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


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

We use a DKT model with 3 layers in the thickness.


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

The mesh contains 2048 elements of type TRIA3.


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

Stress is tested on the lower, middle and upper skin in two layers.


* Layer 1: :math:`\mathrm{-}\mathrm{0.05m}<Z<\mathrm{-}0.0167m`


+--------------------+---------------------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|**Identification**                                                                                                                                        |**Reference type**|**Reference value**  |**Tolerance**             |
+--------------------+---------------------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|:math:`\mathit{INF}`|:math:`X\mathrm{=}\mathrm{0.0m}` :math:`Y\mathrm{=}\mathrm{0.0m}` :math:`Z\mathrm{=}\mathrm{-}\mathrm{0.05m}`  |:math:`\mathit{SIXX}`|'ANALYTIQUE'      |:math:`10.`          |:math:`2.0\text{\%}`      |
+                    +                                                                                                               +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                               |:math:`\mathit{SIYY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.6`               |
+                    +                                                                                                               +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                               |:math:`\mathit{SIXY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.05`              |
+--------------------+---------------------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|:math:`\mathit{MOY}`|:math:`X\mathrm{=}\mathrm{0.0m}` :math:`Y\mathrm{=}\mathrm{1.0m}` :math:`Z\mathrm{=}\mathrm{-}\mathrm{0.0333m}`|:math:`\mathit{SIXX}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.05`              |
+                    +                                                                                                               +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                               |:math:`\mathit{SIYY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.2`               |
+                    +                                                                                                               +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                               |:math:`\mathit{SIXY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.0035`            |
+--------------------+---------------------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|:math:`\text{SUP}`  |:math:`X\mathrm{=}\mathrm{0.0m}` :math:`Y\mathrm{=}\mathrm{2.0m}` :math:`Z\mathrm{=}\mathrm{-}\mathrm{0.0167m}`|:math:`\mathit{SIXX}`|'ANALYTIQUE'      |:math:`\mathrm{-}10.`|:math:`1.5\text{\%}`      |
+                    +                                                                                                               +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                               |:math:`\mathit{SIYY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.5`               |
+                    +                                                                                                               +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                               |:math:`\mathit{SIXY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`{10}^{\mathrm{-}6}`|
+--------------------+---------------------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+


* Layer #3: :math:`\mathrm{0.0167m}<Z<\mathrm{0.05m}`


+--------------------+-----------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|**Identification**                                                                                                                              |**Reference type**|**Reference value**  |**Tolerance**             |
+--------------------+-----------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|:math:`\mathit{INF}`|:math:`X\mathrm{=}\mathrm{4.0m}` :math:`Y\mathrm{=}\mathrm{0.0m}` :math:`Z\mathrm{=}\mathrm{0.0167m}`|:math:`\mathit{SIXX}`|'ANALYTIQUE'      |:math:`10.`          |:math:`1.5\text{\%}`      |
+                    +                                                                                                     +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                     |:math:`\mathit{SIYY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.5`               |
+                    +                                                                                                     +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                     |:math:`\mathit{SIXY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`{10}^{\mathrm{-}4}`|
+--------------------+-----------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|:math:`\mathit{MOY}`|:math:`X\mathrm{=}\mathrm{4.0m}` :math:`Y\mathrm{=}\mathrm{1.0m}` :math:`Z\mathrm{=}\mathrm{0.0333m}`|:math:`\mathit{SIXX}`|'ANALYTIQUE'      |:math:`0.`           |:math:`{10}^{\mathrm{-}4}`|
+                    +                                                                                                     +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                     |:math:`\mathit{SIYY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`{10}^{\mathrm{-}4}`|
+                    +                                                                                                     +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                     |:math:`\mathit{SIXY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`{10}^{\mathrm{-}3}`|
+--------------------+-----------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+
|:math:`\text{SUP}`  |:math:`X\mathrm{=}\mathrm{4.0m}` :math:`Y\mathrm{=}\mathrm{2.0m}` :math:`Z\mathrm{=}\mathrm{0.05m}`  |:math:`\mathit{SIXX}`|'ANALYTIQUE'      |:math:`\mathrm{-}10.`|:math:`1.5\text{\%}`      |
+                    +                                                                                                     +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                     |:math:`\mathit{SIYY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`0.5`               |
+                    +                                                                                                     +---------------------+------------------+---------------------+--------------------------+
|                    |                                                                                                     |:math:`\mathit{SIXY}`|'ANALYTIQUE'      |:math:`0.`           |:math:`{10}^{\mathrm{-}4}`|
+--------------------+-----------------------------------------------------------------------------------------------------+---------------------+------------------+---------------------+--------------------------+