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


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

Discrete elements of stiffness, damping and mass.


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


.. _RefImage_Object_12.svg:

Characteristics of the elements:


.. csv-table::

    "DISCRET:", "nodal mass", "M_T_D_N"
    "", "linear stiffness", "K_T_D_L"
    "", "linear amortization", "A_T_D_L (:math:`c={c}_{\mathrm{critique}}`)"


Boundary conditions: at node :math:`\mathit{N1}` DDL_IMPO DX = DY = DZ = 0.

Node names: :math:`{P}_{1}=\mathrm{N1}`, :math:`{P}_{2}=\mathrm{N2}`.

Calculation methods:


* Integration on a modal basis with Newmark (:math:`\alpha \mathrm{=}\mathrm{0,25}`, :math:`\delta \mathrm{=}\mathrm{0,5}`)

No time :math:`\Delta t\mathrm{=}{10}^{\mathrm{-}3}s`


* Integration on a modal basis with Euler

No time :math:`\Delta t\mathrm{=}{10}^{\mathrm{-}3}s`

Observation time: :math:`\mathrm{0,5}s`.


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

Number of knots: 2

Number of meshes and type: 1 mesh SEG2


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


* Moving point B


.. csv-table::

    "", "**Move**", "**Move**", "", "**Move**", ""
    "**Time**", "**Reference**", "**NEWMARK**", "****", "**Tolerance**", "**EULER**", "**Tolerance**"
    "(:math:`s`)", "(:math:`m`)", "**Aster** (:math:`m`)", "(%)", "**Aster** (:math:`m`)", "(%)"
    "0.06", "1.189014 E—4", "1.18886 E—4", "1.18886 E—4", "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", "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%"



* Point B speed


.. csv-table::

    "", "**Speed**", "**Speed**", "", "**Speed**", ""
    "**Time**", "**Reference**", "**NEWMARK**", "****", "**Tolerance**", "**EULER**", "**Tolerance**"
    "(: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", "3.31363 E—3", "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", "4.93354 E—3", "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", "4.95284 E—3", "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%"



notes
---------

The results are tested at the peak level for the selected observation grain (10-2 s) where the values are the most significant.

The regime becomes almost permanent after the first period; this is what must be observed when conducting a transitory analysis.