2. 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 [1].
the*Hercule software in a mono-support situation [2].
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 \(L/2\) (in the middle of the beam) at various times. In [2] we find the following values obtained with the Hercule software:
Quantity in single-support calculation |
Maximum value |
Value RMS |
Relative DY (\(m\)) |
0.01871 |
0.01031 |
Absolute DY (\(m\)) |
0.02544 |
0.01035 |
We also test the first six natural frequencies of the embedded beam (Hercule software reference):
mode |
1 |
2 |
3 |
3 |
4 |
5 |
6 |
Frequency (\(\mathrm{Hz}\)) |
4.64 |
12.77 |
12.77 |
25.03 |
41.34 |
61.69 |
86.04 |
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.
Succar. Séchaud and Metz, 2000.