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


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

Modeling DKT


.. image:: images/100022BE00001054000010544E9C4231BAE65265.svg
    :width: 210
    :height: 210


.. _RefImage_100022BE00001054000010544E9C4231BAE65265.svg:


.. csv-table::

    "Node names:", "Points", ":math:`A=\mathrm{N1}` "," "," :math:`B=\mathrm{N78}` "," :math:`C=\mathrm{N145}` "," :math:`D=\mathrm{N80}` ", ""
    "", "", ":math:`G=\mathrm{N65}` "," :math:`H=\mathrm{N17}` "," "," :math:`I=\mathrm{N73}` "," :math:`J=\mathrm{N121}` "," :math:`K=\mathrm{N71}`"


**Boundary conditions:**

Cas1 in all the nodes on side :math:`\mathrm{AB}`:


.. code-block:: text

    DDL_IMPO = _F (GROUP_NO = AB DX=0., DY=0., DZ=0., DRX =0., =0. , DRY =0. , DRZ =0.)

Case 2 none


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

Number of knots: 145

Number of meshes and types: 256 TRIA3


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


.. csv-table::

    "", "**Frequency**", "**(** :math:`\mathrm{Hz}` **)**", "", ""
    "**Clean Mode**", "**Reference**", "**Aster**", "**% difference**", "**Tolerance**"


1°: Plate embedded on one side


.. csv-table::

    "1", "8.7266", "8.6718", "—0.63", ""
    "2", "21.3042", "21.2904", "—0.06", ""
    "3", "53.5542", "53.0992", "—0.85", "1. 10—2"
    "4", "68.2984", "67.9269", "—0.54", ""
    "5", "77.7448", "77.4294", "—0.40", ""
    "6", "136.0471", "135.7635", "—0.21", ""



.. csv-table::

    "", "*Aster* :math:`\mathrm{epot}=\mathrm{ecin}`"
    "1", "1.4796 104"
    "2", "1.7331 104"
    "3", "4.3802 104"
    "4", "3.7367 104"
    "5", "5.4956 104"
    "6", "1.3483 105"


2°: Free plate


.. csv-table::

    "7", "33.7119", "33.6839", "—0.08", ""
    "8", "49.4558", "48.9362", "—1.05", ""
    "9", "61.0513", "60.5849", "—0.76", "1.1 10—2"
    "10", "87.5160", "87.0993", "—0.48", ""
    "11", "87.5160", "87.0993", "—0.48", ""



.. csv-table::

    "", "*Aster* :math:`\mathrm{epot}=\mathrm{ecin}`"
    "7", "2.2396 104"
    "8", "4.7270 104"
    "9", "7.2453 104"
    "10", "1.4974 105"
    "11", "1.4974 105"


We calculate the kinetic energy ECIN_ELEM of element DKT (connected to point :math:`A`, one of whose sides is on :math:`\mathrm{AD}`) of problem 1 ("plate embedded on one side"):


+----------+-------------+------------------------------------+---------+----------------+
|**Option**|**Component**|**Reference (** NON_REGRESSION **)**|**Aster**|**% difference**|
+----------+-------------+------------------------------------+---------+----------------+
|          |                                                                             |
+----------+-------------+------------------------------------+---------+----------------+
|ECIN_ELEM |TOTALE       |0.011448                            |0.0114476|3.5 10—4        |
+----------+-------------+------------------------------------+---------+----------------+
|ECIN_ELEM |FLEXION      |2968.79                             |2968.7918|6.1 10—5        |
+----------+-------------+------------------------------------+---------+----------------+


notes
---------


.. code-block:: text

    CALC_MODES OPTION = 'BANDE'
Case 1: FREQ = (8., 140.)
Case 2: FREQ = (32., 90.)

**Contents of the results file:**


.. csv-table::

    "1°:", "6 first natural frequencies, eigenvectors and modal parameters
    deformation energy and kinetic energy of the 6 modes."
    "2°:", "5 natural frequencies, eigenvectors and modal parameters (:math:`f>0`)
    deformation energy and kinetics of the 5 modes."