Comptes Rendus
A simple numerical absorbing layer method in elastodynamics
[Une méthode simple de couche absorbante pour les problèmes élastodynamiques]
Comptes Rendus. Mécanique, Volume 338 (2010) no. 1, pp. 24-32.

La simulation numérique de la propagation d'ondes élastiques en milieux infinis peut s'avérer délicate du fait des réflexions d'ondes parasites sur les frontières du modèle discrétisé. Plusieurs méthodes sophistiquées, telles que les frontières absorbantes, les éléments infinis ou les couches absorbantes (e.g. « Perfectly Matched Layers ») permettent une réduction importante des réflexions parasites. Dans cette Note, une méthode de couche absorbante simple et efficace est proposée dans le cadre de la méthode des éléments finis. Cette méthode s'appuie sur une formulation de l'amortissement dans la couche de type Rayleigh/Caughey et ses principes sont d'abord détaillés. L'efficacité de la méthode est alors démontrée grâce à des simulations unidimensionnelles en considérant un amortissement homogène ou variable dans la couche absorbante. Des modèles bidimensionnels permettent ensuite d'apprécier l'efficacité de la méthode de couche absorbante proposée pour différents types d'ondes (ondes de surface, ondes de volume) et des incidences variées (normale à rasante). La méthode s'avère ainsi efficace pour différents types d'ondes élastiques et pourrait être utilisée pour traiter divers problèmes élastodynamiques en milieux non bornés.

The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques, such as nonreflecting boundary conditions, infinite elements or absorbing layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this Note, a simple and efficient absorbing layer method is proposed in the framework of the Finite Element Method. This method considers Rayleigh/Caughey damping in the absorbing layer and its principle is presented first. The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types (surface waves, body waves) and incidences (normal to grazing). The method is shown to be efficient for different types of elastic waves and may thus be used for various elastodynamic problems in unbounded domains.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2009.12.004
Keywords: Waves, Continuum mechanics, Finite Element Method, Elastodynamics
Mot clés : Ondes, Milieux continus, Méthode des éléments finis, Élastodynamiques

Jean-François Semblat 1 ; Ali Gandomzadeh 1 ; Luca Lenti 1

1 Université Paris-Est, LCPC, 58 boulevard Lefebvre, 75015 Paris, France
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Jean-François Semblat; Ali Gandomzadeh; Luca Lenti. A simple numerical absorbing layer method in elastodynamics. Comptes Rendus. Mécanique, Volume 338 (2010) no. 1, pp. 24-32. doi : 10.1016/j.crme.2009.12.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.12.004/

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