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


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

We use straight Timoshenko POU_D_T beams and DIS_T discrete elements.


.. image:: images/100018180000196D0000082AA82EEF68684B27DF.svg
    :width: 327
    :height: 105


.. _RefImage_100018180000196D0000082AA82EEF68684B27DF.svg:


.. csv-table::

    "Cutting:", ":math:`\mathrm{AD}`: 5 stitches SEG2
    :math:`\mathrm{DB}`: 15 stitches SEG2
    :math:`\mathrm{CD}`: 1 mesh SEG2"
    "", ""
    "Modeling:", "POU_D_Tpour all the meshes of the :math:`\mathrm{AB}` beam
    DIS_Tpour the :math:`\mathrm{CD}` mesh and the :math:`C` stitch
    For the whole structure :math:`\mathrm{DZ}=\mathrm{DRX}=\mathrm{DRY}=0`"



.. csv-table::

    "Boundary conditions:
    In all the knots of
    Beam :math:`\mathrm{AB}`:
    At the knots
    extremities:
    in :math:`C`:", "DDL_IMPO: (GROUP_NO: NPOUTRE DZ:0., DRX :0, DRY :0.)
    (GROUP_NO: A DX: 0., DY: 0.) (GROUP_NO: B DY: 0.)
    (GROUP_NO: CDX: 0., DZ: 0.)"



.. csv-table::

    "Node names:", "Point :math:`A=\mathrm{N1}`
    Point :math:`B=\mathrm{N21}` ", "Point :math:`C=\mathrm{N22}`
    Point :math:`D=\mathrm{N6}`"



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


.. csv-table::

    "Number of knots:", "22", ""
    "Number of meshes and types:", "21 meshes SEG2 ", "1 mesh P0I1"



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

**Frequency (** :math:`\mathrm{Hz}` **)**


.. csv-table::

    ":math:`\lambda` ", "**Clean Mode Order**", "**Reference**"
    ":math:`0.` ", "flexure 1
    Flexion 2", "1.5707
    6.2831"
    ":math:`0.001` ", "1 bend
    2. Flexion
    3 flexure 2", 1" 1.5460
    1.5958
    6.2336"
    ":math:`0.01` ", "1 bend
    2 flexure
    3 flexure 2", 1" 1.4937
    1.6506
    6.2874"



notes
---------

For :math:`\lambda =0`, we did:


.. code-block:: text

    CALC_MODES
OPTION = 'PLUS_PETITE'
CALC_FREQ =_F (NMAX_FREQ = 2)
SOLVEUR_MODAL =_F (METHODE = 'TRI_DIAG')

For :math:`\lambda =0.001`, we did:


.. code-block:: text

    CALC_MODES
OPTION = 'PROCHE'
CALC_FREQ =_F (FREQ = (1.5, 1.6, 6.5))

For :math:`\lambda \mathrm{=}0.01`, we did:

.. code-block:: text

    CALC_MODES
OPTION = 'AJUSTE'
CALC_FREQ =_F (FREQ = (1., 7.))

**Contents of the results file:**

Case 1:2 first natural frequencies, eigenvectors and modal parameters.

Case 2:3 first natural frequencies and modal parameters.

Case 3: first 3 natural frequencies, eigenvectors and modal parameters.