B modeling
==============


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


.. image:: images/Object_6.svg
    :width: 639
    :height: 202


.. _RefImage_Object_6.svg:


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

Number of knots: 224

Number of meshes and type: 384 TRIA3


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


.. csv-table::

    "**Identification**", "Reference [:ref:`bib1 <bib1>`]", "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:`0.383{10}^{\mathrm{-}4}` ", "9.571 [:ref:`bib1 <bib1>`]
    36.084 [: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:`–7.138{10}^{\mathrm{-}4}` ", "1.985 [:ref:`bib1 <bib1>`]
    18.982 [: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:`0.350{10}^{\mathrm{-}4}` ", "40.368 [:ref:`bib1 <bib1>`]
    —64.908 [:ref:`bib2 <bib2>`]"
    "", "", "", "", ""
    "Constraint :math:`\mathit{SIXX}` at point :math:`F` "," :math:`–0.350\mathit{MPa}` "," "," :math:`–0.325\mathit{MPa}` "," "," :math:`–0.470\mathit{MPa}` ", "34.348 [:ref:`bib1 <bib1>`]
    44.682 [:ref:`bib2 <bib2>`]"
    "Constraint :math:`\mathit{SIYY}` at point :math:`F` "," :math:`0.500\mathit{MPa}` "," "," :math:`0.600\mathit{MPa}` "," :math:`0.400\mathit{MPa}` ", "—19.929 [:ref:`bib1 <bib1>`]
    —33.274 [:ref:`bib2 <bib2>`]"



notes
----------


* Values for the CISA_L and CISA_T coefficients 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 displacement w is expressed in the local cylindrical coordinate system :math:`(R,\theta ,z)`, it is the displacement normal to the shell element.


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

The results obtained with a TRIA3 mesh are very similar to those obtained with the QUAD4 mesh.


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


.. image:: images/10000000000003A5000002940E51616F0FAE6ED9.png
    :width: 5.5972in
    :height: 3.6689in


.. _RefImage_10000000000003A5000002940E51616F0FAE6ED9.png:


.. image:: images/10000000000003AD000002972656CB0A7C4EABBD.png
    :width: 5.5972in
    :height: 3.3228in


.. _RefImage_10000000000003AD000002972656CB0A7C4EABBD.png:

The stress profiles obtained by B modeling with TRIA3 are generally close to Batoz solutions.