Browsing by Author "Godoy, Eduardo"

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    A Dirichlet-to-Neumann finite element method for axisymmetric elastostatics in a semi-infinite domain
    (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017) Godoy, Eduardo; Boccardo, Valeria; Duran, Mario
    The Dirichlet-to-Neumann finite element method (DtN FEM) has proven to be a powerful numerical approach to solve boundary-value problems formulated in exterior domains. However, its application to elastic semi-infinite domains, which frequently arise in geophysical applications, has been rather limited, mainly due to the lack of explicit closed-form expressions for the DtN map. In this paper, we present a DtN FEM procedure for boundary-value problems of elastostatics in semi-infinite domains with axisymmetry about the vertical axis. A semi-spherical artificial boundary is used to truncate the semi-infinite domain and to obtain a bounded computational domain, where a FEM scheme is employed. By using a semi-analytical procedure of solution in the unbounded residual domain lying outside the artificial boundary, the exact nonlocal boundary conditions provided by the DtN map are numerically approximated and efficiently coupled with the FEM scheme. Numerical results are provided to demonstrate the effectiveness and accuracy of the proposed method. (C) 2016 Elsevier Inc. All rights reserved.
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    Coastal erosion in central Chile: a new hazard?
    (2018) Martínez Reyes, Carolina del Pilar; Contreras-Lopez, Manuel; Winckler, Patricio; Hidalgo, Hector; Godoy, Eduardo; Agredano, Roberto
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    Computing Green's function of elasticity in a half-plane with impedance boundary condition
    (ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 2006) Duran, Mario; Godoy, Eduardo; Nedelec, Jean Claude
    This Note presents an effective and accurate method for numerical calculation of the Green's function G associated with the time harmonic elasticity system in a half-plane, where an impedance boundary condition is considered. The need to compute this function arises when studying wave propagation in underground mining and seismological engineering. To theoretically obtain this Green's function, we have drawn our inspiration from the paper by Duran et al. (2005), where the Green's function for the Helmholtz equation has been computed. The method consists in applying a partial Fourier transform, which allows an explicit calculation of the so-called spectral Green's function. In order to compute its inverse Fourier transform, we separate (G) over cap as a sum of two terms. The first is associated with the whole plane, whereas the second takes into account the half-plane and the boundary conditions. The first term corresponds to the Green's function of the well known time-harmonic elasticity system in R-2 (cf. J. Dompierre, Thesis). The second term is separated as a sum of three terms, where two of them contain singularities in the spectral variable (pseudo-poles and poles) and the other is regular and decreasing at infinity. The inverse Fourier transform of the singular terms are analytically computed, whereas the regular one is numerically obtained via an FFT algorithm. We present a numerical result. Moreover, we show that, under some conditions, a fourth additional slowness appears and which could produce a new surface wave. (c) 2006 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
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    Modeling and simulation of an acoustic well stimulation method
    (2018) Pérez Arancibia, Carlos Andrés; Godoy, Eduardo; Duran, Mario
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    On the existence of surface waves in an elastic half-space with impedance boundary conditions
    (ELSEVIER SCIENCE BV, 2012) Godoy, Eduardo; Duran, Mario; Nedelec, Jean Claude
    In this work, the problem of surface waves in an isotropic elastic half-space with impedance boundary conditions is investigated. It is assumed that the boundary is free of normal traction and the shear traction varies linearly with the tangential component of displacement multiplied by the frequency, where the impedance corresponds to the constant of proportionality. The standard traction-free boundary conditions are then retrieved for zero impedance. The secular equation for surface waves with impedance boundary conditions is derived in explicit form. The existence and uniqueness of the Rayleigh wave is properly established, and it is found that its velocity varies with the impedance. Moreover, we prove that an additional surface wave exists in a particular case, whose velocity lies between those of the longitudinal and the transverse waves. Numerical examples are presented to illustrate the obtained results. (C) 2012 Elsevier B.V. All rights reserved.
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    THEORETICAL ASPECTS AND NUMERICAL COMPUTATION OF THE TIME-HARMONIC GREEN'S FUNCTION FOR AN ISOTROPIC ELASTIC HALF-PLANE WITH AN IMPEDANCE BOUNDARY CONDITION
    (EDP SCIENCES S A, 2010) Duran, Mario; Godoy, Eduardo; Nedelec, Jean Claude
    This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Duran et al. (cf. [Numer. Math. 107 (2007) 295-314; IMA J. Appl. Math. 71 (2006) 853-876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important advantage because the obtention of explicit expressions for the surface waves. We show, in addition to the usual Rayleigh wave, another surface wave appearing in some special cases. Numerical results are given to illustrate that. This is an extended and detailed version of the previous article by Duran et al. [C. R. Acad. Sci. Paris, Ser. IIB 334 (2006) 725-731].