2. Benchmark solution

2.1. Calculation method used for the reference solution

\(\begin{array}{ccc}{\mu }_{i}& =& \frac{{E}_{i}}{2(1+\nu )}\\ {\lambda }_{i}& =& \frac{\nu {E}_{i}}{(1-2\nu )(1+\nu )}\end{array}\)

\[\]

: label: EQ-None

begin {array} {ccccc} {a} _ {1} _ {1} & =& -0.98097& {b} _ {1} & -1.11741\ {a} _ {2} & =& -1.34405& =& -1.34405& {b} _ {2} & -0.30048end {array}}

For material \(i\), we have:

\(\begin{array}{ccc}{u}_{r}& =& {a}_{i}r+\frac{{b}_{i}}{r}\\ {u}_{z}& =& A\end{array}\)

\(\{\begin{array}{ccc}{\sigma }_{\mathrm{rr}}& =& {\lambda }_{i}(2{a}_{i}+A)+2{\mu }_{i}({a}_{i}-\frac{{b}_{i}}{{r}^{2}})\\ {\sigma }_{\mathrm{rr}}& =& {\lambda }_{i}(2{a}_{i}+A)+2{\mu }_{i}({a}_{i}+\frac{{b}_{i}}{{r}^{2}})\\ {\sigma }_{\mathrm{rr}}& =& 2{\lambda }_{i}{a}_{i}+({\lambda }_{i}+2{\mu }_{i})A\end{array}\)

2.2. Uncertainty about the solution

Analytical solution.