Reference solution
=====================


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

This 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 discretization DSQ [:ref:`bib2 <bib2>`].


.. image:: images/Object_9.svg
    :width: 291
    :height: 126


.. _RefImage_Object_9.svg:

The mesh considered in the reference calculation is a regular mesh of :math:`16\mathrm{\times }16` quadrilateral elements with 4 nodes each.


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

**History of vertical displacement** :math:`\mathrm{DZ}` **in meters at the loaded node** :math:`\mathrm{P1}`


.. csv-table::

    "**Instant**", "**Surface Force** :math:`\mathrm{fz}` **** (**:math:`N`**) **", ":math:`\mathit{DZ}`**in** :math:`\mathrm{P1}`
    **(** :math:`m` **)**"
    "0.2", "0.2", "—1.043E—01"
    "0.4", "0.4", "—3.935E—01"
    "0.7", "0.7", "—5.13E—01"



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