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


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

Axial stress: :math:`{\sigma }_{11}=\frac{q}{h}`

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

Cylinder elongation: :math:`{U}_{x}=\frac{\mathrm{qL}}{\mathrm{Eh}}`

Radial displacement: :math:`{U}_{r}=-\frac{q\nu {R}_{0}}{\mathrm{Eh}}`


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

:math:`{\sigma }_{11}=5\times {10}^{5}\mathrm{Pa}`

:math:`{U}_{x}=9.52\times {10}^{-6}m`

:math:`{U}_{r}=–7.14\times {10}^{-7}m`


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

Analytical solution.


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


1. Guide VPCS — 1990 edition (SSLS 07/89)


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