A colorful stress plot is not proof that an FEA result is correct. One of the most important numerical checks is mesh convergence: refining the mesh and observing whether the result of interest stabilizes.
Why Mesh Size Matters
Finite element models approximate a continuous physical problem using discrete elements. A coarse mesh may miss local gradients, while an unnecessarily fine mesh increases solve time and model size. The right mesh depends on geometry, material behavior, contacts, loads, and the quantity being evaluated.
Start With a Coarse Baseline
Run an initial model with a sensible global element size. Record the quantity that matters to the design: displacement, reaction force, average stress over a defined region, contact pressure, or another engineering result.
Refine Systematically
| Run | Example element size | Result of interest |
|---|---|---|
| 1 | 4 mm | 12.8 mm displacement |
| 2 | 3 mm | 13.4 mm |
| 3 | 2 mm | 13.6 mm |
| 4 | 1.5 mm | 13.7 mm |
The numbers above are illustrative. The important pattern is that the quantity of interest changes less as the mesh is refined. Define an engineering acceptance criterion appropriate to the problem instead of relying on a universal percentage.
Do Not Chase a Singular Peak Blindly
Sharp re-entrant corners, point loads, rigid constraints, and idealized contact edges can create mathematical stress concentrations. A peak value that keeps rising with mesh refinement may be a singularity rather than a useful design stress. Review the physical geometry and evaluate stress away from the singular point when appropriate.
Good Mesh Practice
- Refine around holes, fillets, contacts, and load-transfer regions.
- Use mesh controls rather than making the entire model extremely fine.
- Check element quality and distortion.
- Compare reactions with applied loads.
- Document mesh size and convergence results.
Validation Beyond Mesh
A converged solution can still be wrong if the boundary conditions, material data, contact definitions, or loads are wrong. Compare simple cases with hand calculations whenever possible. For important components, correlate the model with testing or established analytical solutions.
Conclusion
Mesh convergence is a credibility check, not a decorative step. Refine the mesh around important regions, track a clearly defined quantity, investigate singularities, and validate the physical assumptions before using FEA to make a design decision.