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


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


* Radial displacement in local coordinate system

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:


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= -

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where

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= components of the displacement in the global coordinate system

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.


* Yes

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are the constraints in the local coordinate system, the constraints expressed in the global coordinate system are equal to:


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At the local level

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(circumferential stress),

From where

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


* Radial displacement: :math:`{u}_{r}=–7.14\times {10}^{-7}m`


* In the local plan :math:`(x,z)`, :math:`{\sigma }_{\mathrm{yy}}=1.25\times {10}^{5}\mathrm{Pa}`, :math:`{\sigma }_{\mathrm{zz}}=3.75\times {10}^{5}\mathrm{Pa}`


Uncertainty about the solution
---------------------------


* Analytical solution


Bibliographical references
---------------------------


1. R.J. ROARK and W.C. YOUNG: Formulas for stress and strain, 5th edition. New York, McGraw-Hill, 1975