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20 changes: 13 additions & 7 deletions doc/user/source/conf.py
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Expand Up @@ -110,13 +110,19 @@
# further. For a list of options available for each theme, see the
# documentation.
#
# html_theme_options = {
# "repository_url": "https://github.itap.purdue.edu/wenbinyugroup/prevabs",
# "use_repository_button": True,
# "use_issues_button": True,
# "use_edit_page_button": True,
# "use_download_button": True,
# }
html_theme_options = {
'logo': {
'text': 'PreVABS',
},
'show_nav_level': 2,
# "path_to_docs": "doc/source",
# 'use_edit_page_button': True,
# "use_repository_button": True,
# "use_issues_button": True,
# 'collapse_navigation': True,
'navigation_depth': 4,
"announcement": "Documentation is under construction.",
}

html_show_copyright = False

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16 changes: 0 additions & 16 deletions doc/user/source/contents/examples.rst
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234 changes: 117 additions & 117 deletions doc/user/source/contents/examples/example_airfoil.rst
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Expand Up @@ -6,12 +6,12 @@ Airfoil (MH-104)
Problem description
-------------------

.. figure:: /figures/examplemh1040.png
:name: fig_mh104_draw
:width: 5.5in
:align: center
.. figure:: /figures/examplemh1040.png
:name: fig_mh104_draw
:width: 5.5in
:align: center

Sketch of a cross section for a typical wind turbine blade [CHEN2010]_.
Sketch of a cross section for a typical wind turbine blade [CHEN2010]_.

This example demonstrates the capability of building a cross section having an airfoil shape, which is commonly seen on wind turbine blades or helicopter rotor blades.
This example is also studied in [CHEN2010]_.
Expand All @@ -27,86 +27,86 @@ Materials are given in :numref:`Table %s <table_mh104_materials>` and layups are
A complete :math:`6\times 6` stiffness matrix is given in :numref:`Table %s <table_airfoil_result>`.
Complete input files can be found in ``examples\ex_airfoil\``, including ``mh104.xml``, ``basepoints.dat``, ``baselines.xml``, ``materials.xml``, and ``layups.xml``.

.. csv-table:: Dividing points
:name: table_div_pts
:header-rows: 2
:align: center

"Between segments", "Low pressure surface", "High pressure surface"
, ":math:`(x, y)`", ":math:`(x, y)`"
"1 and 2", "(0.004053940, 0.011734800)", "(0.006824530, -0.009881650)"
"2 and 3", "(0.114739930, 0.074571970)", "(0.126956710, -0.047620490)"
"3 and 4", "(0.536615950, 0.070226120)", "(0.542952100, -0.044437080)"

.. figure:: /figures/examplemh1041.png
:name: fig_mh1041
:width: 6.5in
:align: center

*Base point*\ s of the tube cross section.

.. figure:: /figures/examplemh1042.png
:name: fig_mh1042
:width: 6.5in
:align: center

*Base line*\ s of the tube cross section.

.. figure:: /figures/examplemh1043.png
:name: fig_mh1043
:width: 6.5in
:align: center

*Segment*\ s of the tube cross section.

.. figure:: /figures/examplemh1044.png
:name: fig_mh104
:width: 6.5in
:align: center

Meshed cross section viewed in Gmsh.

.. csv-table:: Material properties
:name: table_mh104_materials
:header-rows: 2
:align: center

"Name", "Type", "Density", |e1|, |e2|, |e3|, |g12|, |g13|, |g23|, |nu12|, |nu13|, |nu23|
, , |den_si_k|, |mod_si_g|, |mod_si_g|, |mod_si_g|, |mod_si_g|, |mod_si_g|, |mod_si_g|, , ,
"Uni-directional FRP", "orthotropic", 1.86, 37.00, 9.00, 9.00, 4.00, 4.00, 4.00, 0.28, 0.28, 0.28
"Double-bias FRP", "orthotropic", 1.83, 10.30, 10.30, 10.30, 8.00, 8.00, 8.00, 0.30, 0.30, 0.30
"Gelcoat", "orthotropic", 1.83, 1e-8, 1e-8, 1e-8, 1e-9, 1e-9, 1e-9, 0.30, 0.30, 0.30
"Nexus", "orthotropic", 1.664, 10.30, 10.30, 10.30, 8.00, 8.00, 8.00, 0.30, 0.30, 0.30
"Balsa", "orthotropic", 0.128, 0.01, 0.01, 0.01, 2e-4, 2e-4, 2e-4, 0.30, 0.30, 0.30

.. csv-table:: Layups
:name: table_mh104_layups
:header-rows: 2
:align: center

"Name", "Layer", "Material", "Ply thickness", "Orientation", "Number of plies"
, , , |len_si|, :math:`\circ`,
"layup_1", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 18
"layup_2", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 33
"layup_3", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 17
, 4, "Uni-directional FRP", 0.00053, 30, 38
, 5, "Balsa", 0.003125, 0, 1
, 6, "Uni-directional FRP", 0.00053, 30, 37
, 7, "Double-bias FRP", 0.00053, 20, 16
"layup_4", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 17
, 4, "Balsa", 0.003125, 0, 1
, 5, "Double-bias FRP", 0.00053, 0, 16
"layup_web", 1, "Uni-directional FRP", 0.00053, 0, 38
, 2, "Balsa", 0.003125, 0, 1
, 3, "Uni-directional FRP", 0.00053, 0, 38
.. csv-table:: Dividing points
:name: table_div_pts
:header-rows: 2
:align: center

"Between segments", "Low pressure surface", "High pressure surface"
, ":math:`(x, y)`", ":math:`(x, y)`"
"1 and 2", "(0.004053940, 0.011734800)", "(0.006824530, -0.009881650)"
"2 and 3", "(0.114739930, 0.074571970)", "(0.126956710, -0.047620490)"
"3 and 4", "(0.536615950, 0.070226120)", "(0.542952100, -0.044437080)"

.. figure:: /figures/examplemh1041.png
:name: fig_mh1041
:width: 6.5in
:align: center

*Base point*\ s of the tube cross section.

.. figure:: /figures/examplemh1042.png
:name: fig_mh1042
:width: 6.5in
:align: center

*Base line*\ s of the tube cross section.

.. figure:: /figures/examplemh1043.png
:name: fig_mh1043
:width: 6.5in
:align: center

*Segment*\ s of the tube cross section.

.. figure:: /figures/examplemh1044.png
:name: fig_mh104
:width: 6.5in
:align: center

Meshed cross section viewed in Gmsh.

.. csv-table:: Material properties
:name: table_mh104_materials
:header-rows: 2
:align: center

"Name", "Type", "Density", |e1|, |e2|, |e3|, |g12|, |g13|, |g23|, |nu12|, |nu13|, |nu23|
, , |den_si_k|, |mod_si_g|, |mod_si_g|, |mod_si_g|, |mod_si_g|, |mod_si_g|, |mod_si_g|, , ,
"Uni-directional FRP", "orthotropic", 1.86, 37.00, 9.00, 9.00, 4.00, 4.00, 4.00, 0.28, 0.28, 0.28
"Double-bias FRP", "orthotropic", 1.83, 10.30, 10.30, 10.30, 8.00, 8.00, 8.00, 0.30, 0.30, 0.30
"Gelcoat", "orthotropic", 1.83, 1e-8, 1e-8, 1e-8, 1e-9, 1e-9, 1e-9, 0.30, 0.30, 0.30
"Nexus", "orthotropic", 1.664, 10.30, 10.30, 10.30, 8.00, 8.00, 8.00, 0.30, 0.30, 0.30
"Balsa", "orthotropic", 0.128, 0.01, 0.01, 0.01, 2e-4, 2e-4, 2e-4, 0.30, 0.30, 0.30

.. csv-table:: Layups
:name: table_mh104_layups
:header-rows: 2
:align: center

"Name", "Layer", "Material", "Ply thickness", "Orientation", "Number of plies"
, , , |len_si|, :math:`\circ`,
"layup_1", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 18
"layup_2", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 33
"layup_3", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 17
, 4, "Uni-directional FRP", 0.00053, 30, 38
, 5, "Balsa", 0.003125, 0, 1
, 6, "Uni-directional FRP", 0.00053, 30, 37
, 7, "Double-bias FRP", 0.00053, 20, 16
"layup_4", 1, "Gelcoat", 0.000381, 0, 1
, 2, "Nexus", 0.00051, 0, 1
, 3, "Double-bias FRP", 0.00053, 20, 17
, 4, "Balsa", 0.003125, 0, 1
, 5, "Double-bias FRP", 0.00053, 0, 16
"layup_web", 1, "Uni-directional FRP", 0.00053, 0, 38
, 2, "Balsa", 0.003125, 0, 1
, 3, "Uni-directional FRP", 0.00053, 0, 38



Expand All @@ -115,36 +115,36 @@ Complete input files can be found in ``examples\ex_airfoil\``, including ``mh104
Result
------

.. table:: Effective Timoshenko stiffness matrix
:name: table_airfoil_result

=================================== =================================== =================================== =================================== =================================== ===================================
:math:`\phantom{-}2.395\times 10^9` :math:`\phantom{-}1.588\times 10^6` :math:`\phantom{-}7.215\times 10^6` :math:`-3.358\times 10^7` :math:`\phantom{-}6.993\times 10^7` :math:`-5.556\times 10^8`
:math:`\phantom{-}1.588\times 10^6` :math:`\phantom{-}4.307\times 10^8` :math:`-3.609\times 10^6` :math:`-1.777\times 10^7` :math:`\phantom{-}1.507\times 10^7` :math:`\phantom{-}2.652\times 10^5`
:math:`\phantom{-}7.215\times 10^6` :math:`-3.609\times 10^6` :math:`\phantom{-}2.828\times 10^7` :math:`\phantom{-}8.440\times 10^5` :math:`\phantom{-}2.983\times 10^5` :math:`-5.260\times 10^6`
:math:`-3.358\times 10^7` :math:`-1.777\times 10^7` :math:`\phantom{-}8.440\times 10^5` :math:`\phantom{-}2.236\times 10^7` :math:`-2.024\times 10^6` :math:`\phantom{-}2.202\times 10^6`
:math:`\phantom{-}6.993\times 10^7` :math:`\phantom{-}1.507\times 10^7` :math:`\phantom{-}2.983\times 10^5` :math:`-2.024\times 10^6` :math:`\phantom{-}2.144\times 10^7` :math:`-9.137\times 10^6`
:math:`-5.556\times 10^8` :math:`\phantom{-}2.652\times 10^5` :math:`-5.260\times 10^6` :math:`\phantom{-}2.202\times 10^6` :math:`-9.137\times 10^6` :math:`\phantom{-}4.823\times 10^8`
=================================== =================================== =================================== =================================== =================================== ===================================

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

=================================== =================================== =================================== =================================== =================================== ===================================
:math:`\phantom{-}2.389\times 10^9` :math:`\phantom{-}1.524\times 10^6` :math:`\phantom{-}6.734\times 10^6` :math:`-3.382\times 10^7` :math:`-2.627\times 10^7` :math:`-4.736\times 10^8`
:math:`\phantom{-}1.524\times 10^6` :math:`\phantom{-}4.334\times 10^8` :math:`-3.741\times 10^6` :math:`-2.935\times 10^5` :math:`\phantom{-}1.527\times 10^7` :math:`\phantom{-}3.835\times 10^5`
:math:`\phantom{-}6.734\times 10^6` :math:`-3.741\times 10^6` :math:`\phantom{-}2.743\times 10^7` :math:`-4.592\times 10^4` :math:`-6.869\times 10^2` :math:`-4.742\times 10^6`
:math:`-3.382\times 10^7` :math:`-2.935\times 10^5` :math:`-4.592\times 10^4` :math:`\phantom{-}2.167\times 10^7` :math:`-6.279\times 10^4` :math:`\phantom{-}1.430\times 10^6`
:math:`-2.627\times 10^7` :math:`\phantom{-}1.527\times 10^7` :math:`-6.869\times 10^2` :math:`-6.279\times 10^4` :math:`\phantom{-}1.970\times 10^7` :math:`\phantom{-}1.209\times 10^7`
:math:`-4.736\times 10^8` :math:`\phantom{-}3.835\times 10^5` :math:`-4.742\times 10^6` :math:`\phantom{-}1.430\times 10^6` :math:`\phantom{-}1.209\times 10^7` :math:`\phantom{-}4.406\times 10^8`
=================================== =================================== =================================== =================================== =================================== ===================================

.. note:: The errors between the result and the reference are caused by the difference of modeling of the trailing edge. If reduce the trailing edge skin to a single thin layer, then the difference between the trailing edge shapes is minimized, and the two resulting stiffness matrices are basically the same, as shown in :numref:`Fig. %s <fig_mh104_comparison>`.

.. figure:: /figures/examplemh104_comparison.png
:name: fig_mh104_comparison
:width: 6in
:align: center

Comparison of stiffness matrices after modifying the trailing edge.
.. table:: Effective Timoshenko stiffness matrix
:name: table_airfoil_result

=================================== =================================== =================================== =================================== =================================== ===================================
:math:`\phantom{-}2.395\times 10^9` :math:`\phantom{-}1.588\times 10^6` :math:`\phantom{-}7.215\times 10^6` :math:`-3.358\times 10^7` :math:`\phantom{-}6.993\times 10^7` :math:`-5.556\times 10^8`
:math:`\phantom{-}1.588\times 10^6` :math:`\phantom{-}4.307\times 10^8` :math:`-3.609\times 10^6` :math:`-1.777\times 10^7` :math:`\phantom{-}1.507\times 10^7` :math:`\phantom{-}2.652\times 10^5`
:math:`\phantom{-}7.215\times 10^6` :math:`-3.609\times 10^6` :math:`\phantom{-}2.828\times 10^7` :math:`\phantom{-}8.440\times 10^5` :math:`\phantom{-}2.983\times 10^5` :math:`-5.260\times 10^6`
:math:`-3.358\times 10^7` :math:`-1.777\times 10^7` :math:`\phantom{-}8.440\times 10^5` :math:`\phantom{-}2.236\times 10^7` :math:`-2.024\times 10^6` :math:`\phantom{-}2.202\times 10^6`
:math:`\phantom{-}6.993\times 10^7` :math:`\phantom{-}1.507\times 10^7` :math:`\phantom{-}2.983\times 10^5` :math:`-2.024\times 10^6` :math:`\phantom{-}2.144\times 10^7` :math:`-9.137\times 10^6`
:math:`-5.556\times 10^8` :math:`\phantom{-}2.652\times 10^5` :math:`-5.260\times 10^6` :math:`\phantom{-}2.202\times 10^6` :math:`-9.137\times 10^6` :math:`\phantom{-}4.823\times 10^8`
=================================== =================================== =================================== =================================== =================================== ===================================

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

=================================== =================================== =================================== =================================== =================================== ===================================
:math:`\phantom{-}2.389\times 10^9` :math:`\phantom{-}1.524\times 10^6` :math:`\phantom{-}6.734\times 10^6` :math:`-3.382\times 10^7` :math:`-2.627\times 10^7` :math:`-4.736\times 10^8`
:math:`\phantom{-}1.524\times 10^6` :math:`\phantom{-}4.334\times 10^8` :math:`-3.741\times 10^6` :math:`-2.935\times 10^5` :math:`\phantom{-}1.527\times 10^7` :math:`\phantom{-}3.835\times 10^5`
:math:`\phantom{-}6.734\times 10^6` :math:`-3.741\times 10^6` :math:`\phantom{-}2.743\times 10^7` :math:`-4.592\times 10^4` :math:`-6.869\times 10^2` :math:`-4.742\times 10^6`
:math:`-3.382\times 10^7` :math:`-2.935\times 10^5` :math:`-4.592\times 10^4` :math:`\phantom{-}2.167\times 10^7` :math:`-6.279\times 10^4` :math:`\phantom{-}1.430\times 10^6`
:math:`-2.627\times 10^7` :math:`\phantom{-}1.527\times 10^7` :math:`-6.869\times 10^2` :math:`-6.279\times 10^4` :math:`\phantom{-}1.970\times 10^7` :math:`\phantom{-}1.209\times 10^7`
:math:`-4.736\times 10^8` :math:`\phantom{-}3.835\times 10^5` :math:`-4.742\times 10^6` :math:`\phantom{-}1.430\times 10^6` :math:`\phantom{-}1.209\times 10^7` :math:`\phantom{-}4.406\times 10^8`
=================================== =================================== =================================== =================================== =================================== ===================================

.. note:: The errors between the result and the reference are caused by the difference of modeling of the trailing edge. If reduce the trailing edge skin to a single thin layer, then the difference between the trailing edge shapes is minimized, and the two resulting stiffness matrices are basically the same, as shown in :numref:`Fig. %s <fig_mh104_comparison>`.

.. figure:: /figures/examplemh104_comparison.png
:name: fig_mh104_comparison
:width: 6in
:align: center

Comparison of stiffness matrices after modifying the trailing edge.

32 changes: 16 additions & 16 deletions doc/user/source/contents/examples/example_airfoil_recover.rst
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Expand Up @@ -22,18 +22,18 @@ Complete files can be found in ``examples\ex_airfoil_r\``, including
``mh104.sg.K``, ``mh104.sg.opt``, ``mh104.sg.v0``,
``mh104.sg.v1S``, and ``mh104.sg.v22``.

.. csv-table:: Sectional forces and moments
:name: table_mh104_1dresults
:header-rows: 1
:align: center
.. csv-table:: Sectional forces and moments
:name: table_mh104_1dresults
:header-rows: 1
:align: center

Quantity, Value
":math:`F_1`, N", 1
":math:`F_2`, N", 2
":math:`F_3`, N", 3
":math:`M_1`, Nm", 4
":math:`M_2`, Nm", 5
":math:`M_3`, Nm", 6
Quantity, Value
":math:`F_1`, N", 1
":math:`F_2`, N", 2
":math:`F_3`, N", 3
":math:`M_1`, Nm", 4
":math:`M_2`, Nm", 5
":math:`M_3`, Nm", 6



Expand All @@ -42,10 +42,10 @@ Complete files can be found in ``examples\ex_airfoil_r\``, including
Result
------

.. figure:: /figures/examplemh104r.png
:name: fig_mh104r
:width: 6in
:align: center
.. figure:: /figures/examplemh104r.png
:name: fig_mh104r
:width: 6in
:align: center

Contour plot of recovered nodal stress SN11.
Contour plot of recovered nodal stress SN11.

16 changes: 16 additions & 0 deletions doc/user/source/contents/examples/index.rst
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@@ -0,0 +1,16 @@
Examples
========

.. toctree::
:maxdepth: 1
:caption: Table of Contents

example_box
example_pipe
example_tube
example_channel
example_airfoil
example_airfoil_recover
example_uh60a_fi

.. example_ibeam
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