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


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

In this modeling, the dynamic problem is solved in a linear calculation loop where the complement of nodal forces due to the nonlinearity of the detachment is recalculated each time over the entire time range. We use either a harmonic calculation with a frequency evolution and time feedback by Fourier transform in the classical time-frequency method, or a transient calculation on a physical basis with an alternative strictly temporal method.


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

The model is composed of 55 nodes (285 ddls), 42 elements (32 plate elements DKT and 10 discrete elements DIS_T).


Calculation parameters
--------------------

Each dynamic transient calculation is carried out over an interval of :math:`5s` by time steps of :math:`0.005s` archived every 2 steps. Each harmonic calculation is carried out with a step of :math:`1/20.48\mathrm{Hz}` which makes it possible to restore a time window of :math:`20.48s` sufficient to correctly calculate the FFT of the force of gravity constant over time; the maximum calculation frequency is equal to :math:`25\mathrm{Hz}` and the extended one is :math:`50\mathrm{Hz}` in order to obtain a time step of :math:`0.01s` in the time window restored by FFT.


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


.. csv-table::

    "**Identification**", "**Transition**", "**Harmonic**", "**Difference**"
    ":math:`\mathrm{P3}` — :math:`\mathrm{DX}` (2.33 s) iter=1", "-4.58502E-2", "-4.58588E-2", "0.019%"
    ":math:`\mathrm{P3}` — :math:`\mathrm{DY}` (2.33 s) iter=1", "5.67299E-3", "5.67541E-3", "0.043%"
    ":math:`\mathrm{P3}` — :math:`\mathrm{DX}` (2.34 s) iter=2", "-4.82202E-2", "-4.82436E-2", "0.048%"
    ":math:`\mathrm{P3}` — :math:`\mathrm{DY}` (2.34 s) iter=2", "6.55566E-3", "6.54736E-3", "0.127%"


Comparison of FFT fortran (REST_SPEC_TEMP) and FFT python (CALC_FONCTION):


.. csv-table::

    "**Identification**", "**REST_SPEC_TEMP**", "**CALC_FONCTION**", "**Absolute variance**"
    ":math:`\mathrm{P3}` — :math:`\mathrm{DX}` (2.34 s) iter=2", "-4.82202E-2", "-4.82202E-2", "2.5673907444E-16"
    ":math:`\mathrm{P3}` — :math:`\mathrm{DY}` (2.34 s) iter=2", "6.55566E-3", "6.55566E-3", "-7.4593109467E-17"