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


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

We use C_ PLAN modeling.


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

The mesh contains 121 elements of type QUAD4.


.. image:: images/100000000000017E0000016C648815C9E87487A3.png
    :width: 2.9591in
    :height: 2.8193in


.. _RefImage_100000000000017E0000016C648815C9E87487A3.png:


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

The maximum and minimum stresses on the plate are tested for field SIEF_ELNO:


.. csv-table::

    "**Identification**", "**Reference type**"
    ":math:`\mathit{MAX}` - :math:`\mathit{SIXX}` ", "'NON_REGRESSION'"
    ":math:`\mathit{MIN}` - :math:`\mathit{SIXX}` ", "'NON_REGRESSION'"
    ":math:`\mathit{MAX}` - :math:`\mathit{SIXY}` ", "'NON_REGRESSION'"
    ":math:`\mathit{MIN}` - :math:`\mathit{SIXY}` ", "'NON_REGRESSION'"


The maximum and minimum stresses on the plate are tested for field SIGM_ELNO calculated underground by the operator CALC_ERREUR:


.. csv-table::

    "**Identification**", "**Reference type**"
    ":math:`\mathit{MAX}` - :math:`\mathit{SIXX}` ", "'NON_REGRESSION'"
    ":math:`\mathit{MIN}` - :math:`\mathit{SIXX}` ", "'NON_REGRESSION'"
    ":math:`\mathit{MAX}` - :math:`\mathit{SIXY}` ", "'NON_REGRESSION'"
    ":math:`\mathit{MIN}` - :math:`\mathit{SIXY}` ", "'NON_REGRESSION'"


We test the minimum and maximum constraints on the field plate SISE_ELNO (node of the sub-elements X- FEM) calculated underground by the operator CALC_ERREUR:


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Precision**"
    ":math:`\mathit{MAX}` - :math:`X4` ", "'NON_REGRESSION'", "0.812078942873 MPa ", "1E -04%"
    ":math:`\mathit{MIN}` - :math:`X4` ", "'NON_REGRESSION'", "-0.510118026455 MPa ", "1E -04%"


Finally we test the field for error estimator ERME_ELEM:


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Precision**"
    ":math:`\mathit{MAX}` - :math:`\mathit{ERREST}` ", "'NON_REGRESSION'", "0.000698457464821", "1E -04%"
    ":math:`\mathit{MIN}` - :math:`\mathit{ERREST}` ", "'NON_REGRESSION'", "3.49704197058E-06", "1E -04%"



notes
---------

The constraints obtained calculated at the nodes of the mesh by CALC_ERREUR and by CALC_CHAMP are indeed the same.

The stress field is resolved at Gauss points:


.. image:: images/10000000000002CD00000264394DB487D8B57D71.png
    :width: 3.7646in
    :height: 3.2134in


.. _RefImage_10000000000002CD00000264394DB487D8B57D71.png:

The smoothing done by calculating the stresses at the nodes introduces errors that cause the CALC_ERREURàsous -operator to estimate the error of the asymptotic field at the bottom of the crack.