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1. NAFEMS LE10 Benchmarck

This benchmark is extract from the Abaqus Benchmarks Manual.

1.1. Definition

We focus on the LE10 benchmarks in particular.

1.1.1. 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'.

1.1.2. 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.

1.2. Inputs

We have the following parameters:

Table 1. Inputs
Name Value

\(E\)

\(210\, GPa\)

\(\nu\)

\(0.3\)

\(\rho\)

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

1.3. Outputs

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

1.4. 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.