5. C modeling#
5.1. Characteristics of modeling#
The characteristics used and the mesh are those deduced from the data in paragraph 1. Harmonic response and transfer functions were calculated for reduced frequencies \(>\) (where \(>\)). The results obtained by Mita and Luco for these reduced frequencies are presented in the reference [bib2].
This modeling is used to test the “QUELCONQUE” interface option of the MODE_INTERF keyword with any foundation modes different from rigid body modes. Its results will be compared to those of modeling A.
5.2. Characteristics of the mesh#
The characteristics are those of modeling A.
5.3. Boundary conditions for modeling#
For the representation of the foundation movement, instead of rigid body translation modes, a base of any 30 modes obtained as natural modes, without blocking conditions, on a spring mat established from static ground impedances for the ground defined in §1.2 is used.
We therefore take as values of global rigidities to be distributed under the foundation with option RIGI_PARASOL of AFFE_CARA_ELEM:
\(>\), \(>\), \(>\), \(>\)
5.4. Tested sizes and results#
For case \(>\), the response is necessarily tested after projection on physical coordinates because, unlike modeling A, the modal coordinates do not coincide with the physical coordinates. Since the foundation is rigid and massless, all the nodes undergo the same displacement which is equal to \(>\) in the \(>\) direction for an excitation in the \(>\) direction. Likewise, all the nodes undergo the same displacement which is equal to \(>\) in direction \(>\) for an excitation in direction \(>\).
With a via REST_SPEC_PHYS projection, we get the result:
\(>\) |
|
SPEC N11 “DZ” |
1.0 |
1.00001E+00 |
1.00383E+00 |
A test of type ANALYTIQUE is carried out with a tolerance of \(>\) for “DX” and \(>\) for “DZ”.
For the case with spatial variability, we choose \(\alpha =0.5\) and we test against the results of the literature (SOURCE_EXTERNE) with a tolerance of \(\text{10\%}\).
Results obtained with DYNA_ISS_VARI with a via REST_SPEC_PHYS projection, for \(\alpha =0.5\) and:
\({a}_{0}\) |
|
|
1.0 |
0.767 |
0.770 |
2.0 |
0.437 |
0.438 |
3.0 |
0.251 |
0.252 |
As a reminder, the reference results [bib2], see also §2.2:
\(>\) |
|
|
1.0 |
0.732 |
0.730 |
2.0 |
0.402 |
0.416 |
3.0 |
0.251 |
0.270 |
In addition, a NON_REGRESSION test is done for the values calculated by DYNA_ISS_VARI with a tolerance of \(>\) (by default value).
We also do a AUTRE_ASTER test with respect to the results of modeling A.