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




But
---

In this modeling, we want to validate the modelling/characteristic pairs DIS_T /K_T_D_N and DIS_T /A_T_D_N as well as the pairs DIS_T /K_T_D_L and DIS_T /A_T_D_L, in coordinate system GLOBAL and in coordinate system LOCAL. To do this, the tests EPX bm_str_resl_nl (calculation 1) and bm_str_resg_nl (calculation 2) are reproduced. This modeling also validates the use of circular beams in CALC_EPX.


Description
-----------


Geometry and modeling
~~~~~~~~~~~~~~~~~~~~~~~~~~~~


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+ .. image:: images/10000201000001E8000000EA67BAD9FBCB18491C.png                                                              + .. image:: images/10000201000001E8000001329B6ED683EFA1B70C.png                                                              +
|    :width: 3.3681in                                                                                                         |    :width: 3.3535in                                                                                                         |
+    :height: 1.6189in                                                                                                        +    :height: 2.0327in                                                                                                        +
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|System 1                                                                                                                     |System 2                                                                                                                     |
+-----------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------+


Two systems are compared. In both cases it is a :math:`\mathit{AB}` (POU_D_E) beam of length :math:`1m` connected to a spring in :math:`B`. A mass of :math:`1000\mathit{kg}` is also added to point :math:`B`. In the first system, the beam is connected to a point spring (DIS_T /K_T_D_N+A_T_D_N), in the second to a line spring :math:`\mathit{BC}` oriented along :math:`Y` (DIS_T /K_T_D_L+A_T_D_L).

Circular cross section of the beam: R = 0.02

**Correspondence of node groups to the** **points shown in the figure above.**


.. csv-table::

    "Points", "System 1", "System 2"
    "A", "T_0_0_0", "P_0_0_0", "P_0_0"
    "B", "T_1_0_0", "P_1_0_0"
    "C", "-", "P_1_L_0"



Material properties
~~~~~~~~~~~~~~~~~~~~~~~~~~

**Beam:**

Young's module: :math:`2E11\mathit{Pa}`

Poisson's ratio: :math:`0.`

Density: :math:`7800\mathit{kg}/{m}^{3}`

**Springs/** shock absorbers:

Elements in local coordinate system (DIS_T/SEG2 of calculation 1 only):

 Stiffness according to :math:`X`: :math:`75000.N/m`

 Stiffness according to :math:`Y`: :math:`60000.N/m`

 Stiffness according to :math:`Z`: :math:`50000.N/m`

 Depreciation according to :math:`X`: :math:`7500.N/(m/s)`

 Depreciation according to :math:`Y`: :math:`6000.N/(m/s)`

 Depreciation according to :math:`Z`: :math:`5000.N/(m/s)`

Global coordinate system elements (DIS_T of calculation 2 and DIS_T/POI1 of calculation 1):

 Stiffness according to :math:`X`: :math:`60000.N/m`

 Stiffness according to :math:`Y`: :math:`75000.N/m`

 Stiffness according to :math:`Z`: :math:`50000.N/m`

 Depreciation according to :math:`X`: :math:`6000.N/(m/s)`

 Depreciation according to :math:`Y`: :math:`7500.N/(m/s)`

 Depreciation according to :math:`Z`: :math:`5000.N/(m/s)`


Boundary conditions and loads
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Node :math:`A` is embedded for both systems. For system 2, node :math:`C` is also embedded. Two calculations are carried out.

Calculation 1:

In both systems, a constant force with a value of :math:`1000N` is imposed in :math:`B` according to :math:`Y`.

Calculation 2:

In both systems, constant forces with a value of :math:`1000N` are imposed according to :math:`X`, :math:`Y`, and :math:`Z` in :math:`B`.


Reference values
~~~~~~~~~~~~~~~~~~~~~~

The reference values are given by the EUROPLEXUS tests mentioned in 1.1.


Tested values
---------------


Calculus 1
~~~~~~~


.. csv-table::

    "**GROUP_NO**", "**NUME_ORDRE**", "**Component**", "**Reference**", "**Reference Value**"
    "P_1_0_0", "91609"," :math:`\mathit{DY}` "," "," SOURCE_EXTERNE ", "3.52220E-03"
    "T_1_0_0", "91609"," 91609", ":math:`\mathit{DY}` "," SOURCE_EXTERNE ", "1.29492E-02"



Calcul2
~~~~~~


.. csv-table::

    "**GROUP_NO**", "**NUME_ORDRE**", "**Component**", "**Reference**", "**Reference Value**"
    "P_1_0_0", "25064"," :math:`\mathit{DX}` "," "," SOURCE_EXTERNE ", "-1.62766E-05"
    "T_1_0_0", "25064"," :math:`\mathit{DX}` "," "," SOURCE_EXTERNE ", "-1.62766E-05"
    "P_1_0_0", "25064"," :math:`\mathit{DY}` "," "," SOURCE_EXTERNE ", "3.67804E-03"
    "T_1_0_0", "25064"," :math:`\mathit{DY}` "," "," SOURCE_EXTERNE ", "3.67804E-03"
    "P_1_0_0", "25064"," :math:`\mathit{DZ}` "," "," SOURCE_EXTERNE ", "4.58138E-03"
    "T_1_0_0", "25064"," :math:`\mathit{DZ}` "," "," SOURCE_EXTERNE ", "4.58138E-03"