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Making a 3D system translationally invariant?
Posted 24.06.2014, 04:53 GMT-4 Geometry, Modeling Tools & Definitions, Parameters, Variables, & Functions, Structural Mechanics Version 4.2a 5 Replies
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Hi,
I have this simple question:
I have a COMSOL model for a physical problem (say a structural mechanics problem)
defined on a 3D prismatic body (say a cylinder with axis coinciding with Z axis).
I want to make this body represent a slice of an infinitely extended translationally invariant
system (therefore the length of my simulated 3D cylinder is arbitrary, but not zero!)
Of course the boundary conditions that I want to apply must also be compatible with
the translational invariance .
Is there any clean way to force my dependent variables (say displacements) to be
EXACTLY independent of the z-coordinate?
My initial guess was to mesh the length of the cylinder with a single element, and
then take periodic boundary conditions between the top and bottom ends
of the cylinder.
Unfortunately the results show indeed equal values of the displacement at the ends of the cylinder
but also some remanent z- dependence along the length of the cylinder, that does not
comply with the desired translational invariance.
Of course, I am perfectly aware that this kind of problem could be best treated by using
a 2D model for the cross section, but for reasons long to explain here, I prefer to implement
it as a 3D problem.
So, any clue on forcing the z-independence in a 3D model?
I would be extremely grateful.
Regards,
Alberto.
I have this simple question:
I have a COMSOL model for a physical problem (say a structural mechanics problem)
defined on a 3D prismatic body (say a cylinder with axis coinciding with Z axis).
I want to make this body represent a slice of an infinitely extended translationally invariant
system (therefore the length of my simulated 3D cylinder is arbitrary, but not zero!)
Of course the boundary conditions that I want to apply must also be compatible with
the translational invariance .
Is there any clean way to force my dependent variables (say displacements) to be
EXACTLY independent of the z-coordinate?
My initial guess was to mesh the length of the cylinder with a single element, and
then take periodic boundary conditions between the top and bottom ends
of the cylinder.
Unfortunately the results show indeed equal values of the displacement at the ends of the cylinder
but also some remanent z- dependence along the length of the cylinder, that does not
comply with the desired translational invariance.
Of course, I am perfectly aware that this kind of problem could be best treated by using
a 2D model for the cross section, but for reasons long to explain here, I prefer to implement
it as a 3D problem.
So, any clue on forcing the z-independence in a 3D model?
I would be extremely grateful.
Regards,
Alberto.
5 Replies Last Post 26.06.2014, 04:16 GMT-4
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Posted:
1 decade ago
Hi Alberto,
It would help if you could elaborate on why you don't want to do a 2D analysis.
My guess is that you want to couple the result of this mechanical analysis to another problem that cannot be reduced to 2D. If that's the case, one suggestion would be to solve the mechanical problem in 2D and use a component coupling to extrude it onto the 3D geometry where the second problem is set up.
This would save you computational time and memory compared to doing an unnecessary 3D analysis.
Best regards,
Jeff
It would help if you could elaborate on why you don't want to do a 2D analysis.
My guess is that you want to couple the result of this mechanical analysis to another problem that cannot be reduced to 2D. If that's the case, one suggestion would be to solve the mechanical problem in 2D and use a component coupling to extrude it onto the 3D geometry where the second problem is set up.
This would save you computational time and memory compared to doing an unnecessary 3D analysis.
Best regards,
Jeff
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Posted:
1 decade ago
Hi Jeff,
thanks for your interest.
No, the reason for my request is not what you have guessed.
I will explain it in more detail:
As you know, the 2D structural mechanics models intended
for the simulation of traslationally invariant systems assume the
"plane strain approximation", i. e., assume
the displacements to follow the pattern: u(x,y), and v(x,y) and w=0.
And, accordingly, its implementation in COMSOL does not use the
dependent variable w.
However, this restriction does not exhaust the compatible 2D elasticity
problems. I have worked out the general case and I want to implement it
in COMSOL, but that general case allows for a z-displacement w(x,y) (so-called
warping function), and therefore I need to dispose in COMSOL of the dependent
variable w. Since it is not accessible in 2D models, I have moved to a 3D model,
where one has dependent variables (u,v,w), and tried to force the (x,y) dependence
by the means described in my previous post, but so far I still obtain a remanent
z-dependence in the results.
So my question remains alive:
Is there any procedure to force the dependent variables (in this case the
displacements) in a 3D model to be EXACTLY independent of the z-coordinate?
I would really appreciate any comment or help.
Regards,
Alberto.
thanks for your interest.
No, the reason for my request is not what you have guessed.
I will explain it in more detail:
As you know, the 2D structural mechanics models intended
for the simulation of traslationally invariant systems assume the
"plane strain approximation", i. e., assume
the displacements to follow the pattern: u(x,y), and v(x,y) and w=0.
And, accordingly, its implementation in COMSOL does not use the
dependent variable w.
However, this restriction does not exhaust the compatible 2D elasticity
problems. I have worked out the general case and I want to implement it
in COMSOL, but that general case allows for a z-displacement w(x,y) (so-called
warping function), and therefore I need to dispose in COMSOL of the dependent
variable w. Since it is not accessible in 2D models, I have moved to a 3D model,
where one has dependent variables (u,v,w), and tried to force the (x,y) dependence
by the means described in my previous post, but so far I still obtain a remanent
z-dependence in the results.
So my question remains alive:
Is there any procedure to force the dependent variables (in this case the
displacements) in a 3D model to be EXACTLY independent of the z-coordinate?
I would really appreciate any comment or help.
Regards,
Alberto.
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Posted:
1 decade ago
Thanks for the clarification. But then I don't get why you wouldn't set up the problem for u, v, and w in 2D. Have you looked into using what comsolites refer to as "equation-based modeling"?
Jeff
PS: BTW COMSOL can also tackle the plain stress situation.
Jeff
PS: BTW COMSOL can also tackle the plain stress situation.
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Posted:
1 decade ago
Thanks for the clarification. But then I don't get why you wouldn't set up the problem for u, v, and w in 2D. Have you looked into using what comsolites refer to as "equation-based modeling"?
Jeff
PS: BTW COMSOL can also tackle the plain stress situation.
Uff! It is an option, it crossed my mind at some point, but it would amount to program from
scratch the whole elastic continuum theory by using "equation-based modeling", really
a huge task. I would rather prefer to benefit from the formalism already implemented
in the Structural Mechanics module.
I wonder why the COMSOL people didnt let open the option to work with the w variable
in the 2D models. It doesn't seem to be a great complication and it would make the modeling
more flexible.
Unfortunately the assumptions of the "plane stress approximation" are also too
restricted for my purposes.
Regards,
Alberto.
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Posted:
1 decade ago
Hi,
It seems to me that your first approach with the periodic conditions should be appropriate. Could you please post the model, so that we can see the what happens?
There are some conditions with nonzero w which sometimes are called 'Generalized Plane Strain'. An example of such a model is stress_optical_generalized in the Model Library. In that model, the 2D plane strain is augmented by an out-of-plane deformation.
By the way, if you are looking for computing the warping of a beam, have you checked out the Beam Cross Section physics interface? It is a 2D interface, where the warping function is defined mathematically.
Regards,
Henrik
It seems to me that your first approach with the periodic conditions should be appropriate. Could you please post the model, so that we can see the what happens?
There are some conditions with nonzero w which sometimes are called 'Generalized Plane Strain'. An example of such a model is stress_optical_generalized in the Model Library. In that model, the 2D plane strain is augmented by an out-of-plane deformation.
By the way, if you are looking for computing the warping of a beam, have you checked out the Beam Cross Section physics interface? It is a 2D interface, where the warping function is defined mathematically.
Regards,
Henrik