D modeling
==============


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

Elements POU_D_TG, awkward twisting

:math:`\mathrm{JG}=\{\begin{array}{}5.5556E-8\mathrm{pour}{S}_{1}\\ 4.439822E-11\mathrm{pour}{S}_{2}\end{array}`

In 0 :math:`\mathrm{GRX}=0`


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


* 10 SEG_2 meshes,


* refinement towards embedding.


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

Same results as for modeling C, except for those concerning warping effects.


.. csv-table::

    "**Load**", "**Section**", "**Identification**", "**Reference**"
    ":math:`{F}_{z}=1` "," :math:`\mathrm{S2}` "," :math:`{\theta }_{x}=\mathrm{DRX}` ", "2.62034E-5"
    "", "", ":math:`{u}_{z}=\mathrm{DZ}` ", "1.14578E-6"
    "", "", ":math:`\mathrm{GRX}` ", "1.34652E-5"
    ":math:`{M}_{x}=1` "," :math:`\mathrm{S1}` "," :math:`{u}_{z}=\mathrm{DZ}` ", "5.52E-7"
    "", "", ":math:`\mathrm{GRX}` ", "2.84E-7"
    "", ":math:`\mathrm{S2}` "," :math:`{u}_{z}` ", "2.6203E-5"
    "", "", ":math:`{\theta }_{x}` ", "6.3892E-4"
    "", "", ":math:`\mathrm{GRX}` ", "3.28324E-4"



notes
---------

For :math:`{\theta }_{x}` the solution is (cf [:ref:`bib1 <bib1>`]):

:math:`{\theta }_{x}=\frac{{M}_{x}L}{G{J}_{x}}+\frac{{M}_{x}(1-{e}^{2\alpha L}-2{e}^{\alpha L})}{{\alpha }^{3}EJG(1+{e}^{2\alpha L})}` :math:`{\alpha }^{2}=\frac{GJ}{EJG}`