An infinite element is presented to treat wave propagation problems in unbounded saturated porous media. The porous media is modeled by Biot's theory. Conventional finite elements are used to model the near field, whereas infinite elements are used to represent the behavior of the far field. They are constructed in such a way that the Sommerfeld radiation condition is fulfilled, i.e. the waves decay with distance and are not reflected at infinity. To provide the wave information the infinite elements are formulated in Laplace domain. The time domain solution is obtained by using the convolution quadrature method as the inverse Laplace transformation. The temporal behavior of the near field is calculated using standard time integration schemes, e.g. the Newmark method. Finally, the near and far field are combined using a substructure technique for any time step. The accuracy as well as the necessity of the proposed infinite elements, when unbounded domains are considered, is demonstrated by different examples. Copyright © 2010 John Wiley & Sons, Ltd.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.