=========
Tutorials
=========

Defining the Geometry
=====================

Based on the figure:

.. _conecyl_figure:

.. figure:: ../../../figures/conecyl.png
   :align: center
   :scale: 60%

The geometry can be defined using `H`, `R_1` and `\alpha`, for example, or
any other combination (like `L`, `H`, `R_1`) of the geometric parameters
that will allow the complete definition of the cone / cylinder geometry.

**Example**::

    from compmech.conecyl import ConeCyl

    cc = ConeCyl()
    cc.r1 = 400
    cc.r2 = 200
    cc.H = 200

Defining the Laminate and Material Properties
=============================================

The :mod:`compmech.composite` module is used to calculate the laminate
properties given the stacking sequence, the thicknesses  and
the material properties.

The **stacking sequence** is passed using a container (``list`` or ``tuple``)
with the orientations of each ply, **from inwards to outwards**::

    cc.stack = [0, 0, -45, +45, -30, +30]

The ply thickness is passed using a single value when all the plies have the
same thickness or using a container with the thickness of each ply::

    cc.plyt = 0.125

**or**::

    cc.plyts = [0.125, 0.125, 0.1, 0.1, 0.101, 0.101]

The material properties are given using a tuple:

.. math::

    (E_{11}, E_{22}, \nu_{12}, G_{12}, G_{13}, G_{23})

where `E_{11}` is the elastic modulus along the direction 1 of the ply,
`E_{22}` the modulus along the direction 2, `\nu_{12}` the Poisson's ratio
and `G_{12}`, `G_{13}`, `G_{23}` the shear modules.

**Example**::

    cc.laminaprop = (123.55e3 , 8.708e3,  0.319, 5.695e3, 5.695e3, 5.695e3)

This will assume the same material properties for each ply. When different
properties must be used the user must supply the ``laminaprops`` container.

**Example**::

    prop1 = (123.55e3 , 8.708e3,  0.319, 5.695e3, 5.695e3, 5.695e3)
    prop2 = (100.2e3 , 4.2e3,  0.2, 5.1e3, 5.1e3, 5.1e3)
    prop3 = (100.2e3 , 4.2e3,  0.2, 5.1e3, 5.1e3, 5.1e3)
    cc.laminaprops = [prop1, prop1, prop2, prop2, prop3, prop3]


Linear Static Analysis
======================

The static analysis is executed using the
:meth:`compmech.conecyl.ConeCyl.static` method. The following example will
give an overview of the main steps needed for a linear static analysis.

Defining the geometry::

    >>> cc.laminaprop = (123.55e3 , 8.708e3,  0.319, 5.695e3, 5.695e3, 5.695e3)
    >>> cc.stack = [0, 0, 19, -19, 37, -37, 45, -45, 51, -51]
    >>> cc.r2 = 250.
    >>> cc.H = 510.
    >>> cc.plyt = 0.125
    >>> cc.alphadeg = 30.

Defining the model and boundary conditions::

    >>> cc.model = 'fsdt_donnell_bc1'
    >>> cc.bc = 'cc1'

Defining if the analysis is displacement or load controlled by changing
the boolean parameters ``pd`` (prescribed displacement):

    - prescribed displacement for compression: ``cc.pdC``
    - prescribed displacement for torsion: ``cc.pdT``
    - prescribed load asymmetry ``cc.pdLA``

Applying the axial compression, pressure, torsion and the single-perturbation
loads::

    >>> cc.Fc = 10000.
    >>> cc.T = 100000.
    >>> cc.P = -0.01
    >>> cc.add_SPL(10.)
    >>> cc.add_SPL(4.)

Defining the number of terms in the approximation functions::

    >>> cc.m1 = 80
    >>> cc.m2 = 40
    >>> cc.n2 = 40

Running the analysis::

    >>> cc.static()

The results are stored in the ``cs`` list, and for a linear static analysis
only one entry exists. Plotting the results::

    >>> cc.plot(cc.cs[0], vec='w')



Static Analysis
---------------


where ``NLgeom`` is a flag telling whether or not a geometric non-linear
analysis is to be performed.

The solution is stored in the ``cs`` attribute, which consists of a ``list``
of 1-D ``np.ndarray`` objects. For a linear analysis this list will contain
only one entry while for a non-linear analysis it will contain one entry
for each iteration needed up to the convergence or up to the termination
criterion. To access the last result::

    solution = cc.cs[-1]

The displacement field can be plotted, for example::

    cc.plot(solution, vec='w', filename='my_output.png')

Non-Linear Analysis
===================

Using ``NLgeom=True`` in a static analysis will run a geometrically
non-linear analysis. Many attributes of the ``ConeCyl`` object
are used to control the non-linear analysis (see
:py:func:`ConeCyl.static`).

The converged increments used along the non-linear analysis are stored
in the ``increments`` attribute and the corresponding solutions
stored in the ``cs`` attribute (a ``list`` of 1-D ``np.ndarray`` objects).