Modélisation A
==============


Caractéristiques de la modélisation
-----------------------------------

Éléments discrets de rigidité, amortissement et masse.


.. image:: images/Object_12.svg
    :width: 440
    :height: 159


.. _RefImage_Object_12.svg:

Caractéristiques des éléments :


.. csv-table::

    "DISCRET:", "masse nodale", "M_T_D_N"
    "", "rigidité linéaire", "K_T_D_L"
    "", "amortissement linéaire", "A_T_D_L(:math:`c={c}_{\mathrm{critique}}` )"


Conditions aux limites : au nœud :math:`\mathit{N1}` DDL_IMPO DX = DY = DZ = 0.

Noms des nœuds : :math:`{P}_{1}=\mathrm{N1}` , :math:`{P}_{2}=\mathrm{N2}` .

Méthodes de calcul :


*   Intégration sur la base modale avec Newmark (:math:`\alpha =0,25` , :math:`\delta =0,5` )

Pas de temps :math:`\Delta t={10}^{-3}s`


*   Intégration sur la base modale avec Euler

Pas de temps :math:`\Delta t={10}^{-3}s`

Durée d’observation : :math:`0,5s` .


Caractéristiques du maillage
----------------------------

Nombre de nœuds : 2

Nombre de mailles et type : 1 maille SEG2


Grandeurs testées et résultats
------------------------------


*   Déplacement du point B


.. csv-table::

    "", "**Déplacement**", "**Déplacement**", "", "**Déplacement**", ""
    "**Temps**", "**Référence**", "**NEWMARK**", "**Tolérance**", "**EULER**", "**Tolérance**"
    "(:math:`s` )", "(:math:`m` )", "**Aster** (:math:`m` )", "(%)", "**Aster** (:math:`m` )", "(%)"
    "0,06", "1,18914 E–4", "1,18886 E–4", "0.5 %", "1,18886 E–4", "0.5 %"
    "0,12", "–9,42819 E–5", "–9,42574 E–5", "0.5 %", "–9,47822 E–5", "0.6 %"
    "0,19", "9,97958 E–5", "9,97765 E–5", "0.5 %", "9,96206 E–5", "0.5 %"
    "0,25", "–9,97748 E–5", "–9,97526 E–5", "0.5 %", "–9,99152 E–5", "0.5 %"
    "0,31", "9,78457 E–5", "9,78210 E–5", "0.5 %", "9,83436 E–5", "0.6 %"
    "0,38", "–9,88705 E–5", "–9,88530 E–5", "0.5 %", "–9,84730 E–5", "0.5 %"
    "0,44", "9,99961 E–5", "9,99754 E–5", "0.5 %", "9,99525 E–5", "0.5 %"



*   Vitesse du point B


.. csv-table::

    "", "**Vitesse**", "**Vitesse**", "", "**Vitesse**", ""
    "**Temps**", "**Référence**", "**NEWMARK**", "**Tolérance**", "**EULER**", "**Tolérance**"
    "(:math:`s` )", "(:math:`{\mathrm{m.s}}^{-1}` )", "**Aster** (:math:`{\mathrm{m.s}}^{-1}` )", "(%)", "**Aster** (:math:`{\mathrm{m.s}}^{-1}` )", "(%)"
    "0,03", "3,31400 E–3", "3,31363 E–3", "0.5 %", "3,32568 E–3", "0.5 %"
    "0,09", "–5,13760 E–3", "–5,13729 E–3", "0.5 %", "–5,13627 E–3", "0.65%"
    "0,16", "4,93337 E–3", "4,93354 E–3", "0.5 %", "4,93088 E–3", "0.5 %"
    "0,22", "–5,00087 E–3", "–5,00087 E–3", "0.5 %", "–5,00133 E–3", "0.5 %"
    "0,28", "4,95298 E–3", "4,95284 E–3", "0.5 %", "4,95297 E–3", "0.5%"
    "0,35", "–4,87813 E–3", "–4,87836 E–3", "0.5 %", "–4,87801 E–3", "0.5 %"
    "0,41", "4,98415 E–3", "4,98423 E–3", "0.5 %", "4,98409 E–3", "0.5 %"
    "0,47", "–4,99041 E–3", "–4,99035 E–3", "0.5 %", "–4,99043 E–3", "0.5 %"



Remarques
---------

Les résultats sont testés au niveau des pics pour le grain d’observation retenu (10-2s) où les valeurs sont les plus significatives.

Le régime devient quasi-permanent après la première période, c’est ce que l’on doit observer en menant une analyse transitoire.