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


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

In this modeling we consider the framework of plane deformations (D_ PLAN), the crack is meshed, 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:`30\times 50` QUAD4, respectively along the :math:`x,y` axes (see [:ref:`Figure 3.2‑a <Figure 3.2‑a>`]). The lips of the crack are generated by the two superimposed edges halfway up the plate (thicker line in the figure).


.. image:: images/100000000000022E000003DEBE63EC1573ED0C45.png
    :width: 2.5591in
    :height: 4.5354in


.. _RefImage_100000000000022E000003DEBE63EC1573ED0C45.png:


.. _Ref940879061:

Figure 3.2‑a: Meshing for modeling A. Illustration of boundary conditions and loading


Tested features
-----------------------

The first 8 natural modes of the structure are calculated by considering the contribution of the geometric rigidity due to the prestress induced to equilibrium by the load in question.


.. csv-table::

    "**Orders**", "", ""
    "CALC_MATR_ELEM ", "", "OPTION = 'RIGI_MECA'
    OPTION = 'MASS_MECA'
    OPTION = 'RIGI_GEOM'", ""
    "CALC_MODES "," CALC_FREQ
    SOLVEUR_MODAL "," OPTION = 'PLUS_PETITE'
    NMAX_FREQ = 8
    METHODE = 'SORENSEN'", ""



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", "7.005", "7.005", "0."
    "Frequency mode 2", "24.895", "24.895", "0."
    "Frequency mode 3", "41.820", "41.820", "0."
    "Frequency mode 4", "84.905", "84.905", "0."
    "Mode 5 frequency, "106.179", "106.179", "106.179", "0."
    "Frequency mode 6", "134.298", "134.298", "134.298", "0."
    "Frequency mode 7", "166.198", "166.198", "0."
    "Frequency mode 8", "181.048", "181.048", "181.048", "0."