7. Calculation of a seismic force load#
In the case where TYPE_RESU is equal to “CHARGE”, the result file of the frequency seismic forces of MISS3D is post-processed by CALC_MISS in order to provide the temporal solicitation of seismic forces in a direction of space applied to the ground- (fluid-) structure interface.
7.1. Operand MODELE#
This is the model of the structure to which a superelement comprising a macro-element obtained from the temporal or frequency evolution of the impedance of the ground domain (and possibly of the fluid domain) obtained using the Code_Aster— MISS3D chain is added by the option TYPE_RESU =” FICHIER_TEMPS “or TYPE_RESU =” FICHIER “of CALC_MISS.
7.2. Operand FONC_SIGNAL#
Temporal imposed displacement signal, generally obtained by double temporal integration of an accelerogram. In the data in the Code_Aster— MISS3D string, the latter generally corresponds to an acceleration imposed on the ground surface in a far field. The integrations can be obtained directly in the transitory domain using the operator CALC_FONCTION with the keyword INTEGRE or by going to frequency through option FFT, then by returning to time through the inverse FFT after integration in \(1/{(2\ast \mathit{pi}\ast \mathit{freq})}^{2}\) (cf. test SDNX100H).
7.3. Operand UNITE_RESU_FORC#
Allows you to define the logical unit of the generated file which will contain the frequency seismic forces calculated with the option TYPE_RESU =” FICHIER “of CALC_MISS.
7.4. Operand FREQ_MAX#
This operand provides the cutoff frequency value for calculating the temporal seismic force obtained by combining the frequency seismic forces (entered by UNITE_RESU_FORC) and the imposed moving signal entered by FONC_SIGNAL.
7.5. Operand NOM_CMP#
This operand provides the component, to be chosen between “DX”, “DY” and “DZ”, giving the direction of the seismic load.
A load is calculated for only one direction at a time. In the case of simultaneous stresses in several directions, it is then necessary to create as many different loads with the option TYPE_RESU =” CHARGE “of CALC_MISS.
7.6. Operand GROUP_NO_AFFE#
This operand provides the list of node groups where the seismic load is imposed. These nodes can be real, for example the central node of a foundation linked by a LIAISON_SOLIDE relationship, or fictitious corresponding to modal coordinates linked to the physical coordinates of the dynamic interface of the soil macro-element by a LIAISON_INTERF relationship.
7.7. Operand ISSF#
This operand indicates whether or not we have a fluid domain.
7.8. Operand VARI#
This operand allows you to activate or not the spatial variability functionalities as in the DYNA_ISS_VARI operator.
7.9. Operand UNITE_RESU_IMPE#
Allows you to define the logical unit of the generated file which will contain the frequency impedances calculated with the option TYPE_RESU =” FICHIER “of CALC_MISS.
7.10. Keyword INTERF#
7.10.1. Operand MODE_INTERF#
♦ MODE_INTERF =/'TOUT',
/”CORP_RIGI” /”QUELCONQUE”
This operand makes it possible to characterize the type of interface modes of the model. Three types of interface modes are possible: if we choose a model based on the six rigid body modes, we must enter “CORP_RIGI”, if we work with all the interface modes (finite element unit modes), we enter “TOUT”. For all the other foundation cases (pressed geometry, any representation modes for flexible foundations, case ISSF =” OUI “), enter” QUELCONQUE “.
7.10.2. Operand GROUP_NO_INTERF#
♦ GROUP_NO_INTERF = gr_inter
With this keyword, we define the group of nodes based on the surface meshes that make up the soil-structure interface.
7.11. Keyword MATR_COHE#
7.11.1. Operands VITE_ONDE and PARA_ALPHA#
♦ TYPE = model
You can choose between the coherence function of Mita & Luco (MITA_LUCO) and that of Abrahamson for hard floors (ABRAHAMSON). If we choose MITA_LUCO, then we can enter:
◊ VITE_ONDE = :math:`{c}_{\mathrm{app}}`
◊ PARA_ALPHA = :math:`\alpha`
These are the parameters of the Luco and Wong coherence function (pure incoherence without the effect of wave passage):
\(\mathrm{\gamma }(d)=\text{exp}[-(\mathrm{\alpha }\mathrm{.}f\mathrm{.}\frac{d}{{c}_{\text{app}}}{)}^{2}]\)
where*d* designates the distance between two points i and j on the foundation, \(f\) is the frequency and \({c}_{\mathrm{app}}\) is the apparent surface propagation speed of the SH wave (for example \(200\mathrm{-}\mathrm{600m}\mathrm{/}s\)). Parameter \(\alpha\) is generally taken to be equal to 0.5 (default). The default value for VITE_ONDE is 600.
7.12. Keyword MATR_GENE#
7.12.1. Operands BASE, NUME_DDL_GENE#
♦ BASE = base
Name of the concept based on interface modes.
♦ NUME_DDL_GENE = number
Name of the concept: generalized numbering based on the previous modal base. Generally with full storage
7.13. Operand PRECISION#
◊ PRECISION = prec
By default, this parameter is taken equal to 0.999.
To calculate the seismic forces with spatial variability of the incident field, the spectral decomposition of the coherence matrix \([{\mathrm{\gamma }}_{\mathit{ij}}]\), \(i=\mathrm{1...},M\) is carried out. The parameter prec gives the portion of the « energy » of the matrix that is conserved by retaining only a reduced number of eigenvectors. If we designate by \(K\ll M\) the number of eigenvalues retained (we retain the \(K\) largest eigenvalues), we have
\(\text{prec}=\frac{\sum _{i=1}^{K}{\mathrm{\lambda }}_{i}^{2}}{\sum _{i=1}^{M}{\mathrm{\lambda }}_{i}^{2}}\)