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Eigenfrequencies of a Thin Rectangular Plate

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Hello,

I am trying to run an eigenfrequency analysis on a thin rectangular plate. I selected a random material, Steel AISI 4340, and dimensions of 12 in. x 16 in. x 0.04 in. The boundaries along the thin part of the plate are set to fixed. The mode shapes seem to be correct, but I am getting many errors of the following type:

Error: The relative residual is greater than the relative tolerance.

Error: The relative error is greater than the relative tolerance.

I have tried two different mesh types, but I receive the same type of errors with both. The first mesh that I tired was a free tetrahedral mesh. The second type was a swept mesh that swept from surface to surface through the thinnest part of the plate. With the swept mesh, I have set the distribution of elements to various settings from 3 elements up to 15 elements.

I have attempted to check my answer using plate theory, but so far, the answers do not match. I have attached my file. Also, as a note, I do not have the structural mechanics module, and I am using the base COMSOL Multiphysics.

Does anyone know what the problem is?


10 Replies Last Post 13 juil. 2011, 08:05 UTC−4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 11 févr. 2011, 15:52 UTC−5
Hi

your shape ratio fits better for a "shell" than rather a solid volume model, or you should have a few elements across the thickness to better model the material behaviour.

I get though less than 10Hz change in the frequency if I use a free extra fine 0.48Melement mesh in 3D mode.

And if I set up a shell model, using a thickness og 0.04[in] I have again less than 1 Hz difference ! from solid (if you add a shell to your solid, do not forget to redefine the material (2), this time to apply to boundaries and not to the domains. A material definition can only be used on either domains or boundaries, but not both in present 4.0 and 4.1)

are you sure the results are that wrong ? I do not have my book on eigenfrequencies of shell with me ;)

By the way, why do you use prescribed velocity =0 on the border and not juste fixed ?

(Im running 4.1)


Your model ====== Fixed ========== Solid 0.48Melements == Shell
Eigenfrequency === Frequency (Hz) == Frequency (Hz) ======= Frequency (Hz)

78.55800 78.55790 76.80660 76.75400
132.4296 132.4296 128.8667 128.7825
189.5057 189.5057 180.7307 180.5927
224.3076 224.3076 214.5552 214.4135
238.2506 238.2506 228.7605 228.5882
323.8044 323.8044 309.8770 309.6438

--
Good luck
Ivar
Hi your shape ratio fits better for a "shell" than rather a solid volume model, or you should have a few elements across the thickness to better model the material behaviour. I get though less than 10Hz change in the frequency if I use a free extra fine 0.48Melement mesh in 3D mode. And if I set up a shell model, using a thickness og 0.04[in] I have again less than 1 Hz difference ! from solid (if you add a shell to your solid, do not forget to redefine the material (2), this time to apply to boundaries and not to the domains. A material definition can only be used on either domains or boundaries, but not both in present 4.0 and 4.1) are you sure the results are that wrong ? I do not have my book on eigenfrequencies of shell with me ;) By the way, why do you use prescribed velocity =0 on the border and not juste fixed ? (Im running 4.1) Your model ====== Fixed ========== Solid 0.48Melements == Shell Eigenfrequency === Frequency (Hz) == Frequency (Hz) ======= Frequency (Hz) 78.55800 78.55790 76.80660 76.75400 132.4296 132.4296 128.8667 128.7825 189.5057 189.5057 180.7307 180.5927 224.3076 224.3076 214.5552 214.4135 238.2506 238.2506 228.7605 228.5882 323.8044 323.8044 309.8770 309.6438 -- Good luck Ivar

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Posted: 1 decade ago 11 févr. 2011, 16:58 UTC−5
Hello Ivar,

I appreciate that you took the time to look at the model.

I am not sure that I am getting the right values. They could very well be correct. However, I was worried about it since I was getting an error during the solve (the residual / relative error issue). Also, my frequencies I got from COMSOL did not match what I was getting when I calculated them using plate vibration equations in Matlab. It seems that I need to check my hand calculations again.

I added the prescribed velocity feature, because I didn't know exactly the boundary conditions that "fixed" imposed on the plate. I wanted to make sure that both the displacement and the velocity were equal to 0. Since COMSOL provides the same answer with or without that feature selected, it seems that "fixed' is the only condition that I needed.

Thanks again.
Hello Ivar, I appreciate that you took the time to look at the model. I am not sure that I am getting the right values. They could very well be correct. However, I was worried about it since I was getting an error during the solve (the residual / relative error issue). Also, my frequencies I got from COMSOL did not match what I was getting when I calculated them using plate vibration equations in Matlab. It seems that I need to check my hand calculations again. I added the prescribed velocity feature, because I didn't know exactly the boundary conditions that "fixed" imposed on the plate. I wanted to make sure that both the displacement and the velocity were equal to 0. Since COMSOL provides the same answer with or without that feature selected, it seems that "fixed' is the only condition that I needed. Thanks again.

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

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Posted: 1 decade ago 12 févr. 2011, 01:53 UTC−5
Hi

fixed mean no motion hence also no velocity. You shoul upgrade to the latet version, the default convece settings of the solver are better tuned

--
Good luck
Ivar
Hi fixed mean no motion hence also no velocity. You shoul upgrade to the latet version, the default convece settings of the solver are better tuned -- Good luck Ivar

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Posted: 1 decade ago 15 avr. 2011, 09:41 UTC−4
I think i have a similar problem as in this discusion.

I have made the tutorial of the Structural Mechanical Module first. Now i tried it with a square plate.
The Model is imported from Solid works. I have also used a quad mesh swept over his thickness

The first few parts of the tutorial works with a huge mesh(750 elements). but now i want to do a 'frequency response' calculation. every time i get the same errors as Dustin Mathias
(Error: The relative residual is greater than the relative tolerance.

Error: The relative error is greater than the relative tolerance.)

it doesn't matter witch parameters i changed nothing happens i tried make a shell of the model but that only more worse/ more errors

I hope somebody can help me
I think i have a similar problem as in this discusion. I have made the tutorial of the Structural Mechanical Module first. Now i tried it with a square plate. The Model is imported from Solid works. I have also used a quad mesh swept over his thickness The first few parts of the tutorial works with a huge mesh(750 elements). but now i want to do a 'frequency response' calculation. every time i get the same errors as Dustin Mathias (Error: The relative residual is greater than the relative tolerance. Error: The relative error is greater than the relative tolerance.) it doesn't matter witch parameters i changed nothing happens i tried make a shell of the model but that only more worse/ more errors I hope somebody can help me


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

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Posted: 1 decade ago 15 avr. 2011, 11:06 UTC−4
Hi

first as general rule, when possible do not (start to) mix solid and shell, except if you know exactly what you are doing ;) there are many subtle issues behind, it's possible but it's delicate work, leave it for later when you mater COMSOl perfectly.

But its absolutely worth making one solid and one separate shell model and compare both. specially for cases as yours

Then my advice: delete all unwanted nodes, extra mesh etc.

Finally, if you need to get the flexing modes you need several mesh elements across the thickness, at least in 3D solid !! this is probably your biggest issue.

the warning (not an error) is an indication that you do not resolve well enough your model.

Finally I would use tri instead of quads for the surface mesh (goes quicker), at least to begin with



--
Good luck
Ivar
Hi first as general rule, when possible do not (start to) mix solid and shell, except if you know exactly what you are doing ;) there are many subtle issues behind, it's possible but it's delicate work, leave it for later when you mater COMSOl perfectly. But its absolutely worth making one solid and one separate shell model and compare both. specially for cases as yours Then my advice: delete all unwanted nodes, extra mesh etc. Finally, if you need to get the flexing modes you need several mesh elements across the thickness, at least in 3D solid !! this is probably your biggest issue. the warning (not an error) is an indication that you do not resolve well enough your model. Finally I would use tri instead of quads for the surface mesh (goes quicker), at least to begin with -- Good luck Ivar

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Posted: 1 decade ago 18 avr. 2011, 04:30 UTC−4
Thanks for the tip of the tri mesh. i have still the same problem (Error???) as before! Dependent on which Reletive tollerance i use is het one of the next mesaasges:

reletive Tollerance = 1e-3(standard)
Failed to find a solution for the initial parameter.
The relative error (X) is greater than the relative tolerance
Returned solution has not converged.


reletive Tollerance = 1e-5
Failed to find a solution for all parameters,
even when using the minimum parameter step.
The relative error (X) is greater than the relative tolerance
Returned solution has not converged.


reletive Tollerance = 1e-6
Failed to find a solution.
The relative residual (4.3e-006) is greater than the relative tolerance.
Returned solution has not converged.


I have the messages only in the Frequency Domain calculation! The staic calculation will work with the standard tollerance
Thanks for the tip of the tri mesh. i have still the same problem (Error???) as before! Dependent on which Reletive tollerance i use is het one of the next mesaasges: reletive Tollerance = 1e-3(standard) [QUOTE]Failed to find a solution for the initial parameter. The relative error (X) is greater than the relative tolerance Returned solution has not converged.[/QUOTE] reletive Tollerance = 1e-5 [QUOTE]Failed to find a solution for all parameters, even when using the minimum parameter step. The relative error (X) is greater than the relative tolerance Returned solution has not converged.[/QUOTE] reletive Tollerance = 1e-6 [QUOTE]Failed to find a solution. The relative residual (4.3e-006) is greater than the relative tolerance. Returned solution has not converged.[/QUOTE] I have the messages only in the Frequency Domain calculation! The staic calculation will work with the standard tollerance

Nagi Elabbasi Facebook Reality Labs

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Posted: 1 decade ago 23 avr. 2011, 00:14 UTC−4
It’s interesting that the solution has not converged even though you have a linear frequency domain problem. I suspect it could be due to the ill-conditioned matrices resulting from the high plate aspect ratio. Try a thicker plate to verify.

Nagi Elabbasi
Veryst Engineering
It’s interesting that the solution has not converged even though you have a linear frequency domain problem. I suspect it could be due to the ill-conditioned matrices resulting from the high plate aspect ratio. Try a thicker plate to verify. Nagi Elabbasi Veryst Engineering

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Posted: 1 decade ago 27 avr. 2011, 03:40 UTC−4
i have tried the same calculation with a thicker plate.. it works now perfect!!!
i have tried the same calculation with a thicker plate.. it works now perfect!!!

Nagi Elabbasi Facebook Reality Labs

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Posted: 1 decade ago 27 avr. 2011, 09:10 UTC−4
Good to know! So it probably was the ill-conditioning. For the thinner plate you should then try a shell only model. For the same plate aspect ratio, the matrix conditioning for shell elements is much better than for solid elements.

Nagi Elabbasi
Veryst Engineering
Good to know! So it probably was the ill-conditioning. For the thinner plate you should then try a shell only model. For the same plate aspect ratio, the matrix conditioning for shell elements is much better than for solid elements. Nagi Elabbasi Veryst Engineering

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Posted: 1 decade ago 13 juil. 2011, 08:05 UTC−4
Hello,

I have also the problem that I get the error message for my model:
Error:
Failed to find a solution:
The relative residual (63) is greater than the relative tolerance.
Returned solution has not converged.

However, this happens only on our "big" computer. When I use our older one or even desktop computer the model is solved as it should.

My question is: How does the computer used influnece comsol parameters, that on one system I get the error message above and on the other system the model runs without problems?

Thank you for your help,

Clemens
Hello, I have also the problem that I get the error message for my model: Error: Failed to find a solution: The relative residual (63) is greater than the relative tolerance. Returned solution has not converged. However, this happens only on our "big" computer. When I use our older one or even desktop computer the model is solved as it should. My question is: How does the computer used influnece comsol parameters, that on one system I get the error message above and on the other system the model runs without problems? Thank you for your help, Clemens

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