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


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


+-----------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|                                                                                                                             |Modeling DKT (QUAD4)                                                                                                                                                                                                                                                                                                                                                                                                                               |
+ .. image:: images/10000000000001C8000001502065E0359422B192.png                                                              +                                                                                                                                                                                                                                                                                                                                                                                                                                                   +
|    :width: 2.8839in                                                                                                         | - The plate is located in the plane :math:`Y=0.5`                                                                                                                                                                                                                                                                                                                                                                                                 |
+    :height: 2.2425in                                                                                                        + - Point :math:`A` :math:`(0.4;0.5;0.25)`                                                                                                                                                                                                                                                                                                                                                                                                          +
|                                                                                                                             | - Boundary conditions:                                                                                                                                                                                                                                                                                                                                                                                                                            |
+                                                                                                                             + - - Side :math:`\mathrm{BC}`: - Side :math:`v=0`                                                                                                                                                                                                                                                                                                                                                                                                  +
|                                                                                                                             | :math:`\mathrm{CD}`: :math:`v=0`                                                                                                                                                                                                                                                                                                                                                                                                                  |
+                                                                                                                             +                                                                                                                                                                                                                                                                                                                                                                                                                                                   +
|                                                                                                                             | - Symmetry conditions: (local coordinate system)                                                                                                                                                                                                                                                                                                                                                                                                  |
+                                                                                                                             + - - Side :math:`\mathrm{AB}`: :math:`u={\theta }_{y}=0`                                                                                                                                                                                                                                                                                                                                                                                           +
|                                                                                                                             | - Side :math:`\mathrm{AD}`: :math:`v={\theta }_{x}=0`                                                                                                                                                                                                                                                                                                                                                                                             |
+                                                                                                                             +                                                                                                                                                                                                                                                                                                                                                                                                                                                   +
|                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
+-----------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+



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

Number of knots: 49

Number of meshes and types: 36 QUAD4


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


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference values**", "**Tolerance** :math:`(\text{\%})`"
    ":math:`w(\mathrm{0,}\mathrm{0,}0)` "," ANALYTIQUE ", "0.01507", "1.1"
    ":math:`\mathrm{SIXX}(\mathrm{0,}\mathrm{0,}h/2)` "," SOURCE_EXTERNE ", "2.4216 107", "1.1"
    ":math:`\mathrm{SIYY}(\mathrm{0,}\mathrm{0,}h/6)` layer to :math:`90°`", "SOURCE_EXTERNE ", "5.7810 106", "5.7810 106", "1.1"
    ":math:`\mathrm{SIXY}(a/\mathrm{2,}a/\mathrm{2,}h/2)` "," SOURCE_EXTERNE ", "1.2825 106", "5.1"
    ":math:`\mathrm{SIXZ}(a/\mathrm{2,}\mathrm{0,}0)` "," SOURCE_EXTERNE ", "—2.3526 105", "16"
    ":math:`\mathrm{SIYZ}(\mathrm{0,}a/\mathrm{2,}0)` "," SOURCE_EXTERNE ", "8.8950 104", "4.1"



notes
---------

The components :math:`\mathrm{SIXX}`, :math:`\mathrm{SIYY}`, and :math:`\mathrm{SIYZ}` are the average values of the two cells competing at points :math:`A` and :math:`C`.

The difference obtained on :math:`\mathrm{SIXZ}` is due to the difference in transverse shear modeling: in the reference, a transverse shear correction coefficient of 5/6 is used. In *Code_Aster*, we calculate the distribution of shear in the thickness, which is assumed to be parabolic in each layer.

The sign of :math:`\mathrm{SIXZ}` is the opposite of that of the reference solution.