Singularities
Recognise and correctly handle locations of theoretically infinite stress.
Singularities are locations with theoretically infinite stress — a mathematical artefact of the FEM formulation, not a real physical stress. Knowing how to recognise and handle them is essential for correct result interpretation.
Recognising singularities
Typical locations:
- Point loads or point supports
- Sharp re-entrant corners (90° notches with no fillet)
- Transitions between boundary conditions
If stress keeps increasing as you refine the mesh instead of converging to a stable value, you're looking at a singularity — not a real stress concentration.
How to handle them
- Evaluate stresses away from the singularity
- Model fillets instead of sharp corners
- Use surface loads instead of point loads
- Use submodelling for local detail analysis
Singularity vs. stress concentration
A stress concentration (like a hole in a plate) does not produce a singularity. The stress at the hole edge converges to a finite value as the mesh is refined. This is why the plate-with-hole example is a useful validation case — it has a real, measurable stress concentration but no singularity.
A singularity at a sharp corner, by contrast, grows without limit as the mesh is refined. The FEM solution is mathematically correct — the geometry simply cannot be modelled that way in practice.