Rigid Body Motion in Deformable Cube 1

[RShah7]

Hi,

I am modelling uniaxial loading on a unit cube. I have applied concentrated loads on the vertices to do this. My mesh size is the same as that of the cube, which makes it a single-element model.

However, when I view the displacement results, rigid-boy motion has occurred. I cannot apply a translational BC on the nodes because I want them to be free to move. How do I preven rigid body motion then?

Thank you.

 

[eng23bio]

Hi RShah7,

I am not sure if I understand your question but I think that your problem is that you are not modelling correctly. For a uniaxial test I think the easiest and most adequate method is to take a quarter of a model and impose symmetric boundary conditions. See the attached drawing (sorry i have only paint...) and let me know if you keep having problems. But I think that you are imposing force or displacements on the for nodes of the probe and that should not work.

 

[IceBreakerSours]

Pay close attention to the physics (mechanics, in a structural problem as the one in this thread) of the problem; it has nothing to do with ABAQUS or FEA.

You need to constrain sufficient number of rigid body modes in a given problem. For example, in the image uploaded by eng23bio, there are 3 rigid body modes possible in a 2D coordinate system. However, under the applied displacement boundary condition, pinning nodes in the y direction constrains the rigid body mode, which from a numerical analysis point of view, results in a numerical singularity. [The other boundary condition in the x-direction, as pointed out by eng23bio, is to enforce symmetry]. By the way, and this comes across too many times, there is no need to constrain rotational d.o.f. anywhere in this problem because the applied displacement boundary condition will not cause any rotation. [In cases where the b.c. may cause rotation, you need to be aware of the element type. Depending on the type of element, nodes may or may not have rotational d.o.f. For example, nodes on a 2D/3D continuum/brick element do not have rotational d.o.f.]

Are you new to this forum? If so, please read these FAQ's:

http://www.eng-tips.com/faqs.cfm?fid=376

http://www.eng-tips.com/faqs.cfm?fid=1083

 

[RShah7]

Thanks a lot for your help! I will try out what eng23bio suggested.
About what IceBreakerSours said about rigid body rotation- my problem is that when I apply loads at the nodes, like I said I had done in the previous problem, rigid body rotation does occur. Even though the diplacements I have enforced don't cause the rigid body rotation (they shouldn't be causing rigid body motion either, because they are equal and opposite), it occurs because the equation [K]*{u} = {P} has more than one solution, and all the others include some sort of rigid body motion/rotation. What I was wondering was why Abaqus didn't converge to the solution it would physically converge to. I guess that is because for a static problem it just numerically solves the problem, in which case I can see why eng23bio's suggestion would work by explicitly telling it that there is symmetry in the problem.
Thanks!

 

[IceBreakerSours]

What physical phenomenon are you trying to model? Ku=f has more than one solution in, for example, buckling. If that or some similar physics is of interest, then you need a different solver (using an arc tracing method). Search for buckling in the Analysis User's Manual and look for content related to solvers.

Are you new to this forum? If so, please read these FAQ:

http://www.eng-tips.com/faqs.cfm?fid=376

http://www.eng-tips.com/faqs.cfm?fid=1083

 

[RShah7]

No, this is simple uniaxial loading. What I mean when I say that there are an infinite number of solutions for {F} = [k]*{u} is that these are just equations of equilibrium, and do nothing to prevent rigid body motion, simply because only the differences in the u's are important- basically the final shape of the cube is important. I could take that deformed cube, and put it anywhere is space, and it would still satisfy the equation. Physically this shouldn't happen, since for a cube with balanced forces acting on it, the com should not move.