Feel++

NAFEMS LE1 Benchmarck

This benchmark is extract from the Abaqus Benchmarks Manual.

Definition

We focus on the LE1 benchmarks in particular.

Geometry

The geometry is given here by :
geoLE10

Boundary conditions

We set:

  • \$u_y = 0\$ on DC

  • \$u_x = 0\$ on AB

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

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 \$92.7\, MPa\$.

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.