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


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

The calculations are carried out with 8 calculation codes, for 10 models. The various models are presented below.


.. csv-table::

    "* Castem:", "20 shear free beam elements;"
    "* Dynam2D:", "20 shear free beam elements;"
    "* PERMAS (1):", "20 shear free beam elements;"
    "* NASTRAN:", "20 shear free beam elements;"
    "* SYSTUS (1):", "20 shear free beam elements;"
    "* ABAQUS:", "20 shear beam elements;"
    "* MECHANICA:", "5 girder elements with shear, convergence to degree 7;"
    "* CASTOR:", "10 shear beam elements;"
    "* SYSTUS (2):", "40 girder elements with shear;"
    "* PERMAS (2):", "20 shear beam elements;"


Reduced depreciation :math:`\xi` is equal to 1% across all modes.


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

The frequencies.

The value RMS, for movement at the free end of the beam.


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

Comparison between codes.


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


1. IPSI - Day :math:`{\Phi }^{2}\mathrm{.}\mathrm{AS}` - Vol. XVIII, no. 2. Depreciation in structural calculations. June 21, 1994.