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


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

Comparison with other numerical results obtained with 3D meshes or shells (in particular in the context of the Tripartite Sheet 3455 of CEA, (see references), and with a fairly fine COQUE_3D calculation (D modeling).


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

For a moment applied :math:`\mathrm{MZ}` in :math:`D` of :math:`17000\mathrm{Nm}`, the displacement :math:`\mathrm{DY}` of the same point :math:`D` is equal to:


.. csv-table::

    "**Calculation type**", ":math:`\mathrm{Dy}` **point** :math:`D` **(** :math:`\mathrm{mm}` **)**"
    "Calculation CEA (shells + Victus)", "0.02"
    "Calculation COQUE_3D ", "0.02012 (D modeling)"


For reference, we choose the value :math:`\mathit{Dy}\mathrm{=}0.02\mathit{mm}`.

For out-of-plane bending, the reference value (calculation COQUE_3D fine) is :math:`–1.5657{10}^{\mathrm{-}2}\mathit{mm}`.


Precision on the reference results
----------------------------------------

Since the reference solution is numerical, the accuracy can be evaluated based on [:ref:`§2.2 <§2.2>`] at 2%.


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


1. M.N. BERTON: "Elastoplastic pipe calculations with CASTEM 2000. Formulation VICTUS. Summary of the 3455 sheet". Note CEA/LDM 96/6036


2. J.M. PROIX, A. BEN HAJ YEDDER: "Project CACIP: study of a pipe bent under bending". Rating EDF/DER HI-75/98/001/0