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


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

X

Y

B0X

B1X

B0Y

B1Y

.. image:: images/100000000000045A0000024D55A28A2BE14B6695.png
    :width: 4.7783in
    :height: 2.5634in


.. _RefImage_100000000000045A0000024D55A28A2BE14B6695.png:

**Figure** 3.1-a **: Model A mesh**

Modeling: **DKTG**

Boundary conditions:


* Embedding in :math:`\mathrm{B0X}`,


* :math:`\mathrm{DY}=0.0` on the whole beam.

Temporal integration:


* Diagram: NEWMARK, formulation: DEPLACEMENT,


* No time: :math:`1.{10}^{-3}s` with possible subdivision up to :math:`1.{10}^{-5}s`.


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

Number of knots: 1536, Number of meshes: elements TRI3: 2860, elements SEG2: 210.

The meshes are duplicated twice to affect the two reinforcement grids.


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


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "Frequency (:math:`\mathrm{Hz}`) First mode", "54.67", "54.67", "54.582", "0.160"
    "Frequency (:math:`\mathrm{Hz}`) Third mode", "342.64", "342.64", "338.609", "1.176"
    "Position center of gravity :math:`G` (:math:`m`)", "0.05", "0.05", "0."
    "Inertia :math:`{I}_{\mathrm{yy}}` *(* :math:`G` *)*", "8.611", "8.6038", "0.083"


For the transitory analysis, we test at different times (non-regression test):


* the average of the vertical movements of the points of :math:`\mathrm{B1X}`,


* the resultant of the nodal forces applying to :math:`\mathrm{B1X}`,


* the vertical nodal reaction on :math:`A`.

The total kinetic energy is also tested (by comparison with the results provided by a Python loop).


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "Average vertical movements on :math:`\mathrm{B1X}` (at order number 100)", "— 7.79 10-4", "— 7.7917 10-4", "0.022"
    "Vertical resultant of the forces applied to :math:`\mathrm{B1X}` (at order number 90)", "— 9.48 10+3", "— 9.4833 10+3", "0.035"
    "Vertical nodal reaction on :math:`A` (at order number 100)", "3.72 10+3", "3.7139 10+3", "—0.161"
    "Total kinetic energy (at order number 100)", "9.89588", "9.902", "0.062"