Feel++

NAFEMS LE10 Benchmarck

This benchmark is extract from the Abaqus Benchmarks Manual.

Definition

We focus on the LE10 benchmarks in particular.

Geometry

The geometry is given here by :

geoLE10

where the thickness is \$0.6\$.

In addition, we define the point E which is the midpoint of CC' and E' the midpoint of BB'.

Boundary conditions

We set:

  • \$u_y = 0\$ on DCD’C'

  • \$u_x = 0\$ on ABA’B'

  • \$u_x = u_y = 0\$ on BCB’C'

  • \$\bar{\bar{\varepsilon}}\cdot\mathbf{n}=-1e^6\$ on the top surface.

Inputs

We have the following parameters:

Table 1. Inputs
Name Value

\$E\$

\$210\, GPa\$

\$\nu\$

\$0.3\$

\$\rho\$

\$7800\, kg/m^2\$

Outputs

We want to compare the value of \$\sigma_{yy}\$ at the point D. The reference value is \$5.38\, MPa\$.

Results

The value of \$\sigma_{yy}\$ at the point D is \$5.53\, MPa\$ for \$300 000\$ dofs, which is \$2.78%\$ higher than the target.

One possibility to get a more accurate output is to use a mixed formulation, where the stress tensor would also be an unknown.