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


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

For the gravity load case alone:

The value of the radial displacement field, as a function of :math:`z`, is given by:


.. image:: images/Object_1.svg
    :width: 205
    :height: 53


.. _RefImage_Object_1.svg:

The maximum displacement, in the middle section, is equal to:


.. image:: images/Object_2.svg
    :width: 205
    :height: 53


.. _RefImage_Object_2.svg:

For the case of pressure load, a comparison is made with the results of the C modeling.


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


1. Movement in the middle section, :math:`\mathrm{ur}(E)=0.3566\times {10}^{-6}m`


2. Embedding constraints at point B: :math:`{\sigma }_{\mathrm{zz}}=–0.2496\times {10}^{6}\mathrm{Pa}`


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

Analytical solution for gravity.


Bibliographical reference
-------------------------


1. S. TIMOSHENKO: Material strength, part 1. Librairie Polytechnique Ch.Béranger, Paris, 1947