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


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


.. image:: images/100022A000001AC500002113AD5987BF3E31F67D.svg
    :width: 345
    :height: 426


.. _RefImage_100022A000001AC500002113AD5987BF3E31F67D.svg:

The initial mesh :math:`\mathrm{ma}` (substructuring level :math:`-2`) only contains the 12 QUAD4 of :math:`\mathrm{IJBA}` and :math:`\mathrm{ABCD}`.

The macr_elem_stat :math:`({S}_{1})` is set based on the elements in :math:`\mathrm{ABCD}`. This macr_elem_stat is condensed on the nodes of :math:`\mathrm{AB}` and :math:`\mathrm{CD}` (level :math:`-2`).


.. image:: images/10000FF800001C5200000F66D494C22286F394ED.svg
    :width: 345
    :height: 426


.. _RefImage_10000FF800001C5200000F66D494C22286F394ED.svg:

The :math:`-1` level :math:`\text{ma\_123}` mesh is defined by rotating :math:`\text{S\_1}` twice to represent crown :math:`\mathrm{ABCEGHFDA}`.


.. image:: images/100015120000283400000E78470D1303C995C21E.svg
    :width: 345
    :height: 426


.. _RefImage_100015120000283400000E78470D1303C995C21E.svg:

The macr_elem_stat :math:`\text{S\_123}` is defined using substructures :math:`\mathrm{ABCD}`, :math:`\mathrm{DCEF}`, and :math:`\mathrm{FEGH}`. This macr_elem_stat is condensed on the nodes of :math:`\mathrm{AB}` and :math:`\mathrm{GH}`.

The :math:`\mathrm{mag0}` mesh is defined by the macr_elem_stat :math:`\text{S\_123}`.

The final mesh :math:`\mathrm{mag}` (level :math:`0`) is defined by the mesh :math:`\mathrm{mag0}` that is assembled (ASSE_MAILLAGE) with the initial mesh :math:`\mathrm{ma}` to recover the meshes of :math:`\mathrm{IJBA}`.

The resolution is then done on this final mesh, then the displacements within the macr_elem_stat are calculated using the operator DEPL_INTERNE.


.. image:: images/100010BE0000284F000014778EE6D943539B1567.svg
    :width: 345
    :height: 426


.. _RefImage_100010BE0000284F000014778EE6D943539B1567.svg:


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

Number of knots: 20

Number of meshes and types: 12 QUAD4


Tested sizes and results
------------------------------


.. csv-table::

    "**Identification**", "**Reference**"
    ":math:`\mathrm{P1}` :math:`u` ", "1.88327"
    ":math:`\mathrm{P1}` :math:`v` ", "2.59224 10—2"
    ":math:`\mathrm{P2}` :math:`u` ", "—8.27372 10—2"
    ":math:`\mathrm{P2}` :math:`v` ", "8.27372 10—2"
    ":math:`\mathrm{P3}` :math:`u` ", "2.70375 10—1"
    ":math:`\mathrm{P3}` :math:`v` ", "5.69552 10—1"
    ":math:`\mathrm{P4}` :math:`u` ", "5.17703 10—1"
    ":math:`\mathrm{P4}` :math:`v` ", "5.43387 10—1"
    ":math:`\mathrm{P1}` :math:`u` ", "1.71883"
    ":math:`\mathrm{P1}` :math:`v` ", "—6.04367"
    ":math:`\mathrm{P2}` :math:`u` ", "—4.60196 10—2"
    ":math:`\mathrm{P2}` :math:`v` ", "4.60196 10—2"
    ":math:`\mathrm{P3}` :math:`u` ", "2.26903 10—1"
    ":math:`\mathrm{P3}` :math:`v` ", "—6.14296 10—1"
    ":math:`\mathrm{P4}` :math:`u` ", "—9.57110 10—1"
    ":math:`\mathrm{P4}` :math:`v` ", "—2.53878"