8. G modeling

8.1. Characteristics of the mesh

The structure is modelled by a single finite element of type QUAD4. The interface is therefore present within this element through level sets.

8.2. Boundary conditions

The same reasoning is repeated as for modeling A.

On the lower face a zero displacement is imposed:

\({a}_{\mathrm{ix}}-{b}_{\mathrm{ix}}=0\) and \({a}_{\mathrm{iy}}-{b}_{\mathrm{iy}}=0\).

On the upper face, a displacement along the axis \(Y\) is imposed:

\({a}_{\mathrm{ix}}+{b}_{\mathrm{ix}}=0\) and \({a}_{\mathrm{iy}}+{b}_{\mathrm{iy}}={10}^{-6}\).

These relationships are automated when using the DDL_IMPO keyword on an X- FEM node.

8.3. Analytical resolution

The solution of such a problem is of course still obvious: all the movements following \(x\) are zero, all the movements following \(y\) below the level set are zero and all the movements following \(y\) above the level set are equal to the displacement imposed \({u}_{y}\) at the top of the structure.

8.4. Tested sizes and results

The displacement values are tested after convergence of the iterations of the operator STAT_NON_LINE. We check that we find the values determined in [§ 8.3].

Identification	Reference	Tolerance
\(\mathit{DX}\) for all nodes just below the interface	0.00	1.0E-16
\(\mathit{DY}\) for all nodes just below the interface	0.00	1.0E-16
\(\mathit{DX}\) for all nodes just above the interface	0.00	1.0E-16
\(\mathit{DY}\) for all nodes just above the interface	1.0E-6	1.0E -9%

To test all the nodes at once, we test the MINIMUM and the MAXIMUM of the column.

8.5. Comments

We notice the discontinuity of the field of movement when crossing the interface, which is possible thanks to the enrichment of the elements with the Heaviside degree of freedom.