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


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


.. image:: images/Object_7.svg
    :width: 639
    :height: 202


.. _RefImage_Object_7.svg:


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

Number of knots: 224

Number of meshes and type: 384 TRIA3


Tested values
---------------


.. csv-table::

    "**Identification**", "Numeric reference [:ref:`bib1 <bib1>`]", "Experimental reference [:ref:`bib2 <bib2>`]", "**Aster**", "**% difference**"
    "Move :math:`w` to point :math:`F` "," :math:`1.325{10}^{\mathrm{-}3}m` "," "," :math:`1.35{10}^{\mathrm{-}3}m` "," "," :math:`1.327{10}^{\mathrm{-}3}m` ", "0.154 [:ref:`bib1 <bib1>`]
    —1.701 [:ref:`bib2 <bib2>`]"
    "Move :math:`w` to point :math:`C` "," :math:`–2.45{10}^{\mathrm{-}3}m` "," "," :math:`–2.46{10}^{\mathrm{-}3}m` "," :math:`–2.379{10}^{\mathrm{-}3}m` ", "—2.881 [:ref:`bib1 <bib1>`]
    —3.275 [:ref:`bib2 <bib2>`]"
    "Move :math:`w` to point :math:`D` "," :math:`–0.51{10}^{\mathrm{-}3}m` "," "," :math:`–0.35{10}^{\mathrm{-}3}m` "," "," :math:`–0.529{10}^{\mathrm{-}3}m` ", "3.859 [:ref:`bib1 <bib1>`]
    51.337 [:ref:`bib2 <bib2>`]"
    "", "", "", "", ""
    "Constraint :math:`\mathit{SIXX}` at point :math:`F` "," :math:`1.68\mathit{MPa}` "," "," :math:`1.9\mathit{MPa}` "," :math:`1.643\mathit{MPa}` ", "—2.155 [:ref:`bib1 <bib1>`]
    —13.484 [:ref:`bib2 <bib2>`]"
    "Constraint :math:`\mathit{SIYY}` at point :math:`F` "," :math:`1.8\mathit{MPa}` "," "," :math:`1.55\mathit{MPa}` "," :math:`1.782\mathit{MPa}` ", "—0.986 [:ref:`bib1 <bib1>`]
    —14.984 [:ref:`bib2 <bib2>`]"



notes
----------


* The values of the coefficients CISA_L and CISA_T are not available. As the structure is thin (:math:`h/R=0.045`), it is assumed that the effects of transverse shear are negligible, so we imposed CISA_L = CISA_T = :math:`{10}^{10}`.


* The normal :math:`w` displacement is expressed in the local cylindrical coordinate :math:`(R,\theta ,z)`, it is the displacement normal to the shell element.


Value of normal displacement along CD
------------------------------------------


.. image:: images/100000000000039A000002975DCACD541B56E662.png
    :width: 5.0744in
    :height: 3.5528in


.. _RefImage_100000000000039A000002975DCACD541B56E662.png:

It can be noted that beyond the difference observed in the experimental value at point D, the normal displacement calculated along :math:`\mathrm{CD}` is very close to the theoretically "deep shells" solution adopted by Batoz [:ref:`bib1 <bib1>`].


Stress value along CD
------------------------------------


.. image:: images/10000000000003540000025EF4A70DED45E66968.png
    :width: 5.0736in
    :height: 3.8846in


.. _RefImage_10000000000003540000025EF4A70DED45E66968.png:


.. image:: images/100000000000035300000257F558AC7C363C2271.png
    :width: 5.0917in
    :height: 3.8992in


.. _RefImage_100000000000035300000257F558AC7C363C2271.png:

The stress profiles calculated by the code are generally in agreement with the work of Batoz.