NAFEMS LE10 Benchmarck

This benchmark is extract from the Abaqus Benchmarks Manual.

1. Definition

We focus on the LE10 benchmarks in particular.

2. Running the case

The command line to run this case is

mpirun -np 4 feelpp_toolbox_solid --case "github:{path:toolboxes/solid/NAFEMS-LE10}"

3. Data files

The case data files are available in Github here

3.1. Geometry

The geometry is given here by :

geo

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'.

3.2. 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.

4. Inputs

We have the following parameters:

Table 1. Inputs
Name Value

\(E\)

\(210\, GPa\)

\(\nu\)

\(0.3\)

\(\rho\)

\(7800\, kg/m^2\)

5. Outputs

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

6. 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.