# Tutorials

## Defining the Geometry

Based on the figure:

The geometry can be defined using , and , for example, or any other combination (like , , ) 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 `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:

where is the elastic modulus along the direction 1 of the ply, the modulus along the direction 2, the Poisson’s ratio and , , 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 `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 `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).