Local refinement
Where to spend elements, where not to bother, and how to refine without wrecking element shape.
Meshing 2 min read
Uniform meshes are wasteful. The interesting gradients in a real structure sit in a small fraction of its area (around supports, openings and load introductions), and everywhere else a coarse mesh is exactly as accurate.
Where refinement pays
| Location | Why |
|---|---|
| Around columns supporting a flat slab | Steep moment gradient; hogging peaks are the design case |
| Corners of openings | Stress concentration, and cracking in reality |
| Load introduction points | Local bending that the global mesh smears out |
| Nodal loads on a surface | A point load on a shell is a singularity; the mesh decides what you read |
| Ribs and downstand beams | Sharp stiffness change along a line, with local bending either side |
| Supports of any kind | The gradient is highest where load leaves the structure |
| Changes of thickness | Discontinuity in stiffness |
| Re-entrant corners | Genuine concentration, though see the singularity caveat |
Where it does not
- Mid-span of a uniformly loaded slab. The moment field is smooth; extra elements buy a third decimal place.
- Uniform walls away from openings. In-plane behaviour is close to linear over the panel.
- Anywhere you read an integrated quantity (a design strip moment, a support reaction line), since integration already averages out local variation.
Refining without wrecking the mesh
The transition between fine and coarse matters as much as the fine region itself:
- Grade the transition. Going from 50 mm to 500 mm elements over one row produces badly shaped elements exactly where you are trying to be accurate. Step the size down over two or three rows.
- Keep elements close to square in the refined zone. A refined region of long thin elements is worse than a coarse region of square ones.
- Refine a region, not a line. Refining a single row of elements at a support leaves the gradient to be resolved by its coarse neighbour.
- Extend the refined zone at least one to two slab depths beyond the feature.
A worked approach for a flat slab
- Mesh the whole slab at roughly span/10.
- Refine around each column within a radius of about 1.5 times the slab depth, to about a quarter of the global size.
- Grade the transition over two rows of elements.
- Solve and check convergence. Run the convergence check on the hogging moment at one representative column.
- If it has not converged, refine the local zone only. There is rarely a reason to refine the whole slab a second time.
Refinement will not rescue a singularity
At a true point support the moment increases every time you refine, without limit. That is a sign to stop reading the nodal value, not to refine further: read the design moment at the face, or integrate across a design strip. See Choosing element size.
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