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

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

Full circular section, radius :math:`\mathrm{0.025m}`. The calculated characteristics are then used directly in a calculation of a straight beam (of length :math:`L\mathrm{=}\mathrm{1m}`), in pure tension (:math:`F\mathrm{=}\mathrm{1000N}`). Young's modulus is :math:`2.E11\mathit{Pa}`. The characteristics of the section are given to AFFE_CARA_ELEM using the TABLE_CARA keyword.


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

Number of meshes: 52 TRIA6, 299 QUAD8


Benchmark solution
---------------------

:math:`A=\pi {R}^{2}=1.9635E\text{-}3{m}^{2}`; :math:`{I}_{y}={I}_{z}=\frac{\pi }{4}{R}^{4}=3.06796E\text{-}7{m}^{4}`; :math:`{A}_{y}={A}_{z}=\frac{10}{9}`; :math:`C={I}_{x}=2{I}_{y}=2{I}_{z}`

Pure traction of a beam with a solid circular section, of length :math:`L\mathrm{=}\mathrm{1m}`, subjected to a force :math:`F\mathrm{=}\mathrm{1000N}`: :math:`u(x)=\frac{Fx}{EA}` :math:`u(L)=\frac{FL}{EA}=2.54648E\text{-}6m`


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

For the symmetrized section following :math:`\mathrm{OY}`, the geometric characteristics are:

.. csv-table::

    "**Identification**", "**Reference**", "**Value**", "**Tolerance**"
    ":math:`A` "," ANALYTIQUE ", "1.96E-03"," 0.50%"
    ":math:`{\mathrm{CDG}}_{Y}` "," ANALYTIQUE ", "0.00E+00"," 0.10%"
    ":math:`{\mathrm{CDG}}_{Z}` "," ANALYTIQUE ", "0.00E+00"," 0.10%"
    ":math:`{\mathrm{IY}}_{G}` "," ANALYTIQUE ", "3.07E-07"," 0.90%"
    ":math:`{\mathrm{IZ}}_{G}` "," ANALYTIQUE ", "3.07E-07"," 0.90%"
    ":math:`{\mathrm{IYZ}}_{G}` "," ANALYTIQUE ", "0.00E+00"," 0.10%"
    ":math:`\mathrm{IY}` "," ANALYTIQUE ", "3.07E-07"," 0.90%"
    ":math:`\mathrm{IZ}` "," ANALYTIQUE ", "3.07E-07"," 0.90%"
    ":math:`{Y}_{\mathrm{MIN}}` "," ANALYTIQUE ", "-2.50E-02"," 0.10%"
    ":math:`{Y}_{\mathrm{MAX}}` "," ANALYTIQUE ", "2.50E-02"," 0.10%"
    ":math:`{Z}_{\mathrm{MIN}}` "," ANALYTIQUE ", "-2.50E-02"," 0.10%"
    ":math:`{Z}_{\mathrm{MAX}}` "," ANALYTIQUE ", "2.50E-02"," 0.10%"
    ":math:`\mathrm{JX}` "," ANALYTIQUE ", "6.14E-07"," 0.90%"
    ":math:`\mathrm{AY}` "," ANALYTIQUE ", "1.17E+00"," 0.10%"
    ":math:`\mathrm{AZ}` "," ANALYTIQUE ", "1.17E+00"," 0.10%"
    ":math:`\mathrm{EY}` "," ANALYTIQUE ", "0.00E+00"," 0.10%"
    ":math:`\mathrm{EZ}` "," ANALYTIQUE ", "0.00E+00"," 0.10%"
    ":math:`\mathrm{JG}` "," ANALYTIQUE ", "0.00E+00"," 0.10%"


For the beam tension calculation, the result is:

.. csv-table::

    "**Identification**", "**Reference**", "**Value**", "**Tolerance**"
    "DEPL "," ANALYTIQUE ", "2.55E-06", "1.00E-03"
    "Forc_noda", "ANALYTIQUE ", "1.00E+03", "1.00E-03"