2. Benchmark solution#

2.1. Calculation method used for the reference solution#

  • Radial displacement in local coordinate system

    _images/Object_2.svg

:

_images/Object_3.svg

= -

_images/Object_4.svg

where

_images/Object_5.svg

= components of the displacement in the global coordinate system

_images/Object_6.svg

.

  • Yes

    _images/Object_7.svg

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

_images/Object_8.svg

At the local level

_images/Object_9.svg

(circumferential stress),

From where

_images/Object_10.svg

2.2. Benchmark results#

  • Radial displacement: \({u}_{r}=–7.14\times {10}^{-7}m\)

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

2.3. Uncertainty about the solution#

  • Analytical solution

2.4. Bibliographical references#

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