K modeling
==============

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


.. image:: images/10000000000004230000024608990BF721743CD8.png
    :width: 4.5772in
    :height: 2.2508in


.. _RefImage_10000000000004230000024608990BF721743CD8.png:

Modeling COQUE_SOLIDE:

.. csv-table::

    "Number of nodes", ":math:`2400` ", "", "", ""
    "Number of meshes", ":math:`900` "," HEXA9 ", "", ""



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

+-----------------+---------------------+--------------------+----------------------+-------------------------------+-------------+
|                 |Component            |Nature of clean mode                       |Reference :math:`(\mathrm{Hz})`|Tolerance (%)|
+                 +                     +--------------------+----------------------+                               +             +
|                 |                     |I                   |order                 |                               |             |
+-----------------+---------------------+--------------------+----------------------+-------------------------------+-------------+
|Modes in the plan|:math:`\mathrm{FREQ}`|:math:`2`           |:math:`\mathrm{4,5}`  |:math:`318.36`                 |0.1          |
+                 +                     +--------------------+----------------------+-------------------------------+-------------+
|                 |                     |:math:`3`           |:math:`\mathrm{6,7}`  |:math:`900.46`                 |0.26         |
+                 +                     +--------------------+----------------------+-------------------------------+-------------+
|                 |                     |:math:`4`           |:math:`\mathrm{8,9}`  |:math:`1726.55`                |0.5          |
+                 +                     +--------------------+----------------------+-------------------------------+-------------+
|                 |                     |:math:`5`           |:math:`\mathrm{10,11}`|:math:`2792.21`                |0.9          |
+-----------------+---------------------+--------------------+----------------------+-------------------------------+-------------+
|Transverse modes |:math:`\mathrm{FREQ}`|:math:`2`           |:math:`\mathrm{4,5}`  |:math:`511.`                   |1.23         |
+                 +                     +--------------------+----------------------+-------------------------------+-------------+
|                 |                     |:math:`3`           |:math:`\mathrm{6,7}`  |:math:`1590.`                  |0.42         |
+                 +                     +--------------------+----------------------+-------------------------------+-------------+
|                 |                     |:math:`4`           |:math:`\mathrm{8,9}`  |:math:`3184.`                  |1.75         |
+-----------------+---------------------+--------------------+----------------------+-------------------------------+-------------+

We are also testing option MASS_INER of the POST_ELEM command. The total mass of the ring is easy to evaluate analytically:

.. math::
 :label: eq-2

    m=\ rho\ pi\ times\ left ({R} _ {\ text {ext}}} ^ {2} - {R} _ {\ text {int}} ^ {2}\ right)\ times b=\ mathrm {0.0848230016469242}\ mathit {kg}


.. csv-table::

    "Mass", "Reference", "Precision"
    ":math:`m` "," ANALYTIQUE "," 0.0074%"


The error (very small) comes simply from approximating the curvature by the linear elements.