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Solid Mechanics, Cantilever Displacement Constraints

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Hi

I am trying to control the free end of a 2D cantilever problem whereby the end slope is not allowed to change but where axial displacement can take place ...classical plane sections remain plane type thing.

I have tried using 'prescribed displacements' where u=o and roller constraints but these are preventing axial displacements. I would just like to control the end slope.

Any basic step by step guidance welcomed (new user to COMSOL 5).

Thanks in advance.
CG

5 Replies Last Post Jan 20, 2015, 10:24 a.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 9 years ago Jan 19, 2015, 1:36 p.m. EST
Hi Blighty

If I read you correct, you have a long prismatic beam, fixed at one end and you want to apply forces and moments at the other section end to give it a given shape.

As you say, if you apply a roller condition on the far end, the beam must stretch (in length) while it displaced perpendicular to the beam axis. This is not most intuitive, but it is what happens when you use linear geometry, so I would suggest a) you turn on the geometry non-linear geometry tick in the Solver node, this will turn on the coupled terms in the equations and better follow the true deformations of your beam under "large" displacements, then b) you apply controlled Force and Moment loads

Now either you know the displacements, and you might impose them on the end surface (or via a "Rigid Connector" but this might add extra stress that are not fully "physical" too), or you apply Forces and Moments, and adapt these to get the desired displacement. The later is rather straight-forward in COMSOL if you add some equations:
define a force a moment and their directions as global dependent variables and define a constraint on the beam end "Boundry normal" such that you have your "direction and displacements" (the latter can be though of as a "Definition Coupling Average Operator") and then you dirve the FOrce and moment by the respective displacement and direction desired as equations 0 = average(w) - desired_W_value

--
Good luck
Ivar
Hi Blighty If I read you correct, you have a long prismatic beam, fixed at one end and you want to apply forces and moments at the other section end to give it a given shape. As you say, if you apply a roller condition on the far end, the beam must stretch (in length) while it displaced perpendicular to the beam axis. This is not most intuitive, but it is what happens when you use linear geometry, so I would suggest a) you turn on the geometry non-linear geometry tick in the Solver node, this will turn on the coupled terms in the equations and better follow the true deformations of your beam under "large" displacements, then b) you apply controlled Force and Moment loads Now either you know the displacements, and you might impose them on the end surface (or via a "Rigid Connector" but this might add extra stress that are not fully "physical" too), or you apply Forces and Moments, and adapt these to get the desired displacement. The later is rather straight-forward in COMSOL if you add some equations: define a force a moment and their directions as global dependent variables and define a constraint on the beam end "Boundry normal" such that you have your "direction and displacements" (the latter can be though of as a "Definition Coupling Average Operator") and then you dirve the FOrce and moment by the respective displacement and direction desired as equations 0 = average(w) - desired_W_value -- Good luck Ivar

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Posted: 9 years ago Jan 20, 2015, 4:05 a.m. EST
Hi Ivar

Thank you for your message.

I was perhaps incorrect mentioning "plane sections remaining plane" ...indeed I have a small displacement / linear problem involving a horizontal encastre beam (1 metre length beam, max 5mm end deflection and stresses well below yield) with a vertical end load only.

Under load the beam naturally deflects and the end face exhibits a slope Rz which I would like to constrain to zero. In effect I am trying to have a "Roller" type constraint on the end but one that will allow axial displacements (if this is possible) ...I'm going to try the same problem in Nastran today for comparison.

I don't know the displacements ...using some form of rigid connection across the end of the beam with an Rz constraint applied but allowing u and v displacements is what I am looking for.

Thanks again for your assistance.
Hi Ivar Thank you for your message. I was perhaps incorrect mentioning "plane sections remaining plane" ...indeed I have a small displacement / linear problem involving a horizontal encastre beam (1 metre length beam, max 5mm end deflection and stresses well below yield) with a vertical end load only. Under load the beam naturally deflects and the end face exhibits a slope Rz which I would like to constrain to zero. In effect I am trying to have a "Roller" type constraint on the end but one that will allow axial displacements (if this is possible) ...I'm going to try the same problem in Nastran today for comparison. I don't know the displacements ...using some form of rigid connection across the end of the beam with an Rz constraint applied but allowing u and v displacements is what I am looking for. Thanks again for your assistance.

Nagi Elabbasi Facebook Reality Labs

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Posted: 9 years ago Jan 20, 2015, 8:09 a.m. EST
If you model the beam using the “Beam” physics interface you will have the option to prescribe a zero rotation at the end and keep the translations free. If you model it as a 2D solid body it is a little bit harder but doable. You can use rigid connectors for that.

Nagi Elabbasi
Veryst Engineering
If you model the beam using the “Beam” physics interface you will have the option to prescribe a zero rotation at the end and keep the translations free. If you model it as a 2D solid body it is a little bit harder but doable. You can use rigid connectors for that. Nagi Elabbasi Veryst Engineering

Henrik Sönnerlind COMSOL Employee

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Posted: 9 years ago Jan 20, 2015, 10:20 a.m. EST
Hi,

As long as the problem is treated as geometrically linear, a roller condition at the end will not cause an axial force. The average axial displacement is zero. You can easily verify this by using the roller constraint and integrate the axial stress.

If you incorporate geometric nonlinearity however, then the roller condition will cause significant axial stresses. You must then replace it by a condition which forces all axial displacements to be the same (but unknown). One way of doing this is shown in the Model Library model surface_resistor.

Regards,
Henrik
Hi, As long as the problem is treated as geometrically linear, a roller condition at the end will not cause an axial force. The average axial displacement is zero. You can easily verify this by using the roller constraint and integrate the axial stress. If you incorporate geometric nonlinearity however, then the roller condition will cause significant axial stresses. You must then replace it by a condition which forces all axial displacements to be the same (but unknown). One way of doing this is shown in the Model Library model surface_resistor. Regards, Henrik

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Posted: 9 years ago Jan 20, 2015, 10:24 a.m. EST
Excellent advice and very much appreciated.
Excellent advice and very much appreciated.

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