Model and reference
A 3 × 5 m plate, 0.1 m thick; E = 63,000 MPa, ν = 0.2; downward pressure 10 kN/m². All edges restrain vertical translation; rotations remain free. Three in-plane restraints remove rigid motion. Constant pressure is integrated as nodal forces over each cell.
At the centre, the odd sine terms alternate in sign. We sum 100 × 100 odd terms. D = Et³ / [12(1 − ν²)]. Positive displacement below means downward.
w(a/2,b/2) = 16q/(π⁶D) Σ sin(mπ/2) sin(nπ/2) / [mn(m²/a² + n²/b²)²]
m, n = 1, 3, 5, …, 199
Series reference (mm): 1.283748
Published example (mm): 1.28375
Convergence
Compare absolute errors at equal grid subdivisions: DKT has twice as many cells, but the same nodes as MITC4. This is not a timing benchmark. MITC4 includes transverse shear; the reference is a thin-plate solution. MITC4’s error turns after 8×8; DKT is closer at 16×16.
Smaller absolute error at each grid size: 4×4: MITC4;8×8: MITC4;16×16: DKT;
Absolute-error reduction, 4×4 → 16×16: DKT: 15.78×;MITC4: 1.26×;
Difference (%): 100 × (w / w0 − 1)
Not yet
- MITC9: available in Rust, not exposed by the production web wrapper.
- Other aspect ratios, thickness sweeps, distorted meshes and moment convergence.
- Out-of-plane deformed geometry: this viewer shows the displacement contour on the flat mesh.
- Independent reviews, design certification or experimental validation.
Calculation sources
“Navier (1823)” is the requested historical benchmark label, not a verified publication date. The catalogue cites the Crossref-verified Rectangular Plates chapter (2001); the worked example is Haukaas’s exposition of Timoshenko & Woinowsky-Krieger, Article 28.
Ventsel & Krauthammer (2001), Rectangular Plates
Terje Haukaas, Navier’s Solution for Uniform Load (2018), pp. 1–3