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


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

We use Timoshenko's right beam element: POU_D_T


.. image:: images/100014FE0000297200000A3B2B8B517498B7B1B2.svg
    :width: 534
    :height: 132


.. _RefImage_100014FE0000297200000A3B2B8B517498B7B1B2.svg:

**Problem 1:**


.. csv-table::

    "Cutting:", "beam :math:`\mathrm{AB}`: 40 meshes SEG2"
    "Boundary conditions:
    In all the knots
    in :math:`A`:
    in :math:`B`:", "DDL_IMPO =( GROUP_NO = 'AB', DZ=0., DRX =0, DRY =0.)
    (NOEUD ='A', DX=0., D=0.)
    (NOEUD ='B', DY=0.)"


**Problem 2:**


.. csv-table::

    "Cutting:", "beam :math:`\mathrm{AB}`: 40 meshes SEG2
    2 rigid elements :math:`\mathrm{AC}`, :math:`\mathrm{BC}`: 2 meshes SEG2"
    "Boundary conditions:
    In all the knots
    in :math:`C`:
    in :math:`D`:", "DDL_IMPO = (TOUT =' OUI ', DZ=0., DRX =0, DRY =0.)
    (NOEUD ='C', DX=0., DY=0.)
    (NOEUD ='D', DY=0.)"



.. csv-table::

    "Node names:", "Point :math:`A` = :math:`\mathrm{N100}`
    Point :math:`B` = :math:`\mathrm{N200}` ", "Point :math:`C` = :math:`\mathrm{N300}`
    Point :math:`D` = :math:`\mathrm{N400}`"



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


.. csv-table::

    "Number of knots:", "43"
    "Number of meshes and types:", "42 SEG2"



notes
---------

Definition of rigid beams :math:`\mathrm{AC}` and :math:`\mathrm{BD}`:


* Section: :math:`\mathrm{Hy}=0.2`, :math:`\mathrm{Hz}=0.2`.


* Material: :math:`E={2.10}^{16}`, :math:`\rho =0`.


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

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


.. csv-table::

    "**Clean Mode**", "**Reference**", "**Aster**", "**Tolerance**"
    "**Problem 1**", "", ""
    "flexure 1", "431.555", "431.8916", "0.2%"
    "traction 1", "1265.924", "1266.0056", "0.2%"
    "flexure 2", "1498.295", "1500.7635", "0.2%"
    "flexure 3", "2870.661", "2873.5344", "0.2%"
    "traction 2", "3797.773", "3799.9692", "0.2%"
    "flexure 4", "4377.837", "4370.8206", "0.2%"



.. csv-table::

    "**Clean Mode**", "**Reference**", "**Aster**", "**Tolerance**"
    "**Problem 2**", "", "", ""
    "1", "392.8", "394.4774", "0.5%"
    "coupling 2", "922.2", "922.6072", "0.1%"
    "flexure 3", "1592.0", "1638.2311", "3%"
    "traction 4", "2629.2", "2778.7000", "5.8%"
    "compression 5", "3126.2", "3261.6699", "4.5%"


We calculate the kinetic energy of the first beam element connected to point :math:`A` of problem 1:


.. csv-table::

    "**Option**", "**Component**", "**Reference (** NON_REGRESSION **)**", "**Aster**", "**% difference**"
    "ECIN_ELEM "," TOTALE ", "51366.0", "51366.027", "1%"



notes
---------

Calculations made by:

Problem 1:


.. code-block:: text

    CALC_MODES
OPTION =' AJUSTE '
CALC_FREQ =_F (FREQ =( 430., 4500.))

Problem 2:


.. code-block:: text

    CALC_MODES
OPTION =' AJUSTE '
CALC_FREQ =_F (FREQ =( 380., 300.))

**Contents of the results file:**

Problem 1:

6 first natural frequencies, eigenvectors and modal parameters.

Problem 1:

5 first natural frequencies, eigenvectors and modal parameters.