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


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

The radial displacement at any node of the sphere under external pressure is given by:

:math:`{U}_{r}\mathrm{=}B\text{.}r+\frac{C}{{r}^{2}}`

With

:math:`B\mathrm{=}\frac{1\mathrm{-}2\nu }{E}\text{.}\frac{{r}_{e}^{3}}{{r}_{i}^{3}\mathrm{-}{r}_{e}^{3}}\text{.}P` and :math:`C\mathrm{=}\frac{1+\nu }{2E}\text{.}\frac{{r}_{i}^{3}{r}_{e}^{3}}{{r}_{i}^{3}\mathrm{-}{r}_{e}^{3}}\text{.}P`

where :math:`{r}_{i}\mathrm{=}R\mathrm{-}\frac{t}{2}` and :math:`{r}_{e}\mathrm{=}R+\frac{t}{2}`


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

Move the point :math:`A` to :math:`x`, move the point :math:`B` to the next, move the point to the next :math:`y`, move the point :math:`C` to the next :math:`z`.