Comptes Rendus
Multi-directional and multi-time step absorbing layer for unbounded domain
Comptes Rendus. Mécanique, Volume 342 (2014) no. 9, pp. 539-557.

Variant techniques are proposed for reproducing the elastic wave propagation in an unbounded medium such as the infinite elements, the absorbing boundary conditions or the perfect matched layers. Here, a simplified approach is adopted by considering absorbing layers characterized by the viscous Rayleigh matrix as studied by Semblat et al. [16] and Rajagopal et al. [14]. Here, further improvements to this procedure are provided. First, we start by establishing the strong form for the elastic wave propagation in a medium characterized by the Rayleigh matrix. This strong form will be used for deriving optimal conditions for damping out in the most efficient way the incident waves while minimizing the spurious reflected waves at the interface between the domain of interest and the Rayleigh damping layer. A procedure for designing the absorbing layer is proposed by targeting a performance criterion expressed in terms of logarithmic decrement of the wave amplitude in the layer thickness. Second, the GC subdomain coupling method, proposed by Combescure and Gravouil [9], is introduced for enabling the choice of any Newmark time integration schemes associated with different time steps depending on subdomains. When wave propagation is predicted by an explicit time integrator, the subdomain strategy is of great interest because it enables a different time integrator for the absorbing layer to be adopted. An external coupling software, based on the GC method, is used to carry out multi=time step explicit/implicit co-computations, making interact in time an explicit FE code (Europlexus) for the domain of interest, with an implicit FE code (Cast3m) handling the absorbing boundary layers. The efficiency of the approach is shown in 1D and 2D elastic wave propagation problems.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2014.05.007
Mots clés : Unbounded medium, Absorbing layer, Subdomain coupling, Heterogeneous time integrators, Multi time steps

Eliass Zafati 1 ; Michaël Brun 1 ; Irini Djeran-Maigre 1 ; Florent Prunier 1

1 Université de Lyon, INSA-Lyon, LGCIE, 34, rue des Arts, 69621 Villeurbanne cedex, France
@article{CRMECA_2014__342_9_539_0,
     author = {Eliass Zafati and Micha\"el Brun and Irini Djeran-Maigre and Florent Prunier},
     title = {Multi-directional and multi-time step absorbing layer for unbounded domain},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {539--557},
     publisher = {Elsevier},
     volume = {342},
     number = {9},
     year = {2014},
     doi = {10.1016/j.crme.2014.05.007},
     language = {en},
}
TY  - JOUR
AU  - Eliass Zafati
AU  - Michaël Brun
AU  - Irini Djeran-Maigre
AU  - Florent Prunier
TI  - Multi-directional and multi-time step absorbing layer for unbounded domain
JO  - Comptes Rendus. Mécanique
PY  - 2014
SP  - 539
EP  - 557
VL  - 342
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crme.2014.05.007
LA  - en
ID  - CRMECA_2014__342_9_539_0
ER  - 
%0 Journal Article
%A Eliass Zafati
%A Michaël Brun
%A Irini Djeran-Maigre
%A Florent Prunier
%T Multi-directional and multi-time step absorbing layer for unbounded domain
%J Comptes Rendus. Mécanique
%D 2014
%P 539-557
%V 342
%N 9
%I Elsevier
%R 10.1016/j.crme.2014.05.007
%G en
%F CRMECA_2014__342_9_539_0
Eliass Zafati; Michaël Brun; Irini Djeran-Maigre; Florent Prunier. Multi-directional and multi-time step absorbing layer for unbounded domain. Comptes Rendus. Mécanique, Volume 342 (2014) no. 9, pp. 539-557. doi : 10.1016/j.crme.2014.05.007. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.05.007/

[1] Cast3m, Présentation et utilisation de Cast3m, 2011.

[2] Europlexus, User's manual, 2006.

[3] U. Basu; A. Chopra Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation, Int. J. Numer. Methods Biomed. Eng., Volume 192 (2003), pp. 1337-1375

[4] P. Bettess Infinite elements, Int. J. Numer. Methods Biomed. Eng., Volume 11 (1977), pp. 53-64

[5] M. Brun; A. Batti; A. Limam; A. Combescure Implicit/explicit multi-time step co-computations for predicting reinforced concrete structure response under earthquake loading, Soil Dyn. Earthq. Eng., Volume 33 (2012), pp. 19-37

[6] M. Brun; A. Batti; A. Combescure; A. Gravouil External coupling software based on macro- and micro-time scales for explicit/implicit multi-time-step co-computations in structural dynamics, Finite Elem. Anal. Des., Volume 86 (2014), pp. 101-119

[7] A. Combescure; A. Gravouil A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis, Comput. Methods Appl. Mech. Eng., Volume 191 (2002), pp. 1129-1157

[8] B. Enquist; A. Majda Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., Volume 31 (1977), pp. 629-651

[9] A. Gravouil; A. Combescure A multi-time-step explicit–implicit method for non-linear structural dynamics, Int. J. Numer. Methods Biomed. Eng., Volume 50 (2001), pp. 199-225

[10] T. Hughes The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987

[11] H. Lamb On the propagation of tremors over the surface of an elastic solid, Proc. R. Soc. Lond., Volume 72 (1903), pp. 128-130

[12] K. Meza-Fajardo; A. Papageorgiou A nonconvolutional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: stability analysis, Bull. Seismol. Soc. Am., Volume 98 (2008), pp. 1811-1836

[13] A. Millard CASTEM 2000, Manuel d'utilisation, CEA-LAMBS, Saclay, Paris, 1993 (Rapport CEA-LAMBS, No. 93/007)

[14] P. Rajagopal; M. Drozdz; E.A. Skelton; M.S. Lowe; R.V. Craster On the use of the absorbing layers to simulate the propagation of elastic waves in unbounded isotropic media using commercially available finite element packages, Nondestruct. Test. Eval. Int., Volume 51 (2012), pp. 30-40

[15] J.-F. Semblat Rheological interpretation of Rayleigh damping, J. Sound Vib., Volume 338 (1997), pp. 741-744

[16] J.-F. Semblat; L. Lenti; A. Gandomzadeh A simple multi-directional absorbing layer method to simulate elastic wave propagation in unbounded domains, Int. J. Numer. Methods Biomed. Eng., Volume 85 (2011), pp. 1543-1563

[17] J.P. Wolf Dynamic Soil–Structure Interaction, Prentice-Hall, Englewood Cliffs, NJ, 1985

Cité par Sources :

Commentaires - Politique