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


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

AXIS_FOURIER, T6 meshes


.. image:: images/Shape3.gif


.. _RefSchema_Shape3.gif:


.. image:: images/1000000000000B6D000008089DBF9EA56AEBB145.png
    :width: 4.8752in
    :height: 3.4264in


.. _RefImage_1000000000000B6D000008089DBF9EA56AEBB145.png:


+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++
|Die-cutting:                                                                                                                             |80 elements depending on the length ||
+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++
|                                                                                                                                         |2 elements according to the radius  ||
+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++
|                                                                                                                                         |                                    ||
+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++
|Loads:                                                                                                                                   |                                    ||
+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++
|                                                                                                                                         |                                    ||
+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++
|:math:`\mathrm{C1}`:|vertical gravity (field :math:`\mathrm{Ug}`) in the form of volume density of forces :math:`\rho g=76518\mathrm{Pa}`                                      |
+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++
|:math:`\mathrm{C2}`:|pressure (field :math:`\mathrm{Up}`)                                                                                                                    | |
+--------------------+--------------------------------------------------------------------------------------------------------------------+-----------------------------------+++

Displacement components: :math:`{u}_{r}` (radial), :math:`{u}_{z}` (axial), (axial), :math:`{u}_{\theta }` (circumferential)

Node names:


.. csv-table::

    ":math:`A=\mathrm{N1}` "," :math:`B=\mathrm{N2}` "," :math:`C=\mathrm{N3}` "," "," :math:`D=\mathrm{N4}` "," :math:`E=\mathrm{N249}` "," :math:`F=\mathrm{N87}`"



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

Number of knots: 805

Number of meshes and types: 320 TRIA6


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


.. csv-table::

    "**Location**", "**Value type**", "**Reference**", "**Aster**", "**% difference**"
    "Field :math:`\mathrm{Ug}`
    (for :math:`\theta =0.`)", "", "", "", ""
    "Point :math:`E,F` "," :math:`{u}_{r}(m)`
    :math:`{u}_{\theta }(m)` ", "3.566 x 10—7
    0. ", "3.541 x 10—7
    0. ", "—0.70"
    "Point :math:`B` "," :math:`{\sigma }_{\mathrm{zz}}(\mathrm{Pa})` ", "—2.496 x 105", "—2.60 x 105", "+ 4.1"
    "Field :math:`\mathrm{Up}`
    (for :math:`\theta =0.`)", "", "", "", ""
    "Point :math:`E` "," :math:`{u}_{r}(m)` ", "—7.82 x 10—6", "—7.71 x 10—6", "—1.4"
    "Point :math:`F` ", "", "—7.82 x 10—6", "—7.70 x 10—6", "—1.5"
    "Point :math:`B` "," :math:`{\sigma }_{\mathrm{rr}}(\mathrm{Pa})`
    :math:`{\sigma }_{\mathrm{zz}}(\mathrm{Pa})`
    :math:`{\sigma }_{\theta \theta }(\mathrm{Pa})` ", "1.63 x 106
    5.51 x 106
    1.65 x 106", "1.41 x 106
    5.65 x 106
    1.89 x 106", "—13.4
    2.7
    14.7"
    "Field :math:`\mathrm{Up}+\mathrm{Ug}`
    (for :math:`\theta =0.`)", "", "", "", ""
    "Point :math:`E` "," :math:`{u}_{r}(m)` ", "—7.46 x 10—6", "—7.358 x 10—6", "—1.3"
    "Point :math:`F` "," :math:`{u}_{r}(m)` ", "—7.46 x 10—6", "—7.348 x 10—6", "—1.5"
    "Point :math:`B` "," :math:`{\sigma }_{\mathrm{rr}}(\mathrm{Pa})`
    :math:`{\sigma }_{\mathrm{zz}}(\mathrm{Pa})`
    :math:`{\sigma }_{\theta \theta }(\mathrm{Pa})` ", "1.56 x 106
    5.25 x 106
    1.57 x 106", "1.34 x 106
    5.398 x 106
    1.80 x 106", "—13.7
    2.8
    15.0"



notes
---------


* The reference values for pressure (field :math:`\mathrm{Up}`) are obtained in the C modeling, from a 3D mesh.


* The results obtained are strictly identical to those of modeling A with PESANTEUR.


Contents of the results file
----------------------------

Travel, constraints.