire for your model Another way is to divide your plate into 4 items (with interiour boundaries) along the symmetry line, and add some restrictions to the additional points you get along the lines at x=0 and y=0. Then you can restrain the central point x=0y=0 to Rx=0 Ry=0 s your centre is not moving -- Good luck Ivar

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Posted: 1 decade ago 6 ago 2010, 01:16 GMT-4
Hello,

I am still having great difficulty with this model. The problem is obviously the operator (me), and not the software, but I'm trying my best to understand this program and the instructions given to me.

Regarding Concern 3)
I wish for Y-parallel edges to have constraints: z = 0 and z(theta) =0 [maybe even y=0 and x(theta) = y(theta) = 0, however these cause pecuilar distortions], while I wish for X-parallel edges to have no constraints and the sheet plane to have no constraints either.

With the above constraints [Y parallel edges z = z(theta) = 0] I still observe no Z-deformation as expected (in the plane) and my postprocessing visualization shows the entire plane unexpectedly moving upward in Y-direction.

Q1: I am still confused on how I would divide my plate into 4 items as you've mentioned previously along the symmetry line [which symmetry line?].

I understand that I need to read more to familiarize myself with COMSOL lingo.

I've attached two files that both attempt to model this problem. The first attachment uses Shell application only and attempts to follow your instructions [with Y parallel edges z = z(theta) = 0], and the second attachment uses both Shell and Solid, Stress-Strain (Eigenfrequency) application and attempts to mimic documentation with straight edges (this one has error message). Both models are unsuccessful.

Q2: Would you please glance at these files and maybe give me pointers or recommendations to improve?

This would be greatly appreciated; once again, I'm trying to follow my given instructions, however I'm having great difficulty. I apologize for being a slow student.

Thank you for your time.

Best regards,
Kevin
Hello, I am still having great difficulty with this model. The problem is obviously the operator (me), and not the software, but I'm trying my best to understand this program and the instructions given to me. Regarding Concern 3) I wish for Y-parallel edges to have constraints: z = 0 and z(theta) =0 [maybe even y=0 and x(theta) = y(theta) = 0, however these cause pecuilar distortions], while I wish for X-parallel edges to have no constraints and the sheet plane to have no constraints either. With the above constraints [Y parallel edges z = z(theta) = 0] I still observe no Z-deformation as expected (in the plane) and my postprocessing visualization shows the entire plane unexpectedly moving upward in Y-direction. Q1: I am still confused on how I would divide my plate into 4 items as you've mentioned previously along the symmetry line [which symmetry line?]. I understand that I need to read more to familiarize myself with COMSOL lingo. I've attached two files that both attempt to model this problem. The first attachment uses Shell application only and attempts to follow your instructions [with Y parallel edges z = z(theta) = 0], and the second attachment uses both Shell and Solid, Stress-Strain (Eigenfrequency) application and attempts to mimic documentation with straight edges (this one has error message). Both models are unsuccessful. Q2: Would you please glance at these files and maybe give me pointers or recommendations to improve? This would be greatly appreciated; once again, I'm trying to follow my given instructions, however I'm having great difficulty. I apologize for being a slow student. Thank you for your time. Best regards, Kevin


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

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Posted: 1 decade ago 6 ago 2010, 03:40 GMT-4
Hi

I believe it's more because you need to learn many new things when you start with COMSOL, it more or less ALL physics revisited, and in a particular notation.

For me you need to get your "physics" mind first clear, then one can put that into equations, in the disorder,

to make use of the symmetry, split your big square into 4 identical shell segments with a line intersection at "(0,0)", this will give you access to a few more points that might be used to constrain the "rigid body motions".
This adds 4 "internal boundaries" so your model become slightly more complex but it's still a peace of cake for COMSOL.

Then clearly define which edges are restrained and how:
if you say your line along the "Y" axis are bloked in z=0 and Thz=0 they can still slide along Y and flex along X.
if you block the central POINT (mid position along the "Y" edge) with a restriction y=0 you will blok the sliding motion along Y and you have only a flexing (x displacement and Thy rotation thet are free). Then you need to decide if you do this for both sides along Y, only on 1 etc.

Then depending on your need you must decide (on the edges, limit the use of point constriants) which other degrees of freedom (DoF) you want to fix

Hope this makes it clearer

Note that you have the fixing of the motion of your edges, and the limitations you want to set on the reaction forces (edge forces/pressures and their direction. i.e. a symmetry edge means no displacement normal to the plane of symmetry + only normal surface forces at the plane of symmetry, the latter is a second conditions that differs a symmetry plane from a fixed displacement restriction.

Test it out on your simple model, you need to master well the rigid and flex degrees of freedom if you want to do correct structural analysis. Itwill make far easier for you


--
Good luck
Ivar
Hi I believe it's more because you need to learn many new things when you start with COMSOL, it more or less ALL physics revisited, and in a particular notation. For me you need to get your "physics" mind first clear, then one can put that into equations, in the disorder, to make use of the symmetry, split your big square into 4 identical shell segments with a line intersection at "(0,0)", this will give you access to a few more points that might be used to constrain the "rigid body motions". This adds 4 "internal boundaries" so your model become slightly more complex but it's still a peace of cake for COMSOL. Then clearly define which edges are restrained and how: if you say your line along the "Y" axis are bloked in z=0 and Thz=0 they can still slide along Y and flex along X. if you block the central POINT (mid position along the "Y" edge) with a restriction y=0 you will blok the sliding motion along Y and you have only a flexing (x displacement and Thy rotation thet are free). Then you need to decide if you do this for both sides along Y, only on 1 etc. Then depending on your need you must decide (on the edges, limit the use of point constriants) which other degrees of freedom (DoF) you want to fix Hope this makes it clearer Note that you have the fixing of the motion of your edges, and the limitations you want to set on the reaction forces (edge forces/pressures and their direction. i.e. a symmetry edge means no displacement normal to the plane of symmetry + only normal surface forces at the plane of symmetry, the latter is a second conditions that differs a symmetry plane from a fixed displacement restriction. Test it out on your simple model, you need to master well the rigid and flex degrees of freedom if you want to do correct structural analysis. Itwill make far easier for you -- Good luck Ivar

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Posted: 1 decade ago 6 ago 2010, 23:15 GMT-4
Hello,

I've tried applying the 4 boundaries about center point (0,0) as suggested, but had difficulty with that approach as it indeed seems very complicated. I did, however, use a single boundary (sheet plane) and properly applied straight edge constraints from documentation (finally, a success!), while also holding all 4 corners fixed in the Y,Z,thx,thy and thz directions, so they slide in X-direction as desired. I also kept the center point fixed (Rx = Ry = 0) to produce a behaved solution.

So I've composed a working model; I attached it to this post.

The reason I'm posting another reply is because I've only seen X and Y displacements in my solution.

Q: I was expecting to see ripples/displacement in the Z-direction. Is this possible when I only apply stresses in the X and Y normal directions? A real membrane would surely have Z-displacement, does this imply that an "ideal" membrane would have no Z-displacement? With all this said, is there a way to properly produce Z-displacement or ripples in the Z-direction?

Also, I noticed when changing my Z thickness in Shell mode: Physics>Boundary settings, I saw no difference in the solution. That is to say, for Z = 0.34 nanometers or Z = 20 meters, the solution was identical. Could this be related to my problem with seeing zero Z-displacement?

Thanks for reading.

Best regards,
Kevin
Hello, I've tried applying the 4 boundaries about center point (0,0) as suggested, but had difficulty with that approach as it indeed seems very complicated. I did, however, use a single boundary (sheet plane) and properly applied straight edge constraints from documentation (finally, a success!), while also holding all 4 corners fixed in the Y,Z,thx,thy and thz directions, so they slide in X-direction as desired. I also kept the center point fixed (Rx = Ry = 0) to produce a behaved solution. So I've composed a working model; I attached it to this post. The reason I'm posting another reply is because I've only seen X and Y displacements in my solution. Q: I was expecting to see ripples/displacement in the Z-direction. Is this possible when I only apply stresses in the X and Y normal directions? A real membrane would surely have Z-displacement, does this imply that an "ideal" membrane would have no Z-displacement? With all this said, is there a way to properly produce Z-displacement or ripples in the Z-direction? Also, I noticed when changing my Z thickness in Shell mode: Physics>Boundary settings, I saw no difference in the solution. That is to say, for Z = 0.34 nanometers or Z = 20 meters, the solution was identical. Could this be related to my problem with seeing zero Z-displacement? Thanks for reading. Best regards, Kevin


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

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Posted: 1 decade ago 8 ago 2010, 03:25 GMT-4
Hi

I tried a quick example with the shell set in 4 elements retained by the thz rotations only, I agree the edges do not remain as straight as in your case.
In my example you can turn on the gravity along Z in the Constants (remove the "0*")

I have used a 4 qudrant shell to allow to set it up in symmetry mode and to access intermediate points if needed

--
Good luck
Ivar
Hi I tried a quick example with the shell set in 4 elements retained by the thz rotations only, I agree the edges do not remain as straight as in your case. In my example you can turn on the gravity along Z in the Constants (remove the "0*") I have used a 4 qudrant shell to allow to set it up in symmetry mode and to access intermediate points if needed -- Good luck Ivar

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