Results.
| Example | Reference | Records | Largest deviation |
|---|---|---|---|
| Simply supported square plate, thin plate limit, triangular mesh | Published source | 4 | 9.81% |
| Thick plate, shear deformation | Published source | 3 | 0.393% |
| Clamped square plate, uniformly distributed load, triangular mesh | Published source | 1 | 0.710% |
| Stiffness difference between triangular and quadrilateral elements on the same node grid | Independent calculation | 1 | 1.02% |
Problem. The triangular shell element is tested on the same three plate cases as the quadrilateral. Triangular and quadrilateral discretisations on the same node grid are also compared.
Reference document. The simply supported plate uses the Navier series, the clamped plate Timoshenko & Woinowsky-Krieger Table 35, and the thick plate the Mindlin-Kirchhoff relation. For the triangle against quadrilateral comparison there is no outside reference; two discretisations of the same problem are compared.
The centre deflection of a clamped square plate is taken from Timoshenko & Woinowsky-Krieger Table 35.
Numerical model. The plate is modelled with triangular shell elements (MITC3+), each quadrilateral cell split into two triangles. The support conditions match the quadrilateral section.
Simply supported square plate, thin plate limit, triangular mesh
Published source. Navier series with sixty terms, Kirchhoff plate theory
| Quantity | Condition | Reference | Computed | Deviation |
|---|---|---|---|---|
| Centre deflection | mesh = 4×4×2 triangles · t/a = 0.001 | -0.112316 | -0.101293 | 9.81% |
| Centre deflection | mesh = 8×8×2 triangles · t/a = 0.001 | -0.112316 | -0.110572 | 1.55% |
| Centre deflection | mesh = 16×16×2 triangles · t/a = 0.001 | -0.112316 | -0.112438 | 0.108% |
| Centre deflection | mesh = 32×32×2 triangles · t/a = 0.001 | -0.112316 | -0.112634 | 0.283% |
Thick plate, shear deformation
Published source. The Navier deflection times the Mindlin-Kirchhoff relation
| Quantity | Condition | Reference | Computed | Deviation |
|---|---|---|---|---|
| Centre deflection | mesh = 24×24×2 triangles · t/a = 0.01 · support = uz and edge-normal rotation held | -0.112366 | -0.111925 | 0.393% |
| Centre deflection | mesh = 24×24×2 triangles · t/a = 0.025 · support = uz and edge-normal rotation held | -0.00720856 | -0.00718115 | 0.380% |
| Centre deflection | mesh = 24×24×2 triangles · t/a = 0.05 · support = uz and edge-normal rotation held | -0.000908708 | -0.000905359 | 0.369% |
Clamped square plate, uniformly distributed load, triangular mesh
Parameters. mesh = 16×16×2 triangles · t/a = 0.025
Published source. Timoshenko & Woinowsky-Krieger, Theory of Plates and Shells, Table 35
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Centre deflection | -0.00222953 | -0.00224537 | 0.710% |
Stiffness difference between triangular and quadrilateral elements on the same node grid
Parameters. mesh = 8×8 · t/a = 0.001
Independent calculation. Two different discretisations of the same problem are compared
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Quadrilateral deflection as a ratio of the triangular one | 1 | 1.01022 | 1.02% |
Note. A ratio above one means the triangle is stiffer. The tolerance is a regression band.