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


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


* The value of the axial displacement at the center of the disk (point A) is given by:

:math:`{W}_{a}=-\frac{P{\phi }^{2}}{64\pi D}\times \frac{3+\nu }{1+\nu }`

Where :math:`D=\frac{E{h}^{3}}{12(1-{\nu }^{2})}`


* The value of potential energy (at equilibrium) is given by:

:math:`{E}_{p}=-\frac{1}{2}P{W}_{a}`


* The absolute value of potential energy per radian is:

:math:`{e}_{p}=\frac{1}{2}\frac{P{W}_{a}}{2\pi }`


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


.. csv-table::

    "* Move to point :math:`A`:", ":math:`{W}_{a}=–0.4596\times {10}^{-3}m`"
    "", ""
    "* Potential energy per radian:", ":math:`{e}_{p}=0.012799\mathrm{Nm}/\mathrm{rd}`"



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

Analytical solution.


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


1. R.J. ROARK and W.C. YOUNG Formulas for stress and strain, 5th edition, New York, McGraw-Hill, 1975