Numerical methods for the dynamics of unbounded domains

Mesquita, Euclides; Pavanello, Renato

doi:10.1590/s0101-82052005000100001

Cited by 12 publications

(5 citation statements)

References 40 publications

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“…This disadvantage makes the FEM less efficient than the boundary element method (BEM) in dealing with fracture problems (Datas, 2020;Jing, 2003) The boundaries of the continuum are discretised only in the boundary element method (BEM), whereas the complete domain needs to be discretized in the FDM and FEM methods (Jing and Hudson, 2002;Manouchehrian et al, 2012). In addition, there is no artificial boundaries are required where the common problems in geomechanics are the extended medium to infinity, while the artificial boundaries are required in both FDM and FEM methods (Fahmy, 2021;Mesquita and Pavanello, 2005). BEMs are especially convenient to address the static continuum problems with small boundary to volume ratios, with stress and elastic behaviour or displacements implemented to the boundaries (Gao, 2003).…”

Section: Continuum Approachesmentioning

confidence: 99%

A critical review on coupled geomechanics and fluid flow in naturally fractured reservoirs

Hawez

Sanaee

Faisal

2021

Journal of Natural Gas Science and Engineering

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Section: Continuum Approachesmentioning

confidence: 99%

A critical review on coupled geomechanics and fluid flow in naturally fractured reservoirs

Hawez

Sanaee

Faisal

2021

Journal of Natural Gas Science and Engineering

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“…So many attempts have been made to include radiation damping into FEM schemes presenting finite meshes. Examples of these strategies are in the inclusion of "Infinite Elements", the development of Dirichlet to Newman (DtN) and of Perfectly Matched Layers (PML) schemes to model the unbounded, wave propagating domain (Mesquita and Pavanello, 2005;Zhang et al, 2019).…”

Section: Introductionmentioning

confidence: 99%

Coupling Modal Analysis with the BEM for the Transient Response of Bar Structures Interacting with Three-Dimensional Soil Profiles

Ferraz,

Pacheco,

Carrion

et al. 2023

Lat. Am. j. solids struct.

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This work investigates the transient response of bar structures interacting with three-dimensional soil profiles. The structures are modeled by the Finite Element Method (FEM) and the soil models are described by a three-dimensional Boundary Element Formulation (BEM) in the frequency domain. A classic modal analysis is performed on the structure in terms of the relative displacements with respect to the soil. The dynamic response of the structure is coupled to the soil response, aiming to obtain frequency response functions (FRFs) of the soil-structure system. A new set of modal parameters are extracted from the FRFs of the coupled system. These new parameters allow for the synthesis of a set of orthogonal differential equations in the time domain. These equations are integrated by a classical numerical scheme resulting in the transient response of the structure interacting with the supporting soil. It is shown that for soil profiles that present eigenfrequencies, the system modal basis must be expanded to properly include the soil dynamics. The cases of a structure interacting with a homogeneous half-space and with a horizontal layer over a rigid stratum are considered. The results presented for both soil models are consistent.

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“…To take full advantage of these properties the BEM must be formulated using an auxiliary state (a fundamental solution, a Green's function or similar state) that satisfies simultaneously the operator under analysis and the Sommerfeld radiation condition. An account of the main currently available strategies to perform the dynamic analysis of unbounded domains may be found in Mesquita and Pavanello [48].…”

Section: Introductionmentioning

confidence: 99%

Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

Mesquita

Antes

Thomazo

et al. 2012

Lat. Am. j. solids struct.

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This article analyzes the transient wave propagation phenomena that take place at 2D viscoelastic half-spaces subjected to spatially distributed surface loadings and to distinct temporal excitations. It starts with a fairly detailed review of the existing strategies to describe transient analysis for elastic and viscoelastic continua by means of the Boundary Element Method (BEM). The review explores the possibilities and limitations of the existing transient BEM procedures to describe dynamic analysis of unbounded viscoelastic domains. It proceeds to explain the strategy used by the authors of this article to synthesize numerically fundamental solutions or auxiliary states that allow an accurate analysis of transient wave propagation phenomena at the surface of viscoelastic half-spaces. In particular, segments with spatially constant and linear stress distributions over a halfspace surface are considered. The solution for the superposition of constant and discontinuous adjacent elements as well as linear and continuous stress distributions is addressed. The influence of the temporal excitation type and duration on the transient response is investigated. The present study is based on the numerical solution of stress boundary value problems of (visco)elastodynamics. In a first stage, the solution is obtained in the frequency domain. A numerical integration strategy allows the stationary solutions to be determined for very high frequencies. The transient solutions are obtained, in a second stage, by applying the Fast Fourier Transform (FFT) algorithm to the previously synthesized frequency domain solutions. Viscoelastic effects are taken into account by means of the elastic-viscoelastic correspondence principle. By analyzing the transient solution of the stress boundary value problems, it is possible to show that from every surface stress discontinuity three wave fronts are generated. (continued on next The displacement velocity of these wave fronts can be associated to compression, shear and Rayleigh waves. It is shown that the half-space transient displacement solutions present abrupt jumps or oscillations which can be correlated to the arrival of these wave fronts at the observation point. Such a detailed analysis connecting half-space transient responses to the wave propagation fronts in viscoelastic half-spaces have not been reported in the reviewed literature.

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Numerical methods for the dynamics of unbounded domains

Abstract: Mathematical subject classification: 78A40, 80M10, 80M15.

Cited by 12 publications

References 40 publications

A critical review on coupled geomechanics and fluid flow in naturally fractured reservoirs

A critical review on coupled geomechanics and fluid flow in naturally fractured reservoirs

Coupling Modal Analysis with the BEM for the Transient Response of Bar Structures Interacting with Three-Dimensional Soil Profiles

Transient wave propagation phenomena at visco-elastic half-spaces under distributed surface loadings

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