Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

Average of the results obtained by different mechanical calculation codes, ABAQUS, SYSTUS, SAMCEF, in the context of a test case IPSI - :math:`{\Phi }_{2}` AS [:ref:`bib1 <bib1>`].


Benchmark results
----------------------

Vertical movement of point :math:`\mathrm{PA4}`:


.. csv-table::

    "", ":math:`-\mathrm{0,83}\mathrm{mm}` ", ""
    "SYSTUS "," :math:`-\mathrm{0,82}\mathrm{mm}` ", "That's an average of :math:`-\mathrm{0,81}\mathrm{mm}`"
    "SAMCEF "," :math:`-\mathrm{0,78}\mathrm{mm}` ", ""


Vertical component of the reaction to embedment :math:`\mathrm{LBC4}`:


.. csv-table::

    "ABAQUS "," :math:`110270N` ", ""
    "SYSTUS "," :math:`109500N` ", "That's an average of :math:`108257N`"
    "SAMCEF "," :math:`105000N` ", ""


**NOTE:**

*The forces calculated by Aster axisymmetrically are calculated by radian. So the value to get is* :math:`108257\mathrm{/}2\pi \mathrm{=}17229.58N\mathrm{/}\mathit{rd}`


Uncertainty about the solution
----------------------------

The dispersion around the average value of the vertical displacement in :math:`\mathrm{PA4}` is 4%. The dispersion around the vertical reaction to embedding is 3%.


Bibliographical references
---------------------------


1. I. VAUTIER: "Example of the use of contact functionalities during large movements in the*Code_Aster*", note HI-75/97/034/0.