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epsi1on committed Sep 13, 2023
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8 changes: 0 additions & 8 deletions docs/elements/finiteElements/Bar/behavs.rst
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Expand Up @@ -7,37 +7,31 @@ The possible behaviours for the BarElement is:

- ``BarElementBehaviour.EulerBernoulyBeamY`` : Beam in Y direction based on Euler-Bernouly theory. DoFs are shown in below image:
.. figure:: ../images/bar-b1.png

:align: center

DoFs of ``BarElementBehaviour.EulerBernoulyBeamY``
- ``BarElementBehaviour.EulerBernoulyBeamZ`` : Beam in Z direction based on Euler-Bernouly theory. DoFs are shown in below image:
.. figure:: ../images/bar-b2.png

:align: center

DoFs of ``BarElementBehaviour.EulerBernoulyBeamZ``
- ``BarElementBehaviour.TimoshenkoBeamY`` : Beam in Y direction based on Timoshenko's theory (shear deformation). DoFs are shown in below image:
.. figure:: ../images/bar-b1.png

:align: center

DoFs of ``BarElementBehaviour.TimoshenkoBeamY``
- ``BarElementBehaviour.TimoshenkoBeamZ`` : Beam in Z direction based on Timoshenko's theory (shear deformation). DoFs are shown in below image:
.. figure:: ../images/bar-b2.png

:align: center

DoFs of ``BarElementBehaviour.TimoshenkoBeamZ``
- ``BarElementBehaviour.Truss`` : Only axial load carrying. DoFs are shown in below image:
.. figure:: ../images/bar-truss.png

:align: center

DoFs of ``BarElementBehaviour.Truss``
- ``BarElementBehaviour.Shaft`` : Only torsional moment carrying. DoFs are shown in below image:
.. figure:: ../images/bar-shaft.png

:align: center

DoFs of ``BarElementBehaviour.Shaft``
Expand Down Expand Up @@ -71,14 +65,12 @@ So better to use ``BarElementBehaviours`` unless needed manually define combinat
- ``BarElementBehaviours.FullBeam`` and ``BarElementBehaviours.FullBeamWithShearDefomation``:

.. image:: ../images/bar-fullB.png

:align: center

DoFs of ``BarElementBehaviours.FullBeam`` and ``BarElementBehaviours.FullBeamWithShearDefomation``
- ``BarElementBehaviours.FullFrame`` and ``BarElementBehaviours.FullFrameWithShearDeformation``:

.. image:: ../images/bar-fullframe.png

:align: center

DoFs of ``BarElementBehaviours.FullFrame`` and ``BarElementBehaviours.FullFrameWithShearDeformation``
2 changes: 1 addition & 1 deletion docs/elements/finiteElements/Bar/coords.rst
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Expand Up @@ -43,7 +43,7 @@ code for transforming local to global is in https://github.com/BriefFiniteElemen

code is ported from MATLAB code. from book 'MATLAB Codes for Finite Element Analysis' by 'A. J. M. Ferreira' , section 8.3 (First 3D frame example) page 107 (111 of 236)

.. code-block::
.. code-block::matlab
if x1 == x2 & y1 == y2
if z2 > z1
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4 changes: 3 additions & 1 deletion docs/miscellaneoustopics/solveprocedure.rst
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Expand Up @@ -199,11 +199,13 @@ Rows with all members zero and right side zero will be removed from result, and
Finally there will be a matrix :math:`P_3`\ with `o` rows and `n` columns, that `o<=m` (`m` is total extra equation count) due to removing useless rows. Also as this matrix is RREF form, then there are `o` columns with only one non-zero element. If a member be the only non-zero member in the column, we call that member "pioneer" or "leading" member. Finally we have :math:`P_3*U=R_3`\ where :math:`P_3`\ is in RREF form.

Step 4: Make pioneer members equal to -1 by multiplying whole row with a coefficient
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

we shaould take output of last step, :math:`P_3`\ and :math:`R_3`\. Then multiply each row and corresponding right side member with a coefficient in a way that pioneer member turn into `-1.0`. result is :math:`P_4`\ and :math:`R_4`\.

Step 5: Insert each row into appropriated row of a `nxn` matrix where n is total number of DoFs
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Create and empty :math:`P_5`\ matrix with size `n` by `n`, also a vector :math:`R_5`\ with size `n` by `1`. Then for each i'th row of :math:`P_4`\ with pioneer member at column `j`, insert it into `i`'th row of :math:`P_5`\ and :math:`R_5`\. Next we should replace the zeros on main diagonal of :math:`P_5`\ with `1.0` and no change in :math:`R_5`\.


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