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


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

Discrete elements of stiffness, damping and mass.


.. image:: images/Object_8.svg
    :width: 399
    :height: 159


.. _RefImage_Object_8.svg:

Characteristics of the elements:


.. csv-table::

    "DISCRET:", "nodal masses", "M_ TR_D_N"
    "", "linear stiffness", "K_ TR_D_L"
    "", "linear amortization", "A_ TR_D_L"


No boundary conditions, in all nodes: :math:`\mathrm{DX},\mathrm{DY},\mathrm{DZ},\mathrm{DRX},\mathrm{DRY},\mathrm{DRZ}` free.

Node names: :math:`{P}_{1}=\mathrm{N1}`, :math:`{P}_{2}=\mathrm{N2}`, :math:`{P}_{3}=\mathrm{N3}`.

Calculation method:

Full modal integration with Newmark (:math:`\alpha =\mathrm{0,25}`, :math:`\delta =\mathrm{0,5}`),

No time: :math:`\Delta t={10}^{-\mathrm{4s}}` then modal recombination.

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


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

Number of knots: 3

Number of meshes and type: 2 meshes SEG2


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


* Move point :math:`{P}_{3}`


.. csv-table::

    "**Time**", "**Move**", "**Move**", "**Difference**"
    "(:math:`s`)", "**Reference** (:math:`m`)", "**Aster** (:math:`m`)", "(%)"
    "0.09", "6.7395 E-6", "6.73326 E-6", "-0.093"
    "0.32", "1.1019 E-5", "1.10002 E-6", "-0.171"
    "1.18", "3.6683 E-5", "3.66122-5", "-0.193"
    "4.92", "1.6615 E-4", "1.65849 E-4", "-0.181"



* Point :math:`{P}_{3}` speed


.. csv-table::

    "**Time**", "**Speed**", "**Speed**", "**Speed**", "**Difference**"
    "(:math:`s`)", "**Reference** (:math:`{\mathrm{m.s}}^{-1}`)", "**Aster** (:math:`{\mathrm{m.s}}^{-1}`)", "(%)"
    "0.05", "1.3425 E-4", "1.34131 E-4", "-0.088"
    "0.32", "-6.4111 E-5", "-6.41097 E-4", "-0.002"
    "1.18", "1.6104 E-5", "1.60598 E-5", "-0.274"
    "3.55", "4.4262 E-5", "4.41720 E-5", "-0.203"



* Acceleration of point :math:`{P}_{3}`


.. csv-table::

    "**Time**", "**Acceleration**", "**Acceleration**", "**Difference**"
    "(:math:`s`)", "**Reference** (:math:`{\mathrm{m.s}}^{-2}`)", "**Aster** (:math:`{\mathrm{m.s}}^{-2}`)", "(%)"
    "0.09", "-3.5694 E-3", "-3.56634 E-3", "-0.086"
    "0.18", "-4.3924 E-3", "-4.38933 E-3", "-0.070"
    "0.55", "4.3766 E-3", "4.37283 E-3", "-0.086"
    "1.18", "4.2459 E-3", "4.24264 E-3", "-0.077"
    "4.92", "-4,2233 E-3", "-4,21962 E-3", "-0.087"



* Relative displacement of point :math:`{P}_{3}` in relation to point :math:`{P}_{1}`


.. csv-table::

    "**Time**", ":math:`{u}_{3}-{u}_{1}` "," :math:`{u}_{3}-{u}_{1}` ", "**Difference**"
    "(:math:`s`)", "**Reference** (:math:`m`)", "**Aster** (:math:`m`)", "(%)"
    "0.18", "8.0987 E-6", "8.04800 E-6", "-0.626"
    "0.55", "-6,2246 E-6", "-6,21194 E-6", "-0.203"
    "0.82", "5.3064 E-6", "5.34121 E-6", "0.656"
    "1.18", "-4.5552 E-6", "-4.52071 E-6", "-0.757"
    "1.92", "-3.0416 E-6", "-3.04417 E-6", "0.085"
    "3.55", "1.8448 E-6", "1.82742 E-6", "-0.942"
    "4.92", "1.4832 E-6", "1.47526 E-6", "-0.535"



notes
---------

In addition to the comparison for the values tested, it is checked that the kinematic variables other than those related to the following translation :math:`x` remain zero.