.. _example-channel:

Channel
=======

Problem description
-------------------

.. figure:: /figures/ex_channel_0.png
  :name: fig_channel0
  :width: 3in
  :align: center

  Cross section of the pipe [CHEN2010]_.

This example has a cross section of a highly heterogeneous channel.
This cross section geometry can be defined as shown in :numref:`Fig. %s <fig_channel0>` [CHEN2010]_.
The isotropic material properties are given in :numref:`Table %s <table_channel_materials>`.
The layup is defined having a single layer with the thickness 0.001524 m.
The result is shown in :numref:`Table %s <table_channel_result>` and compared with those in [CHEN2010]_.
Complete input files can be found in ``examples\ex_channel\``, including ``channel.xml`` and ``materials.xml``.

.. figure:: /figures/ex_channel_1.png
  :name: fig_channel1
  :width: 6in
  :align: center

  *Base point*\ s, *Base line*\ s and *Segment*\ s of the channel cross section.

.. figure:: /figures/ex_channel_mesh.png
  :name: fig_channel_mesh
  :width: 4in
  :align: center

  Meshed cross section viewed in Gmsh.

.. csv-table:: Material properties
  :name: table_channel_materials
  :header-rows: 2
  :align: center

  "Name", "Type", "Density", |e|, |nu|
   , , |den_si|, |mod_si_g|,
  "mtr1", "isotropic", 1068.69, 206.843, 0.49

.. csv-table:: Layups
  :name: table_channel_layups
  :header-rows: 2
  :align: center

  "Name", "Layer", "Material", "Ply thickness", "Orientation", "Number of plies"
  , , , |len_si|, :math:`\circ`,
  "layup1", 1, "mtr1", 0.001524, 0, 1




Result
------

.. table:: Results
   :name: table_channel_result

   =================================== ======================== =================================== =================================== =================================== ===================================
   :math:`\phantom{-}1.906\times 10^7` :math:`0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`              :math:`-4.779\times 10^4`           :math:`-1.325\times 10^5`
   :math:`\phantom{-}0.0`              :math:`2.804\times 10^6` :math:`\phantom{-}2.417\times 10^5` :math:`\phantom{-}2.128\times 10^4` :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`
   :math:`\phantom{-}0.0`              :math:`2.417\times 10^5` :math:`\phantom{-}2.146\times 10^6` :math:`-7.663\times 10^3`           :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`
   :math:`\phantom{-}0.0`              :math:`2.128\times 10^4` :math:`-7.663\times 10^3`           :math:`\phantom{-}2.091\times 10^2` :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`
   :math:`-4.779\times 10^4`           :math:`0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}2.011\times 10^3` :math:`\phantom{-}9.104\times 10^2`
   :math:`-1.325\times 10^5`           :math:`0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}9.104\times 10^2` :math:`\phantom{-}1.946\times 10^3`
   =================================== ======================== =================================== =================================== =================================== ===================================

.. table:: Results from reference [CHEN2010]_
   :name: table_channel_result_ref

   =================================== ======================== =================================== =================================== =================================== ===================================
   :math:`\phantom{-}1.903\times 10^7` :math:`0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`              :math:`-4.778\times 10^4`           :math:`-1.325\times 10^5`
   :math:`\phantom{-}0.0`              :math:`2.791\times 10^6` :math:`\phantom{-}2.364\times 10^5` :math:`\phantom{-}2.122\times 10^4` :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`
   :math:`\phantom{-}0.0`              :math:`2.364\times 10^5` :math:`\phantom{-}2.137\times 10^6` :math:`-7.679\times 10^3`           :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`
   :math:`\phantom{-}0.0`              :math:`2.122\times 10^4` :math:`-7.679\times 10^3`           :math:`\phantom{-}2.086\times 10^2` :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`
   :math:`-4.778\times 10^4`           :math:`0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}2.010\times 10^3` :math:`\phantom{-}9.102\times 10^2`
   :math:`-1.325\times 10^5`           :math:`0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}0.0`              :math:`\phantom{-}9.102\times 10^2` :math:`\phantom{-}1.944\times 10^3`
   =================================== ======================== =================================== =================================== =================================== ===================================