AFNOR SSLP02: Tension of perforated membrane

1. Problem definition

• Material properties:

  • Young's modulus, E = 210 GPa
  • Poisson ratio, nu = 0.25

• Thickness properties:

  • Thickness: 1 mm

2. Songeya model

The reference solution is determined analytically using the Kolosov–Muskhelishvili formulation. The assumption in this formulation is an infinitely long and wide plate with a hole and subjected to uni-directional tension. Therefore, the plate dimensions used in the numerical model must be sufficiently large so that the boundaries do not influence the stress distribution around the hole. In the initial configuration, the diameter-to-width ratio was only 0.2, which was not adequate to represent an infinite domain. To better satisfy the assumptions of the analytical solution, the plate dimensions were increased to 300 mm in height and 200 mm in width, while the hole diameter was maintained at 20 mm.

3. Results

3.1 Maps: Membrane stresses

3.1.1 Sxx

3.1.2 Syy

3.2 Cuts: Membrane stresses

3.2.1 Sxx

3.2.2 Syy

4. Comparison

5. Reference

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

Muskhelishvili, N. I. (1953). Some basic problems of the mathematical theory of elasticity (Vol. 15). Groningen: Noordhoff.