D modeling
==============


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


.. image:: images/Object_8.svg
    :width: 639
    :height: 202


.. _RefImage_Object_8.svg:


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

Number of knots: 224

Number of meshes and type: 192 QUAD4


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


.. csv-table::

    "**Identification**", "Reference [:ref:`bib1 <bib1>`]", "Reference [:ref:`bib2 <bib2>`]", "**Aster**", "**% difference**"
    "Displacement :math:`w`
    at point :math:`F` "," :math:`1.325{10}^{-3}m` "," :math:`1.35{10}^{-3}m` "," "," :math:`1.329{10}^{\mathrm{-}3}m` ", "0.365 [:ref:`bib1 <bib1>`]
    —1.494 [:ref:`bib2 <bib2>`]"
    "Displacement :math:`w`
    at point :math:`C` "," :math:`–2.45{10}^{-3}m` "," :math:`–2.46{10}^{-3}m` "," "," :math:`–2.369{10}^{-3}m` ", "—3.274 [:ref:`bib1 <bib1>`]
    —3.667 [:ref:`bib2 <bib2>`]"
    "Displacement :math:`w`
    at point :math:`D` "," :math:`–0.51{10}^{-3}m` "," :math:`–0.35{10}^{-3}m` "," "," :math:`–0.528{10}^{-3}m` ", "3.634 [:ref:`bib1 <bib1>`]
    51.009 [:ref:`bib2 <bib2>`]"
    "", "", "", "", ""
    "Constraint :math:`\mathit{SIXX}`
    at point :math:`F` "," :math:`1.68\mathrm{MPa}` "," :math:`1.9\mathrm{MPa}` "," "," :math:`1.79\mathrm{MPa}` ", "6.616 [:ref:`bib1 <bib1>`]
    —5.729 [:ref:`bib2 <bib2>`]"
    "Constraint :math:`\mathrm{SIYY}`
    at point :math:`F` "," :math:`1.8\mathrm{MPa}` "," :math:`1.55\mathrm{MPa}` "," "," :math:`1.84\mathrm{MPa}` ", "2.465 [:ref:`bib1 <bib1>`]
    18.991 [: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. The displacement :math:`w` tested is that of the global coordinate system (displacement following :math:`z`).


Value of the displacement along CD
-----------------------------------


.. image:: images/100000000000039D0000028BBFBDAA8EB8836B7F.png
    :width: 5.4193in
    :height: 3.7689in


.. _RefImage_100000000000039D0000028BBFBDAA8EB8836B7F.png:

It can be noted that beyond the difference observed in the experimental value at point :math:`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 values along CD
-------------------------------------


.. image:: images/10000000000003480000025191CD57C155DAC552.png
    :width: 5.0752in
    :height: 3.6409in


.. _RefImage_10000000000003480000025191CD57C155DAC552.png:


.. image:: images/100000000000035300000258DE88DF7045DBC615.png
    :width: 5.1972in
    :height: 3.4362in


.. _refImage_100000000000035300000258 DE88DF7045DBC615 .png: