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Stress singularity

A mathematically sharp internal corner gives a theoretically infinite stress in the FEM model: the stress there grows instead of converging as the mesh is refined. The fix is to model a real fillet radius, which removes the singularity and gives a physically correct, finite stress.

\sigma \to \infty \text{ as } r \to 0

singularity at a sharp corner

Symbols

$\sigma$	computed stress at the corner	Pa
$r$	fillet radius	m

Example

Model without a fillet: $\sigma$ grows with every finer mesh.

With a real radius $r > 0$ , $\sigma$ converges to a finite value.

Growing stress under mesh refinement is a warning sign of a singularity, not a real software bug.

Practise element types, meshing and error for free →

← Mesh refinement and convergence

Part of Finite Element Method: Element types, meshing and error.