Results.
| Example | Reference | Records | Largest deviation |
|---|---|---|---|
| Simply supported square plate, locking check at the thin limit, triangular mesh | Published source | 1 | 1.50% |
| Clamped square plate, t/a = 1/1000, alternating diagonal pattern | Published source | 1 | 0.492% |
| Clamped square plate, t/a = 1/1000, fixed diagonal pattern | Published source | 1 | 0.425% |
| Clamped square plate, t/a = 1/1000, random diagonal pattern | Published source | 1 | 0.461% |
Problem. The tests check that the result on a triangular mesh does not depend on the diagonal pattern. The diagonal direction cannot be controlled in an imported mesh, so this is a condition for using the element.
Reference document. Timoshenko & Woinowsky-Krieger Table 35 is used for the clamped plate and the Kirchhoff value for the thin simply supported limit.
In the thin plate limit the centre deflection of a simply supported square plate takes this value.
Numerical model. The locking sweep uses eight by eight cells and the diagonal pattern sweep sixteen by sixteen. Alternating, fixed and random diagonal patterns are tested at a thickness ratio of one thousandth.
Simply supported square plate, locking check at the thin limit, triangular mesh
Parameters. t/a = 0.001 · mesh = 8×8×2 triangles
Published source. Kirchhoff plate theory, simply supported square plate
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Centre deflection | -0.112251 | -0.110572 | 1.50% |
Clamped square plate, t/a = 1/1000, alternating diagonal pattern
Parameters. mesh = 16×16×2 triangles · diagonal pattern = alternating
Published source. Timoshenko & Woinowsky-Krieger, Table 35
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Centre deflection as a ratio of the Timoshenko solution | 1 | 0.995076 | 0.492% |
Clamped square plate, t/a = 1/1000, fixed diagonal pattern
Parameters. mesh = 16×16×2 triangles · diagonal pattern = fixed
Published source. Timoshenko & Woinowsky-Krieger, Table 35
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Centre deflection as a ratio of the Timoshenko solution | 1 | 0.995746 | 0.425% |
Clamped square plate, t/a = 1/1000, random diagonal pattern
Parameters. mesh = 16×16×2 triangles · diagonal pattern = random
Published source. Timoshenko & Woinowsky-Krieger, Table 35
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Centre deflection as a ratio of the Timoshenko solution | 1 | 0.995394 | 0.461% |