C modeling
==============

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

Mesh: the mesh is composed of a QUAD9 mesh with nine knots (:math:`\mathit{N1}`, :math:`\mathit{N2}`, :math:`\mathit{N3}`, :math:`\mathit{N4}`, :math:`\mathit{N5}`, :math:`\mathit{N6}`, :math:`\mathit{N7}`,, :math:`\mathit{N8}`, :math:`\mathit{N9}`).


.. image:: images/100002000000016700000158DF8C84E6DFF179DA.png
    :width: 2.9138in
    :height: 2.6445in


.. _RefImage_100002000000016700000158DF8C84E6DFF179DA.png:


.. image:: images/10000200000001880000018A9224476971DA41E8.png
    :width: 2.6634in
    :height: 2.5945in


.. _RefImage_10000200000001880000018A9224476971DA41E8.png:

For each mesh, there are 9 integration points.

• Node group :math:`\mathit{ENC}` is composed of nodes :math:`\mathit{N1}` and :math:`\mathit{N2}`

• Node group :math:`\mathit{CHA}` is composed of nodes :math:`\mathit{N3}` and :math:`\mathit{N4}`


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

Modeling:

MO= AFFE_MODELE (MAILLAGE =MA,

 AFFE =_F (TOUT =' OUI ', PHENOMENE =' MECANIQUE',

     MODELISATION =' COQUE_3D ',),)

Boundary conditions:

BLOCAGE = AFFE_CHAR_MECA (MODELE =MO,

 DDL_IMPO =_F (GROUP_NO =' ENC ',

     DX=0.0, DY=0.0, DZ=0.0, DRX =0.0, =0.0, DRY =0.0, DRZ =0.0,),

)

Mechanical loading:

CHARGE = AFFE_CHAR_MECA (MODELE =MO,

 FORCE_NODALE =_F (GROUP_NO =' CHA ', FX=0, FX=0, FZ=-100. ),

)

Assignment of the characteristics of the elements:

PLAQUE = AFFE_CARA_ELEM (MODELE =MO,

 COQUE =_F (GROUP_MA =( 'PLA'), EPAIS = 0.5, COQUE_NCOU = 4,),

)


Tested values and results
----------------------------

.. csv-table::

    "Coordinated
    mesh QUA1 ", "Point
    integration", "sub-point", "**Reference**"
    "COOR_X ", "1", "1", "1", "0.058776419"
    "COOR_X ", "1", "2", "0.085839713"
    "COOR_X ", "1", "3", "3", "0.112903006"
    "COOR_X ", "1", "4", "4", "0.112903006"
    "COOR_X ", "1", "5", "5", "0.139966300"
    "COOR_X ", "1", "6", "6", "0.167029594"
    "COOR_X ", "1", "7", "7", "0.167029594"
    "COOR_X ", "1", "8", "8", "0.194092888"
    "COOR_X ", "1", "9", "9", "0.221156182"
    "COOR_X ", "1", "10", "0.221156182"
    "COOR_X ", "1", "11", "0.248219476"
    "COOR_X ", "1", "12", "0.275282770"
    "COOR_Y ", "1", "1", "1", "0.349002918"
    "COOR_Y ", "1", "2", "0.302127918"
    "COOR_Y ", "1", "3", "3", "0.2552529180"
    "COOR_Y ", "1", "4", "4", "0.2552529180"
    "COOR_Y ", "1", "5", "5", "0.2083779180"
    "COOR_Y ", "1", "6", "6", "0.1615029180"
    "COOR_Y ", "1", "7", "7", "0.1615029180"
    "COOR_Y ", "1", "8", "8", "0.1146279180"
    "COOR_Y ", "1", "9", "9", "0.0677529180"
    "COOR_Y ", "1", "10", "0.0677529180"
    "COOR_Y ", "1", "11", "0.0208779180"
    "COOR_Y ", "1", "12", "-0.025997082"
    "COOR_Z ", "1", "1", "1", "-0.027397495"
    "COOR_Z ", "1", "2", "2", "3.852505E-03"
    "COOR_Z ", "1", "3", "3", "0.0351025050"
    "COOR_Z ", "1", "4", "4", "0.0351025050"
    "COOR_Z ", "1", "5", "5", "0.0663525050"
    "COOR_z ", "1", "6", "6", "0.0976025050"
    "COOR_Z ", "1", "7", "7", "0.0976025050"
    "COOR_Z ", "1", "8", "8", "0.1288525050"
    "COOR_z ", "1", "9", "9", "0.1601025050"
    "COOR_Z ", "1", "10", "0.1601025050"
    "COOR_Z ", "1", "11", "0.1913525050"
    "COOR_Z ", "1", "12", "0.2226025050"
    "COOR_Z ", "9", "1", "1", "0.3080127020"
    "COOR_Z ", "9", "2", "2", "0.3392627020"
    "COOR_Z ", "9", "3", "3", "0.3705127020"
    "COOR_Z ", "9", "4", "4", "0.3705127020"
    "COOR_Z ", "9", "5", "5", "0.4017627020"
    "COOR_z ", "9", "6", "6", "0.4330127020"
    "COOR_Z ", "9", "7", "7", "0.4330127020"
    "COOR_Z ", "9", "8", "8", "0.4642627020"
    "COOR_z ", "9", "9", "9", "0.4955127020"
    "COOR_Z ", "9", "10", "0.4955127020"
    "COOR_Z ", "9", "11", "11", "0.5267627020"
    "COOR_Z ", "9", "12", "0.5580127020"


Tolerance is :math:`1.0E-03` for all tests.