.. _v3.05.104-modelisation_A:


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

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

The modeling consists of:

* "POUTA": a "SEG2" between nodes :math:`A` and :math:`B` with a "POU_D_E" pattern.
* "POUTB": a "SEG2" between nodes :math:`A` and :math:`C` with a "POU_D_E" pattern.
* "DISCA": a "SEG2" between nodes :math:`A` and :math:`B` with a "DIS_TR" pattern.
* "DISCB": a "SEG2" between nodes :math:`A` and :math:`C` with a "DIS_TR" pattern.

Node :math:`A` is embedded.

For elements in the :math:`AB` direction, the effort at node :math:`B` in the global coordinate system: :math:`Fb_x = F`

For elements in the :math:`AC` direction, the effort at node :math:`C` in the global coordinate system:

:math:`\left\{ \begin{array}{l}Fc_x = F \cos(\beta)\cos(\alpha)\\Fc_y = F \cos(\beta)\sin(\alpha)\\Fc_z = F \sin(\beta)\end{array}\right.`

The temperature load is a field at the nodes:

.. csv-table::
   :width: 50%
 :align: center

    **Instants**, **Temperature [°C]**
    0, :math:`T_0 = T_{ref} = 20.0°C`
    1, :math:`T_1 = 50°C`
    2, :math:`T_2 = 75°C`
    3, :math:`T_3 = 100°C`


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

The mesh consists of a single "SEG2" mesh per element.


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

The theoretical solutions are written, in the command file, according to the parameters:

* linked to the mesh: :math:`L, \alpha, \beta`
* linked to the geometry of the beams: :math:`H_y, H_z`
* linked to the characteristics of discretes: :math:`K_x`
* related to the material: :math:`E, \alpha_{th}`

The sizes tested:

* at nodes :math:`B` and :math:`C`: the movements, field "DEPL".
* at node :math:`A`: nodal reactions, field "REAC_NODA".
* on beams and discretes: internal forces, field "EFGE_ELNO".