2. Benchmark solution

2.1. Calculation method

There is a known analytical solution to this problem, if we consider \({R}_{1}\) the inner radius and \({R}_{2}\) the outer radius, then the radial stress expressed in polar coordinates is written as:

\({\mathrm{\sigma }}_{\mathit{rr}}(r)=\frac{{R}_{1}^{3}}{{R}_{2}^{3}-{R}_{1}^{3}}\cdot \frac{{R}_{2}^{3}-{r}^{3}}{{r}^{3}}\cdot P\).

So we definitely find \({\mathrm{\sigma }}_{\mathit{rr}}({R}_{1})=P\) and \({\mathrm{\sigma }}_{\mathit{rr}}({R}_{2})=0\).

2.2. Reference quantities and results

We test the contact pressure on the interfaces, in \(r=30\mathit{mm}\), on both sides of the discontinuity. With \({R}_{1}=20\mathit{mm}\) and \({R}_{2}=40\mathit{mm}\), we then have:

\({\mathrm{\sigma }}_{\mathit{rr}}(r)=4.894179894\mathit{MPa}\).

2.3. Uncertainty about the solution

Analytical solution.