Mesh Refinement Simply Supported Beam

Hi there,

I am trying to figure out how Karamba3D works compared to other FEM software I have used.
I am a little puzzled after trying to conduct a mesh refinement analysis on a simple beam. And would appreciate a pointer to what is different in Karamba or where I am off in my line of thought.

I modelled a simply supported beam and increased the number of elements from 2 to a hundred, measuring the displacement at midspan:
image

In the plot I also visualized the analytically computed value. I am surprised that upon increasing the number of elements (line to beam) there is no conversion of my numeric solution, but already with 2 elements my solution has converged. The solution is pretty good considering that the deviation is < 2%, but the behavior after conducting this analysis I do not understand. I would expect that with increasing number of elements my solution would converge to the analytical solution.

Another point, though somewhat related, I am used to from other FEM software that geometry development and meshing are to separate processes. In Karamba they are more closely related, correct? Because with the geometry that I input into e.g. the line to beam component I define my “mesh” or beam elements.

I am also a little confused by the effect of the Length/segment slider under render settings in the model view. This does not have an influence on the results of the analysis,
simplebeam_meshrefinement.gh (64.4 KB)
correct?

Some questions, which are all somewhat related in my mind. Any response is appreciated!
Best,
Chris

Hi @ChrisH2a,
in Karamba3D it is not necessary to refine beams. The result should always be exact.

The approach in Karamba3D is based on power series integration of the beam ordinary differential equation.

Could it be that you neglected shear deformations when comparing the Karamba3D result to the hand-calculation. Here is your example with shear rigid beam elements:
simplebeam_meshrefinement_cp.gh (71.0 KB).

The Length/segment slider controls the spacing of results along beams. There is no influence on the results.

– Clemens

Good morning Clemens,

now I am glad I asked. I appreciate your response! Power series integration of FEM elements. I will have to go back to the theory for that, I do not recall this integration method.

Thank you for pointing out the issue with the shear deformation. I guess I just assumed an Euler Bernoulli beam without considering the issue of shear.

Also good to have certainty on the length/ segment slider.

Nice to keep using Karamba.

Herzliche Grüße,
Christoph