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

This test case is the result of *Code_Aster*'s independent validation campaign for earthquake calculations. This document refers to calculations obtained with the same type and number of finite beam elements and compared:


*the*Castem2000*software in a single-support situation. In [:ref:`1 <1>`], it is indicated that the differences between*Castem2000*and*Code_Aster* obtained on the RMS absolute transverse displacement values in the middle of the beam are less than 0.41%.


*the*Abaqus* software in single-support and multi-support situations [:ref:`1 <1>`].


*the*Hercule* software in a mono-support situation :ref:`[2] <RefNumPara__38295637>`.

However, in the absence of more information on the results obtained in multi-support, the results of the test case are considered to be results of non-regression and inter-comparison between different operators (linear transient calculation on a modal basis, direct linear transient calculation) and different time integration methods (NEWMARK, DEVOGELAERE).

The calculated quantity is the absolute transverse displacement of the point located at :math:`L/2` (in the middle of the beam) at various times. In :ref:`[2] <RefNumPara__38295637>` we find the following values obtained with the *Hercule* software:


.. csv-table::

    "Quantity in single-support calculation", "Maximum value", "Value RMS"
    "Relative DY (:math:`m`)", "0.01871", "0.01031"
    "Absolute DY (:math:`m`)", "0.02544", "0.01035"


We also test the first six natural frequencies of the embedded beam (*Hercule* software reference):


.. csv-table::

    "mode", "1", "2", "3", "3", "4", "5", "6"
    "Frequency (:math:`\mathrm{Hz}`)", "4.64", "12.77", "12.77", "25.03", "41.34", "61.69", "86.04"



1. Note HP-52/97/0168 GUIHOT P., DEVESA G., G., DUMOND G., A., A., WAECKEL Fe.Independent validation of Code_Aster version 3: summary of the validation of the earthquake batch.



.. _RefNumPara__38295637:

2. A. Succar. Séchaud and Metz, 2000.