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


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


.. image:: images/Object_5.svg
    :width: 639
    :height: 202


.. _RefImage_Object_5.svg:


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

Number of knots: 224

Number of meshes and type: 192 QUAD4


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


.. csv-table::

    "**Identification**", "Numerical reference [:ref:`bib1 <bib1>`]", "Experimental reference [:ref:`bib2 <bib2>`]", "**Aster**", "**% differences**"
    "Move :math:`w` to point :math:`F` "," :math:`0.35{10}^{\mathrm{-}4}m` "," "," :math:`0.6{10}^{\mathrm{-}4}m` "," "," :math:`0.373{10}^{\mathrm{-}4}m` ", "6.703 [:ref:`bib1 <bib1>`]
    —37.757 [:ref:`bib2 <bib2>`]"
    "Move :math:`w` to point :math:`C`", ":math:`–0.7{10}^{\mathrm{-}3}m` "," "," :math:`–0.6{10}^{\mathrm{-}3}m` "," :math:`–0.721{10}^{\mathrm{-}3}` ", "3.033 [:ref:`bib1 <bib1>`]
    20.205 [:ref:`bib2 <bib2>`]"
    "Move :math:`w` to point :math:`D` "," :math:`0.25{10}^{\mathrm{-}4}m` "," "," :math:`0.1{10}^{\mathrm{-}3}m` "," "," :math:`0.369{10}^{\mathrm{-}4}` ", "47.689 [:ref:`bib1 <bib1>`]
    -63.078 [:ref:`bib2 <bib2>`]"
    "", "", "", "", ""
    "Constraint :math:`\mathit{SIXX}` at point :math:`F` "," :math:`–0.350\mathit{MPa}` "," "," :math:`–0.325\mathit{MPa}` "," :math:`–0.480\mathit{MPa}` ", "37.339 [:ref:`bib1 <bib1>`]
    47.904 [:ref:`bib2 <bib2>`]"
    "Constraint :math:`\mathit{SIYY}` at point :math:`F` "," :math:`0.500\mathit{MPa}` "," "," :math:`0.600\mathit{MPa}` "," :math:`0.490\mathit{MPa}` ", "-1.901 [:ref:`bib1 <bib1>`]
    -18.259 [:ref:`bib2 <bib2>`]"



Value of the normal displacement W along CD
--------------------------------------------


.. image:: images/10000000000002BC000001ED430BE32A4E424B18.png
    :width: 5.1008in
    :height: 3.5709in


.. _RefImage_10000000000002BC000001ED430BE32A4E424B18.png:

It can be noted that beyond the differences observed on the tested points :math:`C`, :math:`F`, :math:`D`, the normal displacement calculated along :math:`\mathit{CD}` is close to the theoretically "deep shells" solution adopted by Batoz [:ref:`bib1 <bib1>`]. The errors relating to points :math:`F` and :math:`D` can be attributed to the low value of the displacement (of the order of :math:`{10}^{\mathrm{-}5}m`).


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


.. image:: images/10000000000003570000025E9262FCC46918BAC8.png
    :width: 5.2953in
    :height: 3.548in


.. _RefImage_10000000000003570000025E9262FCC46918BAC8.png:


.. image:: images/100000000000035B000002612FAF7B222F125953.png
    :width: 5.1681in
    :height: 3.5in


.. _RefImage_100000000000035B000002612FAF7B222F125953.png:

It can be noted that the constraints calculated along :math:`\mathrm{CD}` are generally in agreement with the theoretically "deep shells" solution adopted by Batoz [:ref:`bib1 <bib1>`].


notes
---------


* Values for the CISA_L and CISA_T coefficients are not available. As the structure is thin (:math:`h\mathrm{/}R\mathrm{=}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 displacement :math:`w` (figure of [:ref:`§4.2 <§4.2>`]) is expressed in the local cylindrical coordinate system :math:`(R,\theta ,z)`, it is the displacement normal to the shell element. The displacement :math:`w` tested in [:ref:`§4.1 <§4.1>`] is for its part expressed in the global coordinate system (displacement following :math:`z`).