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


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

This modeling allows the validation of integration by modal recombination.

**Discreet element of translational rigidity**


.. image:: images/10000DF000001FF0000006345695854C605BA72A.svg
    :width: 412
    :height: 80


.. _RefImage_10000DF000001FF0000006345695854C605BA72A.svg:

Characteristics of the elements


.. csv-table::

    "DISCRETavec ", "nodal masses", "M_T_D_N", "M_T_N", "M_T_N"
    "", "stiffness matrices", "K_T_D_L", "K_T_L"
    "", "damping matrices", "A_T_D_L", "A_T_L"


Block degrees of freedom in :math:`Y` and :math:`Z` for all nodes


.. code-block:: text
 DDL_IMPO: (TOUT: 'OUI' DY: 0., DZ: 0.)

Boundary conditions at extreme knots


.. code-block:: text
 (GROUP_NO: AB DX: 0.)

Node names:


.. csv-table::

    "Point :math:`A=\mathrm{N1}` "," :math:`{P}_{1}=\mathrm{N2}`"
    "Point :math:`B=\mathrm{N10}` "," :math:`{P}_{2}=\mathrm{N3}`"
    "", "..."
    "", ":math:`{P}_{8}=\mathrm{N9}`"


Modal recombination with all modes (i.e. 8),

EULER diagram, resumption of a first calculation at :math:`t=0.455s`

time step used: :math:`\Delta t=1.E–3s`.


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

Number of knots: 10

Number of meshes and types: 9 SEG2

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


.. csv-table::

    "**Time**", "**Reference**"
    "0.09", "4.02 E—5"
    "0.18", "4.22 E—6"
    "0.27", "3.89 E—5"
    "0.37", "5.98 E—6"
    "0.46", "3.73 E—5"
    "0.54", "7.14 E—6"
    "0.63", "3.64 E—5"
    "0.72", "8.07 E—6"
    "0.81", "3.58 E—5"
    "0.9", "8.76 E—6"
    "0.99", "3.52 E—5"
    "1.08", "—3.08 E—5"
    "1.18", "3.02 E—5"
    "1.27", "—2.88 E—5"
    "1.36", "2.80 E—5"
    "1.45", "—2.65 E—5"



notes
---------

The relative minima (:math:`t=0.18,0.54,\dots`) do not have very good precision during the excitation phase with a :math:`\Delta t=0.001` step.