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


Calculation method used to obtain the reference solution
----------------------------------------------------------------

The reference solution [:ref:`bib4 <bib4>`] is the one obtained with the SAMCEF [:ref:`bib1 <bib1>`] software. The modeling is based on a shell theory in resultant efforts with a co‑rotational formulation [:ref:`bib3 <bib3>`] and a regular DSQ [:ref:`bib2 <bib2>`] discretization.


.. image:: images/100005C8000069BB00001B7E2B88C3BDA9CC6BD1.svg
    :width: 283
    :height: 73


.. _RefImage_100005C8000069BB00001B7E2B88C3BDA9CC6BD1.svg:

The mesh considered is a regular mesh of :math:`20\mathrm{\times }1` quadrilateral elements with 4 nodes each.


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

We test the pseudo-temporal evolution of :math:`\mathit{DX}`, :math:`\mathit{DZ}`, :math:`\mathit{DRY}` at the middle point of segment :math:`\mathit{P1P2}`.


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


1. SAMCEF, V7.1 Volume Elements Reference Manual,1998


2. J-L. Batoz, G.Dhatt, "Modeling Structures by Finite Elements: Beams and Plates ", Hermès, Paris, 1992


3. Crisfield M.A., "Non-linear Finite Element Analysis of Solids and Structures", Volume 1: Essentials, John Wiley, Chichester, 1994


4. Ph. JETTEUR, Nonlinear Shell Kinematics. Report SAMTECH, Contract PP/GC-134/96, 1998


5. M. AL MIKDAD, Continuing pressure for COQUE_3D elements, Report No. 99020-1 1999