Choosing element size
Starting mesh densities for slabs, walls and rafts, and the convergence test that decides whether a mesh is fine enough.
Meshing 3 min read
There is no universally correct element size, only a mesh fine enough for the quantity you intend to quote. That is a different question for deflection than for a peak moment next to a column.
Start with the span
A reasonable first mesh divides the shorter span of a plate into 8 to 12 elements. That is usually enough for global behaviour (deflections and span moments) and not enough for local peaks.
| What you need | Starting density |
|---|---|
| Deflection of a slab | 8–10 elements across the shorter span |
| Span moments | 10–12 across the shorter span |
| Moments at a column face | Elements of about the slab depth near the face; smaller ones only sharpen the singularity |
| Shear wall, global stiffness | 6–8 across the length, at least 1 per storey |
| Wall around an opening | 4+ elements between the opening and the nearest edge |
| Raft on elastic foundation | 10+ across the shorter dimension, refined under columns |
The convergence test
This is the only argument that settles the question:
- Solve with your starting mesh. Record the governing quantity: the deflection, the moment, whatever you will actually quote.
- Halve the element size. Solve again and record it again.
- Compare using the table below.
| Change between meshes | Interpretation |
|---|---|
| Under about 2% | Converged. Use the finer result and stop. |
| 2–10% | Not there yet. Halve again. |
| Over 10%, still growing | Either far from converged, or you are reading a singularity. |
| Growing without limit each time | A singularity. Refining will never converge (see below). |
Displacements converge from below, because a displacement-based mesh is stiffer than the structure it models. Stresses have no bound in either direction, and peak values usually grow as you refine, so a coarse mesh is not a conservative one.
Singularities: where refinement never helps
Some results do not converge because the underlying elastic solution is infinite there:
- Point supports in a plate: the moment grows without limit as the mesh refines.
- Point loads on a plate, for the same reason.
- Re-entrant corners: an internal corner with zero radius.
The peak at these locations is an artefact of the idealisation, not a load effect. Instead:
- Read the moment at the face of the support, not at the node.
- Spread the support over its real bearing area: a patch or a small rigid region.
- Integrate the moment across a design strip instead of reading a nodal peak. This is what the codes assume anyway.
Aspect ratio and shape
Element count is not the whole story. Keep elements close to square: aspect ratios beyond about 1:3 degrade accuracy in bending, and beyond 1:5 the results are not worth quoting. A 6 × 6 m panel meshed 12 along and 3 across (36 elements, 1:4) is worse than 6 by 6 (36 elements, square): the same count, spent worse. See Mesh quality checks.
Cost
Solution time grows faster than linearly with degrees of freedom, so halving element size in a plate multiplies element count by four and solution time by more.
Model and iterate on a coarse mesh, then refine once for the run you report.
Reporting
State the element size used, and that a convergence check was performed, with its result. "10 elements across the span; halving changed the peak sagging moment by 1.4%" ends a category of review comment before it is written.
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