H modeling
==============


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

The model is composed of 21 TUYAU_3M elements based on SEG4 meshes. The section is hollow circular with radius :math:`\mathrm{0,1}` and thickness :math:`\mathrm{0,01}`.

The distributed effort is imposed according to axis :math:`y`. So the flexure takes place around :math:`z`.


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

It consists of 21 SEG3 stitches, transformed into SEG4 meshes. The length of the pipe is :math:`L=6m`.


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


Travel
~~~~~~~~~~~~

.. csv-table::

    "", "**Analytical Results**"
    ":math:`{D}_{y}\mathit{maxi}` at point :math:`x=3.115977734`", "9.38888E-03"



Cross-sectional reactions
~~~~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "", "**Analytical Results**"
    ":math:`{R}_{\mathit{Oy}}` ", "-6.0000E+03"
    ":math:`{R}_{\mathit{By}}` ", "-1.2000E+04"



Internal efforts
~~~~~~~~~~~~~~~~~~~~

.. csv-table::

    "", "**Analytical Results**"
    ":math:`{V}_{y}(x=0)` ", "6.0000E+03"
    ":math:`{V}_{y}(x=L=6)` ", "-1.2000E+04"
    ":math:`\mathrm{MFZ}` in :math:`x=2\sqrt{3}` ", "-1.3856E+04"



Constraints
~~~~~~~~~~~~

They are calculated at the abscissa point :math:`x=\frac{L\sqrt{3}}{3}` which corresponds to the maximum moment: :math:`{M}_{z}(x)=\frac{-1000}{9\sqrt{(3)}}{L}^{3}=-13856.41\mathrm{N.m}`

For the angle 0° on the circumference of the pipe (the origin of the angles being the :math:`z` axis), the constraints are zero, and for the 90° angle, they are maximum: :math:`{\sigma }_{\mathrm{xx}}^{\mathrm{max}}=\frac{{M}_{z}^{\mathrm{max}}(R-e/2)}{{I}_{z}}=-4.87363E+07\mathrm{Pa}`


.. csv-table::

    "", "**Reference**", "Tolerance"
    ":math:`{\sigma }_{\mathrm{xx}}(\alpha =0)` ", "0"," 0.10%"
    ":math:`{\sigma }_{\mathrm{xx}}(\alpha =90)` ", "-4.87363E+07"," 1.00%"
    ":math:`\mathrm{MFZ}` ", "-1.3856E+04", "1. %"