Benchmark solution
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Calculation method used for the reference solution
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The deformation due to pressure alone is given by:

:math:`{u}_{r}=\frac{{p}_{0}}{\mathrm{\nu }EL}\times \frac{1}{1-2\mathrm{\nu }}\times \frac{{z}^{2}}{4}\mathrm{sin}(\mathrm{\theta })`; :math:`{u}_{z}=\frac{-{p}_{0}}{\text{}2\mathit{nu}EL}\mathit{rz}\mathrm{sin}(\mathrm{\theta })`; :math:`{u}_{\mathrm{\theta }}=\frac{{p}_{0}}{\mathrm{\nu }EL}\times \frac{1}{1-2\mathrm{\nu }}\times \frac{{z}^{2}}{4}\mathrm{cos}(\mathrm{\theta })`.

The constraint field is equal to:

:math:`{\sigma }_{\mathit{rr}}=-\frac{{p}_{0}r\mathrm{sin}(\theta )}{L}`; :math:`{\sigma }_{\mathit{zz}}=-\frac{1-\nu }{\nu L}{p}_{0}r\mathrm{sin}(\theta )`; :math:`{\sigma }_{\theta \theta }=-\frac{{p}_{0}r\mathrm{sin}(\theta )}{L}`;

:math:`{\sigma }_{\mathit{rz}}=\frac{{p}_{0}z\mathrm{sin}(\theta )}{L}`; :math:`{\sigma }_{r\theta }=0`; :math:`{\sigma }_{\theta z}=\frac{{p}_{0}z\mathrm{cos}(\theta )}{L}`.


Benchmark results
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Radial (:math:`\mathit{DX}`), vertical (:math:`\mathit{DY}`), and ortho-radial (:math:`\mathit{DZ}`) displacements at points :math:`C` and :math:`D` for an angle :math:`\theta =45°`.

Constraints at points :math:`A` and :math:`B`.


Uncertainty about the solution
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* Analytical solution.




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