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

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

In this modeling, we use the operator DYNA_VIBRA (see [:ref:`U4.53.03 <U4.53.03>`]) with the relationship DIS_CHOC. The integration diagram is DIFF_CENTRE.

A DIS_T element on a POI1 mesh is used to model the system.

Relationships between degrees of freedom are used to force the movement to be unidirectional in the :math:`\theta` direction:


.. code-block:: text

    LIAISON_DDL = _F (NOEUD = ('NO1', 'NO1'),

    DDL = ('DX' 'DY'),

    COEF_MULT = (0.707, -0.707),

    COEF_IMPO = 0.)

An obstacle of type PLAN_Z (two parallel planes separated by a game) is used to simulate the sliding plane. We choose to use the :math:`\mathrm{Oy}` axis as the generator of this plane, i.e. NORM_OBST = (0., 1., 0.). The origin of the obstacle is ORIG_OBST = (0.,0.,1.). It remains to define his game, which gives the halfway gap between the planes.

For there to be a reaction force from the plane on the system, the system must be slightly pressed into the plane obstacle by a distance :math:`\delta n` such as: :math:`{F}_{n}={K}_{n}\cdot \mathrm{\delta }n`.

Like :math:`{F}_{n}=\mathrm{mg}`, we then have :math:`\delta n=\mathrm{mg}/{K}_{n}`.

We considered a normal shock stiffness of :math:`20N/m` (fictional stiffness that only makes sense to generate a reaction force from the plane on the system), so we have :math:`\delta n=\mathrm{0,5}`. The obstacle PLAN_Z having its origin in :math:`Z=1` and the solid being in :math:`Z=0`; a game of :math:`\mathrm{0,5}m` will create a hole :math:`\delta n=\mathrm{0,5}m` from where JEU: 0.5

Tangential shock stiffness: :math:`{K}_{T}=400000N/m`: it is greater than the stiffness of the oscillator for the stopping phase to be modelled correctly.

No time used for time integration: :math:`{5.10}^{-4}\mathit{sec}`.


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

Number of knots: 1

Number of meshes and types: 1 POI1


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

Displacement values (in meters) in the :math:`\theta` direction for the times when the speed sign changed over the :math:`(0;0.3s)` time period.

.. csv-table::

    "**Identification**", "**moment (s)**", "**Reference**"
    ":math:`\mathrm{DY}=\mathrm{r2}\mathrm{cos45}` "," :math:`\pi \times {10}^{-2}` ", "—4.596E—4"
    ":math:`\mathrm{DY}=\mathrm{r3}\mathrm{cos45}` "," :math:`2\pi \times {10}^{-2}` ", "3.182E—4"
    ":math:`\mathrm{DY}=\mathrm{r4}\mathrm{cos45}` "," :math:`3\pi \times {10}^{-2}` ", "—1.768E—4"
    ":math:`\mathrm{DY}=\mathrm{r5}\mathrm{cos45}` "," :math:`4\pi \times {10}^{-2}` ", "3.536E—5"