Singularity Warning
Dr.Q reports a suspected singularity or a mesh-dependent result. What it means and what to do.
If you only have 2 minutes
At sharp re-entrant corners and at the edges of fixed supports, linear elasticity theory predicts an infinitely high stress. The peak stress does not converge there: the finer the mesh, the higher the value, without limit. This is not a real stress, but a consequence of the idealised model assumptions. So do not evaluate the stress right at the point, model the real fillet or read the result slightly to the side.
Symptom
During the convergence study Dr.Q reports one or more of the following warnings (in increasing severity):
- Warning 5: a value changed under refinement by more than its previously estimated error. The first, still tentative sign that the result may not be converging as expected at some location.
- Warning 7: Dr.Q suspects a singularity at a location.
- Warning 9: Dr.Q suspected a singularity across multiple iterations and stopped the study; the returned solution is mesh-dependent.
What to do
- Evaluate the stress away from the reported location, not right at the point.
- Model a real fillet at sharp corners. The stress then becomes finite and converges.
- For support singularities, check whether the ideally rigid support is realistic at all.
Never report the peak stress at a singularity as a result. It has no physical meaning and keeps growing with every mesh refinement.
A rising stress alone, however, is not proof: a finite stress concentration can also rise across iterations. How to tell the two apart, and why Dr.Q warns conservatively, is covered in the background on singularities.