Deformation and motion that's too linear

[azirbel]

Hi,

I'm still working on bending elastic beams, but switched from 2D to 3D, which helped. I'm still working on the same fundamental problem, attempting to simulate deflection of an elastic beam when the ends are pushed toward one another. Using the same approach as in the tutorial, I've made some progress, but again would appreciate some help getting un-stuck at a few places. (I've looked for answers elsewhere, but no luck).

When I make and mesh a pre-bent beam, and then put it under some force, the beam bends fairly well as expected. Here's a mid-range force applied to the beam. The left side of the beam is anchored, while the right side is pushed toward the left side. The force is actually applied to the circular cutout in the beam, in an attempt to simulate force coming from an axis through the beam.



Two questions here: one, is there a good way to keep the hole on the right from deforming when I push on it with the force? (Before applying force, it looked like the hole on the left; the beam was just a curved beam with two holes).

The second question is more theoretical, I think. When I apply different forces on this beam, I get exactly linear motion. I don't think this should be happening, but it could be that the way I have set up the simulation (all the modeling is linear elasticity), I have forced the output to be linear. I graphed the deflections of the beam over 20 different forces, where the force applied is applied in only the horizontal direction, from the right hole toward the anchored left hole, and where the deflection is the horizontal distance between the right hole and the left:



It seems to me that the beam should deflect more when it has already deflected a lot; that the force to start the beam's deflection should be greater than the force to continue bending after, say, the deflection shown in the first picture.

Thank you very much for your help!

Alex

[hamed]

Dear Alex
The bending of the beam free end normal to its plane is quite expected since its flexural(bending) rigidity is lower in this direction in comparison to in-plane directions. In order to avoid bending of beam in this direction you can fix the back and front surfaces of the beam by means of a boundary condition like below:

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Boundary Condition 1
Target Boundaries(2) = 1 2  
Displacement 3 = 0.0
End

And your second question, as you know in linear elasticity the relation between the stress and strain is linear (i.e. S=Ee , E is the young modulus), so the relation between the force and displacement must be linear from the linear elasticity point of view. Note also that according to “bending theory of beams” the relation between the stress and force is also linear (you can check it in any books of “Mechanics of Materials”, e.x. that of Beer&Johnston ).

Regards, Hamed

[raback]

Hi Alex,

There exists an undocumented nonlinear solver as well. To take it to use change the line

Code: Select all

Procedure = "StressSolve" "StressSolver"

to

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Procedure = "ElasticSolve" "ElasticSolver"

For the basic operation these are almost equal but the StressSolver has more features built-in and the keyword conventions may vary slightly. There are also some rudimentary examples in $ELMER_HOME/tests (elasticity & fsi_beam).

-Peter

[azirbel]

Thank you both! Confining the side walls of the beam was helpful. Using ElasticSolver worked unbelievably well; all the simulations now turn out with different force vs. displacement profiles in ways that make sense.