when I use mesh size 0.001 the finite element results resembles theoritical results as I get 6.28 radians torsion angle( due to the exerted moment )that was obtained by theory before.but when I use mesh size 0.0005 I get another angle. I attached the abaqus file and theoritical formulation.
You have to perform mesh sensitivity analysis. Finer mesh provides better solution and is more acceptable. The difference with theoretical results may be due to material and geometrical non linearity. Or may be due to improper contact. Try changing material behavior and failure criteria.
According to .cae, torsional moment at step end is equal to 0.0046. Corresponding exact value of torsional angle is 0.1586. Abaqus gives the next results:
For mesh size 0.001 (approximate global size for seeding) torsional angle is 0.1486,
for mesh size 0.0005 torsional angle is 0.1489,
for mesh size 0.0002 torsional angle is 0.1502.
I think that exact solution can’t be achieved because actual loading corresponds to theoretical only in integral sense.
Masoud,
When you compare model responses, you should be sure that both models share the same hypothesis.
Behind the formula you shared there are assumptions that may (or not) be shared by your finite element model.
This is source of discrepancies that you cannot eliminate refining the mesh.
Regards
Simone Coniglio
The exact solution implies deplanation of all cross-sections, whereas this FE model is more stiff due to encastre BC at the fixed end and rigid body constraint at the loaded end.
thank you guys for your response, I concluded that there is no doubt when you make the mesh finer you will receive more precise answer,and finally it converges.the problem was in theoretical solution and solved .at last the finite element and theoretical results coincided.
best regards.
Sometimes too finer a mesh could result in over-accumulation of errors. Each finite element comes with its own share of approximation (and hence corresponding error as well). So, there is a balance between mesh size and problem physics. For example, in a stress singularity problem, such as sharp crack, no amount of fine mesh can do the job (which, incidentally, prompted people like Barsoum to come-up with quarter point elements, etc.). In a way, capturing stress gradients is an objective of p-element. However, for regular h elements that we all use, over enthusiasm leads to higher mesh densities, but in the absence of corresponding arithmetic precision, the numerical computations can lead to cascading of errors and sometimes even run-away chains.
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