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.
Accepté le :
Publié le :
@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] 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] Infinite elements, Int. J. Numer. Methods Biomed. Eng., Volume 11 (1977), pp. 53-64
[5] 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] 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 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] Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., Volume 31 (1977), pp. 629-651
[9] 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] The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987
[11] On the propagation of tremors over the surface of an elastic solid, Proc. R. Soc. Lond., Volume 72 (1903), pp. 128-130
[12] 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] CASTEM 2000, Manuel d'utilisation, CEA-LAMBS, Saclay, Paris, 1993 (Rapport CEA-LAMBS, No. 93/007)
[14] 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] Rheological interpretation of Rayleigh damping, J. Sound Vib., Volume 338 (1997), pp. 741-744
[16] 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] Dynamic Soil–Structure Interaction, Prentice-Hall, Englewood Cliffs, NJ, 1985
Cité par Sources :
Commentaires - Politique
Sijia Li; Michael Brun; Irini Djeran-Maigre; ...
C. R. Méca (2020)
Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems
Loïc Zuchowski; Michael Brun; Florent De Martin
C. R. Méca (2018)
A two level domain decomposition preconditioner based on local Dirichlet-to-Neumann maps
Frédéric Nataf; Hua Xiang; Victorita Dolean
C. R. Math (2010)