Benchmark solution
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Calculation method used for the reference solution
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:math:`\begin{array}{ccc}{\mu }_{i}& =& \frac{{E}_{i}}{2(1+\nu )}\\ {\lambda }_{i}& =& \frac{\nu {E}_{i}}{(1-2\nu )(1+\nu )}\end{array}`


.. math::
: label: EQ-None

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

For material :math:`i`, we have:

:math:`\begin{array}{ccc}{u}_{r}& =& {a}_{i}r+\frac{{b}_{i}}{r}\\ {u}_{z}& =& A\end{array}`

:math:`\{\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}`


Uncertainty about the solution
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Analytical solution.