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


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

We consider a portion of an infinite plate with a circular central hole, subjected to unidirectional unit loading in the :math:`\mathit{Ox}\sigma \mathrm{=}1{e}_{x}\mathrm{\otimes }{e}_{x}` direction.

The analytical solution to this problem is [:ref:`bib1 <bib1>`]:


.. image:: images/Object_7.svg
    :width: 349
    :height: 148


.. _RefImage_Object_7.svg:

where:


* :math:`a` is the radius of the hole,


* :math:`(r,\theta )` the polar coordinates.


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

Analytical solution.


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


1. Zhu-Zienkiewicz: The superconvergent patch recovery and a posteriori error estimates- Part1: the recovery technique (Int. J. for Num. Methods in Engineering vol. 33, p. 1355 (May 1992)).