2. Benchmark solution

2.1. Calculation method used for the reference solution

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

\({U}_{r}\mathrm{=}B\text{.}r+\frac{C}{{r}^{2}}\)

With

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

where \({r}_{i}\mathrm{=}R\mathrm{-}\frac{t}{2}\) and \({r}_{e}\mathrm{=}R+\frac{t}{2}\)

2.2. Benchmark results

Move the point \(A\) to \(x\), move the point \(B\) to the next, move the point to the next \(y\), move the point \(C\) to the next \(z\).