G modeling
==============


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.


Boundary conditions
----------------------

The same reasoning is repeated as for modeling A.

On the lower face a zero displacement is imposed:

:math:`{a}_{\mathrm{ix}}-{b}_{\mathrm{ix}}=0` and :math:`{a}_{\mathrm{iy}}-{b}_{\mathrm{iy}}=0`.

On the upper face, a displacement along the axis :math:`Y` is imposed:

:math:`{a}_{\mathrm{ix}}+{b}_{\mathrm{ix}}=0` and :math:`{a}_{\mathrm{iy}}+{b}_{\mathrm{iy}}={10}^{-6}`.

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


.. _Ref127877638:


Analytical resolution
---------------------

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


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 [§ :ref:`8.3 <Ref127877638>`].


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    ":math:`\mathit{DX}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DY}` for all nodes just below the interface", "0.00", "1.0E-16"
    ":math:`\mathit{DX}` for all nodes just above the interface", "0.00", "1.0E-16"
    ":math:`\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.


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.