AFNOR SSLS26: Simply supported rectangular plate with bending moment

1. Problem definition

• Material properties:

  • Young's modulus, E = 1 Pa
  • Poisson ratio, nu = 0.3
  • Shear modulus, G = 80.8 GPa

• Thickness properties:

  • Thickness: 1 m

• Supports:

  • Fix TZ at B, C and D

• Loads:

  • A: FZ = -2 N, MX = 20 Nm, MY = -10 Nm
  • B: MX = 20 Nm, MY = 10 Nm
  • C: MX = -20 Nm, MY = 10 Nm
  • D: MX = -20 Nm, MY = -10 Nm

2. Songeya model

In the reference solution, shell bending is captured using the Kirchhoff–Love theory, which neglects transverse shear deformation and is therefore only suitable for thin shells. Songeya implements the DKMQ and DKMT elements, which are based on the Reissner–Mindlin formulation with discrete Kirchhoff constraints. These are general-purpose elements which capture the effects of transverse shear deformation and do not suffer from shear locking. They are suitable for both thin and thick shells. The shear effects in this problem are not negligeable. Nevertheless, to approximate the thin shell behaviour used in the reference solution, the shear modulus has been made infinitely large so that shear deformation is eliminated.

3. Results

3.1 Total deformation

4. Comparison

5. Reference

Société française des mécaniciens. (1990). Guide de validation des progiciels de calcul de structures. Afnor.