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


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


.. image:: images/10001396000069D500002F2192DBE4272AE86F4A.svg
    :width: 372
    :height: 166


.. _RefImage_10001396000069D500002F2192DBE4272AE86F4A.svg:

**Figure 3.1-a: Modeling of the anti-seismic device**

The jaws that insert the device are each modeled by a discrete element with 3 degrees of freedom DIS_T.

The anti-seismic device is simulated using the keyword factor ANTI_SISM of the operator DYNA_VIBRA.

Node :math:`\mathrm{NO1}` is subject to enforced acceleration :math:`{\gamma }_{1}(t)`, node :math:`\mathrm{NO11}` to :math:`{\gamma }_{2}(t)=0`. We calculate the relative displacement of node :math:`\mathrm{NO2}` and its absolute displacement.

The time integration is carried out with the Euler algorithm and a time step of :math:`\mathrm{1,25}\mathrm{.}{10}^{-5}` seconds. The calculations are archived every 80 steps.

We consider reduced damping :math:`{\xi }_{i}` to zero for all of the two calculated modes.


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

The mesh consists of 4 knots and 4 DIS_T meshes.


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

The absolute displacement of the node :math:`\mathrm{NO2}`: NO2_DX_A and the force in the anti-seismic device are calculated. The values are compared to those calculated by a MATLAB function.


.. csv-table::

    "", "**Reference**"
    "Maximum effort (N)", "1,266E+04"
    "Effort — RMS ", "7,912E+03"
    "NO2_DX_A max (m)", "1.670E—02"
    "NO2_DX_A — RMS ", "1,180E—02"
    "NO2_DX_R max (m)", "1.266E—06"
    "NO2_DX_R — RMS ", "7,798E—07"


We trace the evolution of the force that is exerted in the device as a function of the absolute displacement of the node :math:`\mathit{NO2}`. Comparisons are made to the measured quantities.


.. image:: images/Object_4.svg
    :width: 372
    :height: 166


.. _RefImage_Object_4.svg:

Taking into account the approximation of the excitation imposed on the vibrating table in one sine, the model implanted in*Code_Aster* is representative of the device tested.

The temporal evolution of the movement of the device is also traced:


.. image:: images/Object_5.svg
    :width: 372
    :height: 166


.. _RefImage_Object_5.svg:

Time (s)