1. Reference problem#

1.1. Geometry#

The geometry consists of two hemispheres of identical radius, a cross section of which is shown in the figure below.

_images/1000050000001C6C0000136EA235B717267D9113.svg

Given the mesh differences, the positions of the nodes \(H\) and \(I\) shown here approximately are different in the 3 models.

1.2. Material properties#

\(E=20000.\mathrm{MPa}\)

\(\nu =0.3\)

1.3. Boundary conditions and loads#

Crush imposed on the spheres:

      • \(\mathrm{DY}\) imposed \(–2\mathrm{mm}\) for the nodes of \(\mathrm{AB}\)

      • \(\mathrm{DY}\) imposed \(+2\mathit{mm}\) for the nodes of \(\mathit{CD}\)

For axisymmetric calculations:

      • \(\mathrm{DX}\) stuck on the \(\mathit{AC}\) axis

For calculations \(\mathrm{3D}\) (2 quarters of a sphere modelled):

      • symmetry conditions on each quarter of a sphere