Reference solution
=====================


Locking procedure
--------------------

We take as a reference the solution given by the calculation code *GEFDYN*. This procedure has been validated on numerous industrial structures. The opening of the joint after claving is tested.


Sawing procedure
-------------------

As with sawing, we do not have a solution from an external code. The latter is then validated theoretically in the C and D models, which accept a :math:`\mathrm{1D}` solution.

First, a homogeneous compression :math:`{\delta }_{\mathit{impo}}` is applied to the left side of the pad. The load is almost :math:`\mathrm{1D}` and we therefore have the equivalent of stresses in the joint and in the pad, which allows us to estimate the value of the applied stress :math:`\sigma`:


.. csv-table::

    ":math:`{\delta }_{\mathit{plot}}+{\delta }_{\mathit{joint}}={\delta }_{\mathit{impo}}` "," :math:`\sigma 2L/E+\sigma /\text{pena\_contact}/{K}_{N}={\delta }_{\mathit{impo}}` ", ""


This results in:

:math:`\sigma ={\delta }_{\mathit{impo}}/(\frac{1}{2LE}+\frac{1}{\text{pena\_contact}{K}_{N}})`

Once the constraint is known, we can apply the law of behavior in order to find the opening of the joint: :math:`{\delta }_{\mathit{joint}}=\sigma /\text{pena\_contact}/{K}_{N}`.

In case of sawing the value of :math:`{\delta }_{\mathit{impo}}` is reduced by the thickness of the saw, which parametrizes the sawing.

These :math:`\sigma \text{et}{\delta }_{\mathit{joint}}` values are then tested in the C and D models.