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


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

The characteristics used and the mesh are those deduced from the data in paragraph 1. Harmonic response and transfer functions have been calculated for reduced frequencies :math:`>` (where :math:`>`). The results obtained by Mita and Luco for these reduced frequencies are presented in the reference [:ref:`bib2 <bib2>`].


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

The circular foundation mesh is shown below (see §1.1):


.. image:: images/10000000000001A100000190030C5696E4A21E7F.png
    :width: 2.5189in
    :height: 2.4161in


.. _RefImage_10000000000001A100000190030C5696E4A21E7F.png:


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

For the case with spatial variability, we choose :math:`>` and we test against the results of the literature (SOURCE_EXTERNE) with a tolerance of :math:`>`.

Results achieved with DYNA_ISS_VARIpour :math:`>` and:


.. csv-table::

    ":math:`>` "," :math:`>` "," :math:`>`"
    "1.0", "0.767", "0.767"
    "2.0", "0.437", "0.437"
    "3.0", "0.251", "0.251"
    "", "", ""




As a reminder, the reference results [:ref:`bib2 <bib2>`], see also §2.2:


.. csv-table::

    ":math:`>` "," :math:`>` "," :math:`>`"
    "1.0", "0.732", "0.730"
    "2.0", "0.402", "0.416"
    "3.0", "0.251", "0.270"


In addition, a NON_REGESSION test is done for the values calculated by DYNA_ISS_VARI with a tolerance of :math:`>` (by default value).

Comparison of transfer functions :math:`>` obtained with DYNA_ISS_VARI and with Mita and Luco:


.. image:: images/1000000000000230000001A40DE48FD0C8552805.png
    :width: 3.85in
    :height: 2.8874in


.. _RefImage_1000000000000230000001A40DE48FD0C8552805.png:

For case :math:`>`, we test the response after projection onto physical coordinates. Since the foundation is rigid and massless, all the nodes undergo the same displacement which is equal to 1.0 in direction :math:`>` for an excitation in direction :math:`>`.

:math:`>`

:math:`>` is the modal impedance matrix, :math:`>` the modal response and :math:`>` for a seismic excitation in the :math:`>` direction and :math:`>` for a vertical earthquake.


.. csv-table::

    ":math:`>` "," :math:`>` "," :math:`>`"
    "1.0, 2.0 3.0", "1.0
    1.0
    1.0", "1.0
    1.0
    1.0"


With a *via* REST_SPEC_PHYS projection, we get the result:


.. csv-table::

    ":math:`>` "," SPEC N11 'DX'", "SPEC N11 'DZ'"
    "1.0", "1.00527E+00", "1.03014E+00"


A test of type ANALYTIQUE is carried out with a tolerance of :math:`>` for 'DX' and :math:`>` for 'DZ'.