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Infinite elements in a poroelastodynamic FEM
Author(s) -
Nenning Mathias,
Schanz Martin
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010092
Subject(s) - biot number , poromechanics , finite element method , infinity , mathematical analysis , rayleigh wave , field (mathematics) , physics , semi infinite , domain (mathematical analysis) , wave propagation , geometry , mathematics , porous medium , mechanics , porosity , geology , optics , pure mathematics , geotechnical engineering , thermodynamics
Wave propagation phenomena in unbounded domains occur in many engineering applications, e.g., soil structure interactions. When simulating unbounded domains, infinite elements are a possible choice to describe the far field behavior, whereas the near field is described through conventional finite elements. Finite element formulations for porous materials in terms of Biot's theory [1] have been published, e.g., by Zienkiewicz [2]. For infinite elements, several approaches are described in [3,4]. Infinite elements are based on special shape functions to approximate the semi‐infinite geometry as well as the Sommerfeld radiation condition, i.e., the waves decay with distance and are not reflected at infinity. If there is only one wave traveling in the media, a formulation in time‐domain can be established. But in poroelastodynamics, there are three body waves and eventually also a Rayleigh wave. Unfortunately, the extension to more than one wave is not straight forward. Here, an infinite element is presented which can handle all wave types, as it is needed in poroelasticity. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)