Description of document versions
====================================


.. csv-table::

    "**Version** **Aster**", "**Author (s)**
    **Organization (s)**", "**Description of changes**"
    "6", "A.M DONORE,
    F. MEISSONNIER
    EDF -R&D/ AMA ", "initial text"
    "7,4", "A.M DONORE,
    F. MEISSONNIER
    EDF -R&D/ AMA ", ""


We consider the following loading history (which for the example is considered to be of the constraint type):


.. csv-table::

    "Point number", "1", "2", "3", "3", "3", "3", "4", "4", "5", "6", "9", "10", "11", "12", "13", "13", "13", "13", "13", "13", "14", "15"
    "Instant", "0. ", "1. ", "2. ", "3. ", "4. ", "5. ", "6. ", "7. ", "8. ", "9. ", "10. ", "11. ", "12. ", "13. ", "14."
    "Loading", "0. ", "40. ", "—10. ", "60. ", "20. ", "50. ", "30. ", "80. ", "—70. ", "30. ", "—50. ", "20. ", "—30. ", "25. ", "0."



.. image:: images/10000616000016BD0000191DD6C3D65ED86114E6.svg
    :width: 293
    :height: 324


.. _RefImage_10000616000016BD0000191DD6C3D65ED86114E6.svg:

The loading history rearrangement stage leads to the next load:


.. csv-table::

    "Point number", "8", "9", "10", "10", "10", "11", "11", "12", "13", "14", "15", "2", "3", "4", "5", "5", "5", "5", "5", "5", "6", "7"
    "Loading", "80. ", "—70. ", "30. ", "—50. ", "20. ", "—30. ", "25. ", "0. ", "40. ", "—10. ", "60. ", "20. ", "50. ", "30."



.. image:: images/100006C40000182F00001C02C817271F2450CBA4.svg
    :width: 293
    :height: 324


.. _RefImage_100006C40000182F00001C02C817271F2450CBA4.svg:

The second step consists in extracting the elementary cycles. The first cycle extracted is the cycle defined by points 12 and 13 since :math:`\mid \mathrm{\sigma }(\text{12})-\mathrm{\sigma }(\text{13})\mid` is less than :math:`\mid \mathrm{\sigma }(\text{14})-\mathrm{\sigma }(\text{13})\mid` and :math:`\mid \mathrm{\sigma }(\text{12})-\mathrm{\sigma }(\text{13})\mid` is less than :math:`\mid \mathrm{\sigma }(\text{12})-\mathrm{\sigma }(\text{11})\mid`.

Cycle 1: :math:`\mathrm{VALMAX}=20` and :math:`\mathrm{VALMIN}=-30`.

Once the cycle has been extracted, we remove these two points from the loading story, and we start again with the remaining story.

The next cycle extracted is the cycle defined by points 14 and 15.

Cycle 2: :math:`\mathrm{VALMAX}=25` and :math:`\mathrm{VALMIN}=0`.

The story left after removing these two points is:


.. image:: images/100005F6000016A200001A265BB7B37F449AFE4E.svg
    :width: 293
    :height: 324


.. _RefImage_100005F6000016A200001A265BB7B37F449AFE4E.svg:

The cycle defined by points 10 and 11 is then extracted.

Cycle 3: :math:`\mathrm{VALMAX}=30` and :math:`\mathrm{VALMIN}=-50`.

We go back to the following loading story:


.. image:: images/1000053E000017FA00001A90773603F4818B3B40.svg
    :width: 293
    :height: 324


.. _RefImage_1000053E000017FA00001A90773603F4818B3B40.svg:

The next extracted cycle is defined by points 2 and 3.

Cycle 4: :math:`\mathrm{VALMAX}=40` and :math:`\mathrm{VALMIN}=-10`.

The remaining load story is (it's the residue of the load story):


.. image:: images/100003E4000018CE00001C1D1101CFD0CDEBBABE.svg
    :width: 293
    :height: 324


.. _RefImage_100003E4000018CE00001C1D1101CFD0CDEBBABE.svg:

You can't extract any more cycles, because you've gone through the whole loading history.

We therefore move on to the third stage, which consists in treating the residue:


.. image:: images/10000722000018CE00001C1D6019E993D8DD5855.svg
    :width: 293
    :height: 324


.. _RefImage_10000722000018CE00001C1D6019E993D8DD5855.svg:

The same residue is added after it, and the second stage is repeated on this loading.

The next extracted cycle is defined by points 6 and 7.

Cycle 5: :math:`\mathrm{VALMAX}=50` and :math:`\mathrm{VALMIN}=30`.

The remaining load story is:


.. image:: images/100005880000172700001A759F52053949A61ECA.svg
    :width: 293
    :height: 324


.. _RefImage_100005880000172700001A759F52053949A61ECA.svg:

The next extracted cycle is defined by points 4 and 5.

Cycle 6: VALMAX = 60. and VALMIN = 20.

The remaining load story is:


.. image:: images/1000050C0000172700001A75EEC86C935FEA1277.svg
    :width: 293
    :height: 324


.. _RefImage_1000050C0000172700001A75EEC86C935FEA1277.svg:

The last cycle extracted is a cycle defined by points 8 and 9.

Cycle 7: :math:`\mathrm{VALMAX}=80` and :math:`\mathrm{VALMIN}=-70`.


.. image:: images/100004140000181500001C3732DC325BC953F269.svg
    :width: 293
    :height: 324


.. _RefImage_100004140000181500001C3732DC325BC953F269.svg:

It should be noted that when counting RAINFLOW is applied to the set consisting of the two residues, the initial residue is obtained again at the end of counting.