Modeling A
==============


Characteristics of modeling
-----------------------------------

A 3D modeling with the mesh crack is considered and the classical finite element method is used to perform the calculation. This modeling will serve as a reference and will allow comparison with the X- FEM method.


Characteristics of the mesh
----------------------------

The structure is modelled by a regular mesh composed of :math:`5\times 30\times 50` HEXA8, respectively along the axes :math:`x` *,* :math:`y` *,* :math:`z` (see [:ref:`Figure 3.2-a <Figure 3.2-a>`]). The two superimposed surfaces are the lips of the crack.


.. image:: images/10000000000001980000035C5C9BE1B34521ECEC.png
    :width: 1.5917in
    :height: 3.0835in


.. _RefImage_10000000000001980000035C5C9BE1B34521ECEC.png:


.. _Ref940879061:

Figure 3.2-a: The mesh for modeling A


Tested sizes and results
------------------------------

For this modeling, non-regression tests on the natural frequencies of the first 8 modes are considered.


.. csv-table::

    "**Identification**", "**Reference**", "**Code_Aster**", "**% difference**"
    "Frequency mode 1", "1.363", "1.363", "1.363", "0."
    "Frequency mode 2", "3.220", "3.220", "3.220", "0."
    "Frequency mode 3", "4.815", "4.815", "0."
    "Frequency mode 4", "7.195", "7.195", "7.195", "0."
    "Frequency mode 5", "10.098", "10.098", "10.098", "0."
    "Frequency mode 6", "11.789", "11.789", "11.789", "0."
    "Frequency mode 7", "17.484", "17.484", "17.484", "0."
    "Frequency mode 8", "18.281", "18.281", "18.281", "0."