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


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

The reference solution was obtained numerically with ABAQUS 5.5. The mesh used consists of ELBOW31 elements with 2 nodes with 6 Fourier modes. The discretization used is as follows:

• Part :math:`\mathit{AB}`: 24 elements,

• Part :math:`\mathrm{BC}`: 8 elements,

• Part :math:`\mathrm{CD}`: 12 elements.

The integration in the section is as follows:

• 7 layers in thickness,

• 18 sectors in the circumferential direction.


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

Limit moment = :math:`253.4{10}^{3}\mathit{N.m}` for a rotation around :math:`z` from :math:`0.22\mathit{rad}` to point :math:`D`.


Uncertainties about the solution
----------------------------

Lower than :math:`\text{2\%}`


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

[:ref:`1 <1>`] ABAQUS/StandardVersion 5.5: Example Problems Manual Volume 2, pp 4.2.2-1.