Mesh quality
Aspect ratio, skew and warping — what degrades a result, what the mesher reports, and how to tell whether the elements you are worried about matter.
Meshing 3 min read
A mesh can be fine enough and still be bad. Element shape controls how well an element reproduces the strain field it represents, and distorted elements lose accuracy long before they produce anything that looks like an error.
What the mesher reports
Each mesh comes back with a minimum and a mean element quality. Every element is a quadrilateral (the mesher does not produce triangles), so shape is the only thing to screen. A low minimum against a healthy mean means a few bad elements somewhere, which is a different problem from a uniformly poor mesh.
The measures, and where they start to hurt
| Measure | What it means | Watch beyond | Do not quote beyond |
|---|---|---|---|
| Aspect ratio | Longest side over shortest | 3 : 1 | 5 : 1 |
| Skew | Departure from 90° corner angles | 30° | 45° |
| Taper | Variation in area across the element | 0.5 | — |
| Warping | Out-of-plane twist of a quad's four nodes | 5° | 10° |
The two that matter most in practice are aspect ratio and warping.
Aspect ratio
Bending accuracy degrades quickly with elongation. An element of aspect ratio 5:1 can report a bending moment noticeably below the true value, and the contour plot still looks perfectly smooth.
Warping
A four-node quadrilateral whose corners are not coplanar is warped. Flat slabs never warp; the problem appears in curved surfaces, folded plates, ramps and anywhere a surface is meshed across a change of plane. The element corrects for warping: each node is carried onto the element's mean plane as a rigid offset, so a rigid motion strains nothing and a twisted surface converges instead of locking. The facet itself stays flat, though, and beyond about 10° of warping its approximation of the curved surface is too coarse to quote. Refine so that each element spans less curvature.
What to do about a poor element
The question is whether the poor elements are somewhere that matters:
- Locate them. Distorted elements at a boundary far from the governing result are usually acceptable.
- If they are in a region you will quote, fix them. Refine locally, adjust the surface subdivision, or change the transition.
- Re-solve and compare the governing quantity before and after. If it barely moved, the elements were not the constraint; if it moved materially, you have learned something important about the previous run.
A poor element is not an error and a clean mesh is not a correct answer. What matters is whether the numbers you are about to quote depend on the elements you are worried about.
Before reporting
- No aspect ratios above about 5:1 in regions you quote.
- No warping above 10° anywhere it carries bending.
- Unsmoothed contours checked in the governing region, and the jumps acceptable.
- A convergence check run on the final mesh, not an earlier one.
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