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


Calculation method
------------------

The reference solutions for stress intensity factors come from Murakami's "Stress Intensity Factors Handbook" [:ref:`bib1 <bib1>`]. The reference solutions for error estimation are non-regression solutions. The error estimators were validated in the thesis of J. Delmas [:ref:`bib2 <bib2>`].


Reference quantities and results
-----------------------------------

The reference results for stress intensity factors are:


.. csv-table::

    "", ":math:`{K}_{I}` "," :math:`{K}_{\mathrm{II}}`"
    "Problem 1", "9.37", "-"
    "Problem 2", "33.93", "4.53"
    "Problem 3", "6,33", "1,86"


**Table** 2.2-1 **:**: ** Reference quantities and results


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


1. Y. Murakami, "Stress Intensity Factors Handbook", Pergamon Press Oxford, 1987.


2. J. Delmas, "Error control strategies in the calculation of industrial structures. Implementation of error estimation in quantity of interest and mesh adaptation", Doctoral thesis, University of Picardy Jules Verne, 2008.