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


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

analytics:

If the pressure varies like:


.. image:: images/Object_5.svg
    :width: 148
    :height: 45


.. _RefImage_Object_5.svg:

then the circumferential component of the stress tensor is equal to:


.. image:: images/Object_6.svg
    :width: 148
    :height: 45


.. _RefImage_Object_6.svg:

and the displacement field is equal to:


.. image:: images/Object_7.svg
    :width: 148
    :height: 45


.. _RefImage_Object_7.svg:


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

Here, :math:`{\lambda }_{p}\mathrm{=}0`.


+-+----------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+
|X|                                                                                              |                                                                                               |                                                                                                         |
+ + .. image:: images/Object_9.svg                                                               + .. image:: images/Object_10.svg                                                               + .. image:: images/Object_11.svg                                                                         +
| |    :width: 148                                                                               |    :width: 159                                                                                |    :width: 205                                                                                          |
+ +    :height: 45                                                                               +    :height: 45                                                                                +    :height: 93                                                                                          +
| |                                                                                              |                                                                                               |                                                                                                         |
+ + (:math:`m`)                                                                                  + (:math:`m`)                                                                                   + (:math:`\mathit{Pa}`)                                                                                   +
| |                                                                                              |                                                                                               |                                                                                                         |
+-+----------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+
|0|5d-11                                                                                         |0                                                                                              |100                                                                                                      |
+-+----------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+
|1|0                                                                                             |7.5d-11                                                                                        |0                                                                                                        |
+-+----------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------+



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

Analytical solution.


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


* PILKEY W.D.: "Formulas for stress, strain, and structural matrices." Wiley & Sons, New York, 1994.