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


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

The reference solution was obtained with a finite shell element DKT24 (4x6 mesh) at 4 nodes with 6 degrees of freedom per node in Total Lagrangian Formulation. This solution is described in detail in [:ref:`bib2 <bib2>`].


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


.. csv-table::

    ":math:`{W}_{A}`
    :math:`\times {10}^{-\mathrm{3m}}` ", "Charge :math:`P`
    (:math:`\mathrm{KN}`)", "Charge :math:`P/\mathrm{Pmax}` ", "", ":math:`{W}_{A}`
    :math:`\times {10}^{-\mathrm{3m}}` ", "Charge :math:`P`
    (:math:`\mathrm{KN}`)", "Charge :math:`P/\mathrm{Pmax}` ", "", ":math:`{W}_{A}`
    :math:`\times {10}^{-\mathrm{3m}}` ", "Charge :math:`P`
    (:math:`\mathrm{KN}`)", "Charge :math:`P/\mathrm{Pmax}`"
    "0.0", "0.000", "0.0000", "", "0.0000", "", "—16.4", "0.480", "0.8000", "", "—14.0", "—0.295", "—0.295", "—0.295", "—0.295", "—0.4916"
    "—1.7", "0.150", "0.2500", "", "0.2500", "", "—16.7", "0.415", "0.6916", "", "—14.3", "—0.345", "—0.345", "—0.345", "—0.345", "—0.5750"
    "—3.5", "0.265", "0.4416", "", "0.4416", "", "—16.9", "0.350", "0.5833", "", "—15.0", "—0.370", "—0.370", "—0.370", "—0.6166"
    "—4.9", "0.345", "0.5750", "", "—17.0", "—17.0", "0.290", "0.4833", "", "—16.1", "—16.1", "—0.380", "—0.380", "—0.6333"
    "—6.8", "0.410", "0.6833", "", "0.6833", "", "—17.3", "0.375", "—0.375", "—0.375", "—0.375", "—0.6250"
    "—8.4", "0.475", "0.7916", "", "—7916", "", "—17.1", "0.150", "0.2500", "", "—18.7", "—0.350", "—0.350", "—0.350", "—0.350", "—0.350", "—0.350", "—0.350", "—0.350", "—0.5833"
    "—9.8", "0.520", "0.8666", "", "", "—17.0", "0.090", "0.1500", "", "—20.3", "—0.3", "—0.305", "—0.305", "—0.305", "—0.5083"
    "—11.1", "0.555", "0.9250", "", "9250", "", "—16.8", "—16.8", "—0.230", "—0.230", "—0.230", "—0.3833"
    "—12.2", "0.580", "0.9666", "", "—666", "", "—16.4", "—0.035", "—0.0583", "", "—23.5", "—23.5", "—0.120", "—0.120", "—0.2000"
    "—13.1", "0.595", "0.9916", "", "0.9916", "", "—16.0", "—0.085", "—0.1416", "", "—25.2", "0.025", "0.025", "0.0416"
    "—14.0", "0.600", "1.0000", "", "1.0000", "", "—15.3", "—0.130", "—0.2166", "", "—26.8", "1.0000", "0.210", "0.210", "0.3500"
    "—14.9", "0.585", "0.9750", "", "0.9750", "", "—14.8", "—0.155", "—0.2583", "", "—28.5", "0.9750", "0.445", "0.445", "0.7416"
    "—15.5", "0.565", "0.9416", "", "", "—14.2", "—0.195", "—0.3250", "", "", ""
    "—16.1", "0.525", "0.8750", "", "—8750", "", "—14.0", "—0.240", "—0.4000", "", "", ""



.. image:: images/100033DC000069D500003EF17795564614650635.svg
    :width: 503
    :height: 299


.. _RefImage_100033DC000069D500003EF17795564614650635.svg:


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

Less than 2%, digital solution


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


1. HAMMADI Fodil: Formulation and evaluation of finite elements with C° continuity of geometry for the linear and non-linear analysis of shells.


2. JAAMEI S.,: Study of various Lagrangian formulations for the nonlinear analysis of thin elasto-plastic plates and shells in large displacements and rotations, Doctoral thesis, University of Technology of Compiègne 1986.