Reference problem
=====================


Geometry
---------

The analysis consists in extracting the elementary cycles from a history of stress loading.


* First call to POST_FATIGUE:

The elementary cycles are extracted using the cycle counting method RAINFLOW, based on the loading history :math:`{\sigma }_{1}(t)`.


* Second call to POST_FATIGUE:

The elementary cycles are extracted using the cycle counting method RCCM, based on the loading history :math:`{\sigma }_{1}(t)`.


* Third call to POST_FATIGUE:

The elementary cycles are extracted by the cycle counting method RAINFLOW, on the loading history :math:`{\sigma }_{2}(t)` and a stress concentration coefficient :math:`{K}_{T}=2` is used.


* Fourth call to POST_FATIGUE:

The elementary cycles are extracted by the cycle counting method RCCM, on the loading history :math:`{\sigma }_{2}(t)` and a stress concentration coefficient :math:`{K}_{T}=2` is used.

**Charging history**


.. csv-table::

    ":math:`t` ", "0. ", "1. ", "2. ", "3. ", "4. ", "5. ", "6. ", "7. ", "8."
    ":math:`{\sigma }_{1}(t)` ", "0. ", "500. ", "200. ", "40. ", "300. ", "500. ", "-300. ", "200. ", "-500."



.. csv-table::

    ":math:`t` ", "0. ", "1. ", "2. ", "3. ", "4. ", "5. ", "6. ", "7. ", "8."
    ":math:`{\sigma }_{2}(t)` ", "0. ", "250. ", "100. ", "200. ", "150. ", "250. ", "-150. ", "100. ", "-250."