Toolbox is available at CSM Toolbox.

1. NAFEMS LE1 Benchmarck

This benchmark is extract from the Abaqus Benchmarks Manual.

1.1. Definition

We focus on the LE1 benchmarks in particular.

1.1.1. Geometry

The geometry is given here by :
geoLE10

1.1.2. Boundary conditions

We set:

  • \(u_y = 0\) on DC

  • \(u_x = 0\) on AB

  • \(\bar{\bar{\varepsilon}}\cdot\mathbf{n}=1e^7\) on BC.

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 \(92.7\, MPa\).

1.4. Results

The value of \(\sigma_{yy}\) at the point D is \(94.09\, MPa\) for \(32 000\) dofs, which is \(1.49%\) 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.