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


.. image:: images/10000000000001D9000001886349DDE9FC145C8E.png
    :width: 4.9268in
    :height: 4.0835in


.. _RefImage_10000000000001D9000001886349DDE9FC145C8E.png:

M266 ROAD


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

Number of knots: 169

Number of meshes and type: 288 TRIA3


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


.. csv-table::

    "**Identification**", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    ":math:`\mathrm{DZ}(\mathrm{A1})` ", "'ANALYTIQUE'", "2.433 10-4"," 6%"
    ":math:`\mathrm{MXX}(\mathrm{A1})` ", "'ANALYTIQUE'", "4050. "," 2%"
    ":math:`\mathrm{KXX}(\mathrm{A1})` ", "'ANALYTIQUE'", "7.21 10-4"," 5%"



+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|**Identification**                                                |**Reference type**|**Reference**|**Tolerance (%)**|
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{MXX}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |4044.16      |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{KXX}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |7.1996 10-4  |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+


* The quantities are expressed in the coordinate system defined by the nautical angles :math:`\alpha \mathrm{=}33°` and :math:`\beta \mathrm{=}12°`.


.. csv-table::

    "**Identification**", "**Reference Type**", "**Reference**", "**Tolerance (%)**"
    ":math:`\mathrm{DZ}(\mathrm{A1})` ", "'ANALYTIQUE'", "2.433 10-4"," 6%"
    ":math:`\mathit{MXX}(\mathit{A1})` ", "'NON_REGRESSION'", "2847.47", "1.e-6"
    ":math:`\mathit{MYY}(\mathit{A1})` ", "'NON_REGRESSION'", "1198.15", "1.e-6"
    ":math:`\mathit{MXY}(\mathit{A1})` ", "'NON_REGRESSION'", "-1852.21", "1.e-6"
    ":math:`\mathit{KXX}(\mathit{A1})` ", "'NON_REGRESSION'", "5.0692 10-4", "1.e-6"
    ":math:`\mathit{KYY}(\mathit{A1})` ", "'NON_REGRESSION'", "2.1330 10-4", "1.e-6"
    ":math:`\mathit{KXY}(\mathit{A1})` ", "'NON_REGRESSION'", "-3.2974 10-4", "1.e-6"



+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|**Identification**                                                |**Reference type**|**Reference**|**Tolerance (%)**|
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{MXX}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |2842.56      |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{MYY}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |1197.70      |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{MXY}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |-1849.40     |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{KXX}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |5.0605 10-4  |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{KYY}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |2.1322 10-4  |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+
|:math:`\mathit{KXY}`|:math:`\mathit{M266}`|:math:`\mathit{Point}3`|'NON_REGRESSION'  |-3.2924 10-4 |1.e-6            |
+--------------------+---------------------+-----------------------+------------------+-------------+-----------------+


notes
---------

The coefficients of the following elasticity matrices, used during the calculations, were calculated with :math:`{\nu }_{b}=0`:


1. Membrane elasticity matrix: :math:`\left\{\begin{array}{ccc}4614.& 0& 0\\ 0& 4614.& 0\\ 0& 0& 2142.\end{array}\right\}{10}^{6}N\mathrm{/}m`


2. Flexural elasticity matrix: :math:`\left\{\begin{array}{ccc}5.617& 0& 0\\ 0& 5.617& 0\\ 0& 0& 2.57\end{array}\right\}{10}^{6}N/m`

To be certain of staying within the elastic domain, the elastic limits, expressed in the orthotropy coordinate system, are set arbitrarily to a very high value:

Elastic limits in positive flexure:

 Direction :math:`x`: :math:`{1.10}^{10}\mathrm{MNm}/\mathrm{ml}`

 Direction :math:`y`: :math:`{1.10}^{10}\mathrm{MNm}/\mathrm{ml}`

Elastic limits in negative flexure:

 Direction :math:`x`: :math:`–{1.10}^{10}\mathrm{MNm}/\mathrm{ml}`

 Direction :math:`y`: :math:`–{1.10}^{10}\mathrm{MNm}/\mathrm{ml}`

As the structure remains in the elastic domain, the kinematic recall coefficient (Prager constant) can take any value.