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


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

**Discreet element in type translation** **DIS_T**


.. image:: images/10000262000010F30000048C5BF6BDB2083723BD.svg
    :width: 218
    :height: 58


.. _RefImage_10000262000010F30000048C5BF6BDB2083723BD.svg:

Characteristics of the elements:

At nodes :math:`\mathrm{P1}` and :math:`\mathrm{P2}`: mass matrices of type M_T_D_N with :math:`m=100\mathrm{kg}`.

Between :math:`\mathrm{P1}` and :math:`\mathrm{P2}`: a K_T_D_L stiffness matrix with :math:`{K}_{x}={10}^{6}N/m`

Boundary conditions:

All degrees of freedom are locked except degree of freedom :math:`\mathrm{DX}` from node :math:`\mathrm{P2}`.


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

Number of knots: 2

Number of meshes and types: 1 SEG2, 2 POI1


Features tested
-----------------------

We test the linear transient calculation functionalities on a physical basis and on a modal basis of the operator DYNA_VIBRA.


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

**Dynamic response**



The position of the mass is tested after a period of time, i.e. 2 seconds. In addition, the value of mode 1 modal participation is tested. Since it is a unique mode and is standardized according to the node that carries the mass, modal participation is identical to displacement.


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    "DYNA_VIBRA /physical base (NEWMARK)", ":math:`1\text{m}` ", "1.E-4%"
    "DYNA_VIBRA /physical base (DIFF_CENTRE)", ":math:`1\text{m}` ", "1.E-4%"
    "DYNA_VIBRA /modal_base (EULER)", ":math:`1\text{m}` "," 0.01%"
    "DYNA_VIBRA (modal participation)", ":math:`1\text{m}` "," 0.01%"


     We also test the value of the speed (in m/s) of the mass at t = 1.5 s, i.e. when it passes through the static equilibrium position :math:`(x=0)`.


.. csv-table::

    "DYNA_VIBRA /physical base (NEWMARK)", ":math:`\pi` ", "1.E-4%"
    "DYNA_VIBRA /modal_base (EULER)", ":math:`\pi` "," 0.1%"