Results.
| Example | Reference | Records | Largest deviation |
|---|---|---|---|
| Simply supported square plate, uniaxial compression | Published source | 1 | 1.36% |
| Simply supported square plate, equal biaxial compression | Published source | 1 | 1.36% |
Problem. In a shell the geometric stiffness comes from the membrane forces. A square plate simply supported on four edges is tested under uniaxial and equal biaxial compression.
Reference document. Timoshenko & Gere, Theory of Elastic Stability, chapter nine, is used.
The critical membrane force of a square plate simply supported on all four edges is given by these relations for uniaxial and biaxial compression.
Numerical model. The plate is modelled with ten by ten quadrilateral shell elements, and only the vertical translation is held on the edges. In the uniaxial case the in-plane restraint is given at a single node, so the Poisson expansion of the edge is not restrained.
Simply supported square plate, uniaxial compression
Parameters. mesh = 10×10 · b = 4 · t = 0.02
Published source. Timoshenko & Gere, with the coefficient taken as 4 for a square plate
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Critical membrane force | 361.524 | 366.423 | 1.36% |
Simply supported square plate, equal biaxial compression
Parameters. mesh = 10×10 · b = 4 · t = 0.02
Published source. Timoshenko & Gere, for a square plate under biaxial compression
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Critical membrane force | 180.762 | 183.212 | 1.36% |