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


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

At a point with the x coordinate:


1. radial displacement: :math:`{U}_{r}=-\frac{\gamma R\nu x}{E}`


2. axial displacement: :math:`{U}_{x}=\frac{\gamma {x}^{2}}{2E}`


3. generator rotation: :math:`\psi =-\frac{\gamma R\nu }{E}`


4. axial stress: :math:`{\sigma }_{11}=\gamma x`


5. Circumferential stress: :math:`{\sigma }_{22}=0`


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


1. High end axial displacement: :math:`{U}_{x}=2.99\times {10}^{-6}m`


2. Radial displacement at low end: :math:`{U}_{r}=–4.49\times {10}^{-7}m`


3. :math:`\psi =–1.12\times {10}^{-7}\mathrm{rad}`


4. :math:`{\sigma }_{11}=3.14\times {10}^{5}\mathrm{Pa}`, at the low end


5. :math:`{\sigma }_{22}=0` everywhere


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

Analytical solution.


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


* Guide VPCS — 1990 edition (SSLS 09/89)


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