Illustrative: FE Stress Singularity Misinterpreted as Failure
How a point constraint produced a mesh-dependent stress singularity that was misinterpreted as a real stress concentration — the danger of trusting peak nodal stress without checking convergence.
Case type
Illustrative analysis failure. This case demonstrates the well-known FEA pitfall of stress singularities at point constraints and sharp re-entrant corners.
Illustrative analysis failure. The mechanism — mesh-dependent stress singularity misinterpreted as a real stress concentration — is a classic FEA modelling error documented in FEA best-practice literature.
1. The system or structure
A bracket component analysed by linear static FEA. The bracket has a bolted attachment at one end and a loaded lug at the other. The FEA model used a single node constraint at the bolt hole to represent the fixed boundary.
2. What failed?
No physical failure occurred. The failure was an engineering decision: the analyst reported a peak stress of 850 MPa at the constraint node — above the material yield strength of 470 MPa — and concluded that the bracket was under-designed. A redesign was initiated that added unnecessary mass. Subsequent investigation showed the peak stress was a singularity artefact.
3. The failure of analysis
The mechanism is a numerical stress singularity at a point constraint.
- Point constraint: a single node fixed at the bolt hole creates a reaction force at a single point. In continuum mechanics, a point load produces infinite stress at the point (the Boussinesq solution)
- Mesh dependence: as the mesh is refined around the constrained node, the peak stress increases without bound. This is the hallmark of a singularity
- Three mesh refinements: 4 mm mesh → 470 MPa; 2 mm mesh → 620 MPa; 1 mm mesh → 850 MPa. The stress is diverging — not converging
- Correct approach: distribute the constraint over the bolt hole surface using coupling or contact, then extract stress at a distance from the constraint (St Venant’s principle)
4. Why did it happen?
- Physical cause: none — the component was adequately designed
- Contributing factor: the analyst used a point constraint without recognising the singularity risk
- Contributing factor: no mesh convergence study was performed — the analyst accepted the first mesh result
- Contributing factor: the peak stress was at a constraint node, not a physical feature — it was a boundary condition artefact
9. Engineering lessons
- A point constraint or point load produces a stress singularity — the stress is mesh-dependent and does not converge
- Always perform a mesh convergence study: refine the mesh and check whether the stress of interest converges or diverges
- Distribute constraints over a physical surface (coupling, contact, or bearing pressure) rather than at a single node
- Distinguish between a real stress concentration (converges with mesh refinement) and a singularity (diverges)
- Do not report peak stress at a constraint or load application point as a design stress