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

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

Code averages: Lice, ADL,, TITUS -T.

Validation guide for structural calculation packages- AFNOR - 1990 (for modal calculation). The values provided in the sheet are underestimated and were subsequently corrected in 1992. However, they were retained for calculations with a diagonal mass matrix.


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

.. csv-table::

    "Modal calculation:", "9 first natural frequencies."
    "Spectral response:", "displacement of nodes :math:`\mathrm{N3}` :math:`\mathrm{N5}` and :math:`\mathrm{N7}`, :math:`\mathrm{N9}`, :math:`\mathrm{N11}`.
    Support reaction at nodes :math:`\mathrm{N1}`, :math:`\mathrm{N15}`.
    Widespread efforts from nodes :math:`\mathrm{N3}`, :math:`\mathrm{N7}`, :math:`\mathrm{N11}`."



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

In the order of :math:`\text{1\%}` on the first 5 modes.

Between 1 and :math:`\text{2,5\%}` for modes 6 to 9.


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


1. Guide VPCS AFNOR Technical- 1990


2. W. HOVGAARD "Stress in three dimensional pipe bens", Trans of ASME vol.57, FSP 75-12 P401-416.