Singularities

A singularity is a location with theoretically infinite stress. It is not a calculation error and not an artefact of the FEM: at that location the FEM faithfully reproduces what linear elasticity theory predicts. The artefact lies in the idealised assumptions. Knowing how to recognise and handle singularities is essential for correct result interpretation.

What is a stress singularity?

An ideally sharp corner has no length scale, and a purely linear-elastic material never yields; together they drive the computed stress to infinity. A real component always has at least a small fillet, and a real material yields or cracks before the stress becomes infinite. The infinite value is therefore not a real physical stress, but a consequence of the model idealisation.

For the convergence study this means: at a singularity the estimated error still decreases, but only very slowly, while the peak stress at the point itself keeps rising with every refinement. Refining further does not give you a "more correct" value there, only a higher one.

Where they occur

Typical locations:

• Sharp re-entrant corners (notches with no fillet)
• Edges and transitions of fixed supports (a jump from finite to infinite stiffness)

Singularity or stress concentration?

A rising stress alone is not yet a singularity. Even at a genuine stress concentration the stress can rise across iterations, because it approaches its finite value from below. What matters is not whether the value rises, but how the jumps between refinements behave: if they shrink, the stress converges to a finite value, that is a stress concentration. If they stay the same size or grow, the stress runs on without limit, that is a singularity.

Handling singularities

• Evaluate stresses away from the singularity
• Model fillets instead of sharp corners; the stress then becomes finite and converges
• For support singularities, check whether the idealised rigid support is realistic in the first place