.. _v6.08.122-modelisation_A:


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

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

The modeling is shown in the figure below:

.. figure:: figures/v6.08.122_maillage.png
    :width: 70%
 :align: center

    Modeling A, Geometry mesh.


Characteristics of the mesh
----------------------------
The dimensions of the geometry:

* :math:`L_x = L_y = 2.0~cm`.
* :math:`e_x = e_y = 0.5~cm`.
* All nodes are at :math:`z=0`, except for nodes 2 and 8 which are at the same coordinates :math:`x` and :math:`y` as nodes 1 and 7, but at :math:`z=-0.02~cm`.


The mesh consists only of discrete ones:

* "DIS_T_D_N" are affected on nodes 3, 4, 5, 5, 6, 9, 10, 11, 12.
* a "DIS_T_D_L" is assigned between the nodes (6, 10).
* "DIS_TR_D_L" are assigned between nodes (1, 2) and (7, 8).

Mechanical characteristics
---------------------------
The only characteristics are for discrete elements. These characteristics are not physical, they only serve to give a certain stiffness to the system.


Loads
-----------
Moves imposed at node 1:

.. csv-table::
    :width: 50%
 :align: center

    **Instants**, Node 1 :math:`D_x`, Node 1 :math:`D_y`
    0, :math:`0.0 *e_x`, :math:`-0.0* e_y`
    1, :math:`0.0 *e_x`, :math:`-1.0* e_y`
    2, :math:`0.0 *e_x`, :math:`-2.0* e_y`
    3, :math:`0.0 *e_x`, :math:`-3.0* e_y`
    4, :math:`1.0 *e_x`, :math:`-3.0* e_y`
    5, :math:`2.0 *e_x`, :math:`-2.0* e_y`
    6, :math:`3.0 *e_x`, :math:`-1.0* e_y`
    7, :math:`3.0 *e_x`, :math:`-0.0* e_y`
    8, :math:`0.0 *e_x`, :math:`-0.0* e_y`
    9, :math:`1.0 *e_x`, :math:`-0.0* e_y`
    10, :math:`2.0 *e_x`, :math:`-0.0* e_y`
    11, :math:`3.0 *e_x`, :math:`-0.0* e_y`
    12, :math:`3.0 *e_x`, :math:`-1.0* e_y`
    13, :math:`2.0 *e_x`, :math:`-2.0* e_y`
    14, :math:`1.0 *e_x`, :math:`-3.0* e_y`
    15, :math:`0.0 *e_x`, :math:`-3.0* e_y`
    16, :math:`0.0 *e_x`, :math:`-0.0* e_y`


.. figure:: figures/v6.08.122_deplacement_B.png
    :width: 70%
 :align: center

    Modeling A, Node 1 displacement vs time.

.. figure:: figures/v6.08.122_trajectoire_B.png
    :width: 70%
 :align: center

    Modeling A, Node Trajectory 1.


Tested sizes and results
------------------------------
The quantities tested are the displacements at node 7, those at node 1 are the data:

.. csv-table::
    :width: 50%
 :align: center

    **Instants**, Node 1 :math:`D_x`, Node 1 :math:`D_y`, Node 1, Node 7 :math:`D_x`, Node 7 :math:`D_y`
    5.0, 1.00e-02, -1.00e-02, 5.00e-03, 0.00e-00
    13.0, 1.00e-02, -1.00e-02, 0.00e-02, 0.00e-00, -5.00e-03


.. figure:: figures/v6.08.122_deplacement_C.png
    :width: 70%
 :align: center

    Modeling A, Node 7 displacement vs time.