MacNeal-Harder rectangular plate
Static (shells)PASS · 0.83%Rectangular plate/shell benchmark family with aspect ratios 1 and 5, in simply-supported and clamped variants, under either uniform pressure or a concentrated center load. Center-point deflection is compared against a normalized coefficient table, making this a classical check against plate-bending locking and load-application errors.Rectangular plate/shell benchmark family with aspect ratios 1 and 5, in simply-supported and clamped variants, under either uniform pressure or a concentrated center load. Center-point deflection is compared against a normalized coefficient table, making this… show full text
- Tolerance:
- 5%
Problem statement
- Geometry
- Flat rectangular plate, evaluated at aspect ratios 1:1 and 5:1, meshed with shell elements.
- Material
- Isotropic elastic material as defined by the MacNeal-Harder problem set.
- Boundary conditions
- Simply-supported and clamped edge variants; loading is either a uniform transverse pressure or a concentrated point load at the plate center.
- Measured quantity
- Normalized center-point displacement coefficient, checked against the MacNeal-Harder reference table: uniform pressure cases 4.062, 12.97, 1.26, 2.56; concentrated-load cases 11.60, 16.96, 5.60, 7.23 (four combinations of aspect ratio and support condition per load type).
Results comparison
| Reference value | MacNeal-Harder coefficients: pressure 4.062/12.97/1.26/2.56·10⁻³force 11.60/16.96/5.60/7.23·10⁻³ |
| Our result | 4.065·10⁻³, 12.895·10⁻³, 1.264·10⁻³, 2.567·10⁻³, 11.612·10⁻³, 16.922·10⁻³, 5.576·10⁻³, 7.170·10⁻³ |
| Deviation | 0.83% |
| Tolerance | 5% |
| Status | PASS · 0.83% |
| Element family | Shell element |
| Mesh details | MITC4 shells, 16×16 (1:1) and 80×16 (5:1), t/a=0.01, all 8 MacNeal-Harder combinations |
Updated: 2026-07-10 · WebCAE solver