1. Reference problem#

1.1. Geometry#

We consider a hemisphere divided into 4 pieces (by symmetry around the equatorial planes).

_images/100002010000032D0000022BAD420090D7F3AB79.png

Radius of the sphere: \(R=10m\)

Thickness of the sphere: \(t=\mathrm{0,04}m\)

The hole is open: 18°

1.2. Material properties#

The sphere is made of aluminum. The material is linear isotropic elastic.

\(E\mathrm{=}6.825{10}^{7}\mathit{Pa}\), \(\nu \mathrm{=}0.3\)

1.3. Boundary conditions and loads#

On a quarter of the hemisphere, symmetry conditions are applied on all three planes (which are therefore QUAD4):

  • Plan \((12)\): \(\mathit{DZ}=0\);

  • Plan \((13)\): \(\mathit{DY}=0\);

  • Plan \((23)\): \(\mathit{DX}=0\).

Moreover, a loading in the form of a point force is applied to points A and B such as:

  • Point A: \(\mathit{FX}=\mathrm{0,5}N\);

  • Point B: \(\mathit{FY}=-\mathrm{0,5}N\).