3. B modeling

In this modeling, for pressure loading, loading is applied using a constant distributed pressure for load No. 1, and a distributed pressure based on \(y\) for load No. 2.

In this modeling, for line force loading, loading is applied using constant line forces for load 1, and linear forces that are functions of \(y\) for load 2.

3.1. Characteristics of the mesh

In 2D, the structure is meshed with quadrangles with 4 nodes. The number of elements is as small as possible, i.e. 2 elements along the \(\mathrm{Ox}\) axis (in order to be able to define the nodes in the middle plane at \(x=\mathrm{LX}/2\)), 5 elements along the \(\mathrm{Oy}\) axis. Along the \(\mathrm{Oy}\) axis, the number of elements is odd so that the interface does not coincide with the faces of the elements; the 3 layers of central elements use X- FEM elements, and the 2 layers of elements at the top and bottom use conventional elements.

Figure 3.1-1 : 2D mesh

3.2. Tested features

The PRES_REP keyword of the AFFE_CHAR_MECA [U4.44.01] operator makes it possible to apply a constant distributed pressure to skin elements. When pressure is a function or a formula, we use the PRES_REP keyword from AFFE_CHAR_MECA_F [U4.44.01]). This feature is tested with load #2. Indeed, with X- FEM, you cannot define an upper and lower lateral edge as a group of elements. In the present case, a single group of elements comprising all the 1D lateral cells is defined, and a pressure that is a function of \(y\) is applied to this group of elements.

The FORCE_CONTOUR keyword of the AFFE_CHAR_MECA [U4.44.01] operator makes it possible to apply a constant linear force to skin elements. When linear force is a function or a formula, we use the FORCE_CONTOUR keyword from AFFE_CHAR_MECA_F [U4.44.01]).

3.3. Tested sizes and results

For each lateral face of the structure (\(x=0\) and \(x=\mathrm{LX}\)), we test the movements of the nodes located just above and just below the level set.

3.3.1. Compression loading (pressure loading)

Identification	Reference
\(\mathrm{DX}\) for all nodes on the left surface located just below the interface	10-6
\(\mathrm{DX}\) for all nodes on the left surface located just above the interface	10-6
\(\mathrm{DX}\) for all nodes on the right surface located just below the interface	-10-6
\(\mathrm{DX}\) for all nodes on the right surface located just above the interface	-10-6

3.3.2. Compression loading/traction (pressure loading)

Identification	Reference
\(\mathrm{DX}\) for all nodes on the left surface located just below the interface	-10-6
\(\mathrm{DX}\) for all nodes on the left surface located just above the interface	10-6
\(\mathrm{DX}\) for all nodes on the right surface located just below the interface	10-6
\(\mathrm{DX}\) for all nodes on the right surface located just above the interface	-10-6

3.3.3. Compression loading (surface force loading)

Identification	Reference
\(\mathrm{DX}\) for all nodes on the left surface located just below the interface	10-6
\(\mathrm{DX}\) for all nodes on the left surface located just above the interface	10-6
\(\mathrm{DX}\) for all nodes on the right surface located just below the interface	-10-6
\(\mathrm{DX}\) for all nodes on the right surface located just above the interface	-10-6

3.3.4. Compression/tensile loading (surface force loading)

Identification	Reference
\(\mathrm{DX}\) for all nodes on the left surface located just below the interface	-10-6
\(\mathrm{DX}\) for all nodes on the left surface located just above the interface	10-6
\(\mathrm{DX}\) for all nodes on the right surface located just below the interface	10-6
\(\mathrm{DX}\) for all nodes on the right surface located just above the interface	-10-6

To test all the nodes at once, we test the minimum and the maximum of the column.