F modeling
==============

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

The modeling consists of 112 COQUE_3D elements for the tubular section, and 2 pipe elements to apply the boundary conditions. The length of the shell mesh is :math:`\mathrm{0.98m}`. The length of each pipe element is :math:`\mathrm{0.01m}`.

A COQUE_TUYAU connection is applied to each end of the shell mesh, with a pipe element. In addition, the degrees of freedom of the pipes that correspond to mode 3 of ovalization are blocked: :math:`\mathrm{U03}`, :math:`\mathrm{V03}`, :math:`\mathrm{W03}`

.. csv-table::

    "Single pull:", "(ECRO_LINE)"
    "Pure bending:", "without work hardening"



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

112 QUAD9 stitches and 2 SEG3 stitches.


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

Traction:

.. csv-table::

    ":math:`{\mathrm{DX}}_{(B)}` ", "**Order Number**", "**Identification**", "**Identification**", "**Reference Type**", "**Tolerance**"
    ":math:`2{\mathrm{DX}}^{e}` ", "11", "N", "ANALYTIQUE "," "," :math:`9.47E+04` "," :math:`1.10\text{\%}`"
    ":math:`3{\mathrm{DX}}^{e}` ", "21", "N", "ANALYTIQUE "," "," :math:`9.565E+04` "," :math:`1.10\text{\%}`"


Flexion:

.. csv-table::

    ":math:`{\mathrm{DRZ}}_{(B)}` ", "**Order Number**", "**Identification**", "**Identification**", "**Reference Type**", "**Tolerance**"
    ":math:`{\mathrm{DRZ}}^{e}` ", "1"," MFZ "," "," ANALYTIQUE "," :math:`4.642E+03` "," :math:`0.10\text{\%}`"
    ":math:`2.8{\mathrm{DRZ}}^{e}` ", "19"," MFZ "," "," ANALYTIQUE "," :math:`5.7824E+03` "," :math:`0.50\text{\%}`"