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


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

Discrete elements of stiffness, damping and mass.


.. image:: images/Object_9.svg
    :width: 300
    :height: 109


.. _RefImage_Object_9.svg:

Characteristics of the elements:


.. csv-table::

    "DISCRET:", "nodal mass", "M_T_D_N"
    "", "linear stiffness", "K_T_D_L (:math:`{k}_{\mathrm{N1N2}}=k/10`, :math:`{k}_{\mathrm{N2N3}}=\mathrm{10k}`)"
    "", "linear amortization", "A_T_D_L"


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

Node names: :math:`A=\mathrm{N1}`, :math:`C=\mathrm{N2}`, :math:`B=\mathrm{N3}`.

Calculation methods:


* Integration into physical space with Newmark (:math:`\alpha =\mathrm{0,25}`, :math:`\delta =\mathrm{0,5}`)

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


* Full modal integration with Euler

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


* Full modal integration with 2nd order adaptive :math:`\Delta t`

No initial time :math:`\Delta t={10}^{-3}s` then modal recombination


* Full modal integration with :math:`\Delta t` adaptive using the Runge-Kutta order method (32). Relative error tolerance is :math:`{10}^{-5}`.


* Full modal integration with :math:`\Delta t` adaptive using the Runge-Kutta order method (54). Relative error tolerance is :math:`{10}^{-6}`.

Observation time: 3 s.


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

Number of knots: 3

Number of meshes and type: 2 meshes SEG2


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


* Move (:math:`m`) from point :math:`B`


.. csv-table::

    "", ""
    "**Time**", "**Reference**"
    "(:math:`s`)", ""
    "0.27", "3.0927 E-3"
    "0.53", "8.7953 E-4"
    "0.80", "2.4669 E-3"
    "1.25", "-1.0980 E-3"
    "1,51", "7,8754 E-4"
    "1.78", "-5.6508 E-4"
    "2.05", "4.0502 E-4"
    "2.31", "-2.9012 E-4"
    "2.58", "2.0831 E-4"
    "2.85", "-1.4943 E-4"



* Speed (:math:`{\mathrm{m.s}}^{-1}`) of point :math:`B`


.. csv-table::

    "", ""
    "**Time**", "**Reference**"
    "(:math:`s`)", ""
    "0.11", "1.8347 E-2"
    "0.39", "-1.3140 E-2"
    "0.66", "9.3509 E-3"
    "0.93", "-6.7080 E-3"
    "1.11", "-1.5863 E-2"
    "1.37", "1.1157 E-2"
    "1.64", "-7.9838 E-3"
    "1.90", "5.7108 E-3"
    "2.17", "-4.0998 E-3"
    "2.44", "2.9405 E-3"
    "2.71", "-2.1073 E-3"
    "2.97", "1.5105 E-3"



notes
---------

The results are tested at the level of the respective peaks of movement and speed where the values are the most significant.