4. Modal transitory post-processing — option “IMPACT”#
4.1. Common practice for post-treatment of heart stones#
Prior to the development of post-processing in Code_Aster, SEPTEN used the CLASH [bib2] code developed by BELGONUCLEAIRE for its sizing verification needs. This software calculates the seismic response of a queue of assemblies. This code provides a set of detailed information for each shock point and for each impact.
Each result consists of a table by shock point, an example of which is in Annexe 1. This table includes the following information:
the moment of the peak of impact,
the maximum impact force reached,
the impulse exchanged, defined as the integral of the shock force over time,
the total duration of the shock,
the relative speed before impact.
These elements are particularly interesting for the SEPTEN because in addition to the very limited contractual information, they make it possible to know the number and composition of impacts, as well as the essential physical quantities associated with them. The relative speed before impact and the impulse are for example very valuable information in the specification of experimental tests for the dynamic buckling of assembly grids.
4.2. Calculations for post-treatment of impacts#
As for the previous post-treatment, it is considered that the impact conditions are determined as before by exceeding a threshold force \(\mathrm{Smax}\) and a distinction is made in the same way as for global shock and elementary shock by the concept of rest time.
The calculation performs a loop on all shock nonlinearities and an identical treatment for each.
Then, for each global shock identified, the following magnitudes will be determined:
Shock onset time: \({T}_{\mathrm{début}}\text{tel que}{F}_{\mathrm{choc}}({T}_{\mathrm{début}})>{S}_{\mathrm{max}}\)
Global shock end time:
\({T}_{\mathrm{fin}}\text{tel que}{F}_{\mathrm{choc}}({T}_{\mathrm{fin}})\le {S}_{\mathrm{max}},{F}_{\mathrm{choc}}({T}_{\mathrm{fin}}-\Deltat )\ge {S}_{\mathrm{max}}\)
\(\text{et}\forall t\in [{T}_{\mathrm{fin}},{T}_{\mathrm{fin}}+{T}_{\mathrm{repos}}]{F}_{\mathrm{choc}}(t)\le {S}_{\mathrm{max}}\)
\(\text{où}\Deltat \text{est le pas de temps d'intégration}\)
Total shock duration: \({T}_{\mathrm{choc}}={T}_{\mathrm{fin}}-{T}_{\mathrm{début}}\)
Maximum force upon impact: \({F}_{\mathrm{max}}={\mathrm{max}}_{T\in [{T}_{\mathrm{début}},{T}_{\mathrm{fin}}]}({F}_{\mathrm{choc}}(t))\)
The moment of maximum shock force,
The impulse exchanged during the shock: \(I=\underset{t={T}_{\mathrm{début}}}{\overset{{T}_{\mathrm{fin}}}{\int }}{F}_{\mathrm{choc}}(t)\cdot \mathrm{dt}\)
Relative normal speed before impact: \({V}_{\mathrm{choc}}=V({T}_{\mathrm{début}}-\Deltat )\)
The number of elementary impacts accumulated in the global shock:
\({N}_{\mathrm{impacts}\mathrm{élémentaires}}=\mathrm{card}\left\{t\in [{t}_{\mathrm{début}},{T}_{\mathrm{fin}}]/{F}_{\mathrm{choc}}(t)>{S}_{\mathrm{max}}\text{et}{F}_{\mathrm{choc}}(t+\deltat )\le {S}_{\mathrm{max}}\right\}\)
In order to synthesize the information, we will also determine:
the absolute maximum shock force, on a given shock connection, for the duration of analysis,
To be determined more precisely, the maximum shock force will not be obtained as the maximum in time over all the shocks for each shock node (to avoid the bias in archiving accuracy) but determined in the transitory calculation over all the calculation steps and archived in the tran_gene result concept. It is this information that will be used.
the average value of the shock force extremes as well as their standard deviation.
a histogram of the probability density of the maximum impact forces.
This histogram will be relatively brief and will give for \({N}_{C}\) classes the probability density of the maximum shock force.
The classes will be defined as follows:
\({\mathrm{classe}}_{i={\mathrm{1..N}}_{C}}=\left\{{F}_{\mathrm{max}}/\frac{i-1}{{N}_{C}}{F}_{\mathrm{max}}^{\mathrm{absolu}}\le {F}_{\mathrm{max}}\le \frac{i}{{N}_{C}}{F}_{\mathrm{max}}^{\mathrm{absolu}}\right\}\)
4.3. Data structure table POST_IMPACT associated with option “IMPACT”#
4.3.1. Table POST_IMPACT#
A table-like data structure for the IMPACT option **of the POST_DYNA_MODA_T operator of*Code_Aster* is produced.
The result structure will be a table indexed by the names of shock links, of the type POST_IMPACT **, containing the names of the tables it contains.
The content of each cell in this table is a table name stored in CHARACTER *24. Three types of table are contained: a table called IMPACT, a table called GLOBAL and a table called PROBA.
It therefore has 3 parameters: IMPACT, **, **GLOBAL, and PROBA. The access variable corresponds to the name of the shock link in question.
4.3.2. Table IMPACT#
Table IMPACT is of type TABL_IMPACT and has 6 access parameters: INST, **, **, **, ** and has 6 access parameters: **, **V_ IMPACT, NB_IMPACT. MAX CHOC IMPULS
The contents of each cell in this table are REAL*8.
4.3.3. Table GLOBAL#
Table GLOBAL is of type TABL_FMAX and has 3 access parameters:
F_ MAX_ABS, which allows access to the absolute maximum impact force on all the shocks observed,
F_ MAX_MOY, which provides access to the average value of the shock force maxima observed,
F_ MAX_ETYP, which provides access to the standard deviation of shock force extremes.
The contents of each cell in this table are REAL*8.
4.3.4. Table PROBA#
Table PROBA is of type TABL_HISTO and has 3 access parameters:
**** DEBUT **, which allows access to the minimum force value for class \(i\),
**** FIN **, which allows access to the maximum force value for class \(i\),
**** PROBA **, which allows access to the probability density of the maximum force variable for class \(i\).
The content of each cell in this table is a REAL *8.