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Fundamental solutions in 3D elastodynamics for the BEM: a review (Q2420336)

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Language	Label	Description	Also known as
English	Fundamental solutions in 3D elastodynamics for the BEM: a review	scientific article

Statements

scholarly article

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Fundamental solutions in 3D elastodynamics for the BEM: a review (English)

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George D. Manolis

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Petia S. Dineva

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Engineering Analysis with Boundary Elements

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publication date

6 June 2019

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zbMATH Keywords

elastodynamics

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boundary elements

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fundamental solutions

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Green's functions

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1016/j.enganabound.2019.04.003

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Field due to a Point Source in an Inhomogeneous Elastic Medium

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A linear \(\theta\) time-marching algorithm in 3D BEM formulation for elastodynamics

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Fundamental solutions of a multi-layered transversely isotropic saturated half-space subjected to moving point forces and pore pressure

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A Laplace‐transform‐based three‐dimensional BEM for poroelasticity

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Runge-Kutta convolution quadrature for the boundary element method

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The thin-layer method in a cross-anisotropic 3D space

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Approximation of boundary element matrices

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A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems

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Green’s tensor and its potentials for inhomogeneous elastic media

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Theory of Elasticity and Consolidation for a Porous Anisotropic Solid

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Mechanics of Deformation and Acoustic Propagation in Porous Media

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Multi-Level Fast Multipole BEM for 3-D Elastodynamics

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Introduction to hierarchical matrices with applications.

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Incompressible porous media models by use of the theory of mixtures

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Compressible porous media models by use of the theory of mixtures

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Elastic waves in anisotropic media

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RAYLEIGH WAVES IN TRANSVERSELY ISOTROPIC MEDIA

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AN EIGENFUNCTION EXPANSION OF THE ELASTIC WAVE GREEN'S FUNCTION FOR ANISOTROPIC MEDIA

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THE SINGULARITY ON THE PLANE LIDS OF THE WAVE SURFACE OF ELASTIC MEDIA WITH CUBIC SYMMETRY

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LAMB'S PROBLEM FOR AN ANISOTROPIC HALF-SPACE

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Fundamental elastodynamic solutions for anisotropic media with ellipsoidal slowness surfaces

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Propagation of Elastic Pulses and Acoustic Emission in a Plate—Part 1: Theory

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A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain

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A Preconditioned 3-D Multi-Region Fast Multipole Solver for Seismic Wave Propagation in Complex Geometries

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Recent advances on the fast multipole accelerated boundary element method for 3D time-harmonic elastodynamics

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A new fast multipole formulation for the elastodynamic half-space Green's tensor

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Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics

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Dynamical Response of an Elastic Half-Space to Tangential Surface Loadings

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Transient boundary element formulation for linear poroelasticity

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Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. I: Two-dimensional solution

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Time domain fundamental solution to Biot's complete equations of dynamic poroelasticity. II: Three-dimensional solution

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Numerical evaluation of harmonic Green's functions for triclinic half-space with embedded sources—Part II: a 3D model

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Green's function for a transversely isotropic multi-layered half-space: an application of the precise integration method

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Green's function evaluation for three-dimensional exponentially graded elasticity

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A direct formulation and numerical solution of the general transient elastodynamic problem I

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A time-domain harmonic BEM implementation for non-homogeneous 3D solids

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Effects of Holistic Nursing Course

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A modification of cagniard’s method for solving seismic pulse problems

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Sub-surface crack in an inhomogeneous half-plane: wave scattering phenomena by BEM

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Elastic wave propagation in a class of cracked, functionally graded materials by BIEM

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Site effects due to wave path inhomogeneity by BEM

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An Integral Formulation for Dynamic Poroelasticity

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Boundary element approach for dynamic poroelastic problems

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Numerical evaluation of three-dimensional time-harmonic Green's functions for a nonisotropic full-space

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Three-dimensional time-harmonic Green's functions for a triclinic full-space using a symbolic computation system

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ON THE TORSIONAL IMPULSIVE LOADING OF AN ELASTIC HALF SPACE

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A fundamental solution for the transversely isotropic and nonhomogeneous media

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A complete solution of the wave equations for transversely isotropic media

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Green's functions of an exponentially graded transversely isotropic half-space

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Displacement field of a point force acting on the surface of an elastically anisotropic half-space

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The method of fundamental solutions for scattering and radiation problems.

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``Causal'' shape functions in the time domain boundary element method

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Convolution quadrature time-domain boundary element method for 2-D and 3-D elastodynamic analyses in general anisotropic elastic solids

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Time 2D fundamental solution for saturated porous media with incompressible fluid

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Two-dimensional transient thermo-hydro-mechanical fundamental solutions of multiphase porous media in frequency and time domains

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Direct boundary integral equations for elastodynamics in 3-D half-spaces

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Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics

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Elastodynamic Green's functions for a smoothly heterogeneous half-space

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On the analysis of wave motions in a multi-layered solid

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A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices

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Response of poroelastic halfspace to steady-state harmonic surface tractions

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Calderon's preconditioning for periodic fast multipole method for elastodynamics in 3D

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Green’s Functions for Axially Symmetric Elastic Waves in Unbounded Inhomogeneous Media Having Constant Velocity Gradients

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Integral equation methods in potential theory. I

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Dynamic response of a poroelastic half-space to horizontal buried loading.

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Time domain 3D fundamental solutions for saturated poroelastic media with incompressible constituents

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Revisiting displacement functions in three-dimensional elasticity of inhomogeneous media

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Thin‐layer method: Formulation in the time domain

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Fundamental Solutions in Elastodynamics

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Lamb's problem at its simplest

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Fundamental solutions of Biot's equations of dynamic poroelasticity

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Asymmetric wave propagation in a transversely isotropic half-space in displacement potentials

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Three-dimensional dynamic Green's functions for a multilayered transversely isotropic half-space

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Boundary-integral equation method for elastodynamic scattering by a compact inhomogeneity

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Dynamic Green's function for a three-dimensional concentrated load in the interior of a poroelastic layered half-space using a modified stiffness matrix method

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The multi-domain FMM-IBEM to model elastic wave scattering by three-dimensional inclusions in infinite domain

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The fast multi-pole indirect BEM for solving high-frequency seismic wave scattering by three-dimensional superficial irregularities

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Fundamental solution for a layered porous half space subject to a vertical point force or a point fluid source

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A 2.5-D dynamic model for a saturated porous medium. I: Green's function

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A 2.5-D dynamic model for a saturated porous medium. II: Boundary element method

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Convolution quadrature and discretized operational calculus. I

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Convolution quadrature and discretized operational calculus. II

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Uniform asymptotic expansions at a caustic

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Three-dimensional transient thermo-hydro-mechanical fundamental solutions of unsaturated soils

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Wave Propagation in Unsaturated Poroelastic Media: Boundary Integral Formulation and Three-dimensional Fundamental Solution

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Integral formulation and fundamental solutions of dynamic poroelasticity and thermoelasticity

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Green's function for the vector wave equation in a mildly heterogeneous continuum

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Wave scattering by cracks in inhomogeneous continua using BIEM

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Free-field dynamic response of an inhomogeneous half-space

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Dynamic fracture analysis of a smoothly inhomogeneous plane containing defects by BEM

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Seismic wave propagation in non-homogeneous elastic media by boundary elements

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Numerical behavior of time domain BEM for three-dimensional transient elastodynamic problems.

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On Green's function for a three–dimensional exponentially graded elastic solid

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Localized boundary-domain integral formulations for problems with variable coefficients

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The field and radiation impedance of mechanical radiators on the free surface of a semi-infinite isotropic solid

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Green functions for an incompressible linearly nonhomogeneous half-space

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Green functions for a compressible linearly non homogeneous half-space

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On the propagation of elastic waves in aeolotropic media I. General principles

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Three-dimensional BEM for scattering of elastic waves in general anisotropic media

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Direct 3d BEM for scattering of elastic waves in a homogeneous anisotropic half-space

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Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and poroelastic solids

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Radiation from a point source and scattering theory in a fluid-saturated porous solid

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Point Force Solution for an Infinite Transversely Isotropic Solid

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Dislocation in an infinite poroelastic medium

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A symmetric boundary integral approach to transient poroelastic analysis

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Three-dimensional Green's functions in anisotropic bimaterials

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Three-Dimensional Green’s Functions in an Anisotropic Half-Space With General Boundary Conditions

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Static Green's Functions in Anisotropic Media

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Three-dimensional BEM for transient elastodynamics based on the velocity reciprocal theorem

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Earthquakes site effects modeling by hybrid M-BIEM: the case study of Sofia, Bulgaria

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THE SEISMIC SURFACE PULSE

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THE SEISMIC BURIED PULSE

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Elastodynamic fundamental solutions for certain families of 2d inhomogeneous anisotropic domains: basic derivations

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Wave propagation in a restricted class of orthotropic inhomogeneous half-planes

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Generalization of Lamb’s problem to a class of inhomogeneous elastic halfspaces

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A time domain BEM for 3-D elastodynamic analysis using the \(B\)-spline fundamental solutions

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Rapid solution of integral equations of scattering theory in two dimensions

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Far field dynamic Green's functions for BEM in transversely isotropic solids

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Evaluation of the anisotropic Green's function and its derivatives

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Application of `operational quadrature methods' in time domain boundary element methods

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A new visco- and elastodynamic time domain boundary element formulation

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A boundary element formulation in time domain for viscoelastic solids

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Application of 3D time domain boundary element formulation to wave propagation in poroelastic solids

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A comparative study of Biot's theory and the linear theory of porous media for wave propagation

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Dynamic fundamental solutions for compressible and incompressible modeled poroelastic continua

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Mindlin's problem for an incompressible elastic half-space with an exponential variation in the linear elastic shear modulus

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FOURIER-TRANSFORM SOLUTION OF A BOUSSINESQ PROBLEM FOR A HEXAGONALLY AEOLOTROPIC ELASTIC HALF-SPACE

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The construction of some efficient preconditioners in the boundary element method

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THE SEISMOLOGICAL IMPLICATIONS OF AEOLOTROPY IN CONTINENTAL STRUCTURE

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Dislocations and Cracks in Anisotropic Elasticity

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Steady State Problems in Anisotropic Elasticity

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Elastic Waves in Anisotropic Media

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Green's function for two-and-a-half dimensional elastodynamic problems in a half-space

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Fundamental solutions for a fluid-saturated, transversely isotropic, poroelastic solid

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A fast BIEM for three-dimensional elastodynamics in time domain.

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Transmission of Elastic Waves through a Stratified Solid Medium

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A Reformation of the Equations of Anisotropic Poroelasticity

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Sextic formalism in anisotropic elasticity for almost non-semisimple matrix N

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Multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects

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Dispersion law of rayleigh-type waves in a compressible gibson half-space

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Asymptotic Green's function in homogeneous anisotropic viscoelastic media

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Green's functions for vertical point load on an elastic half-space with depth-degrading stiffness

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Fourier integral representation of the Green function for an anisotropic elastic half-space

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Transient fundamental solutions for a transversely isotropic elastic half space

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A new method to obtain 3-D Green's functions for anisotropic solids

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Three-dimensional time-harmonic elastodynamic Green <sup>’</sup> s functions for anisotropic solids

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Lamb's problem for solids of general anisotropy

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Wave propagation in an inhomogeneous cross-anisotropic medium

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The Stroh formalism for anisotropic materials that possess an almost extraordinary degenerate matrix \(\mathbf N\)

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A time domain integral formulation of dynamic poroelasticity

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A low frequency elastodynamic fast multipole boundary element method in three dimensions

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Self-similar problems in elastodynmics

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SH‐wave propagation in a continuously inhomogeneous half‐plane with free‐surface relief by BIEM

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Three-dimensional Green's functions of steady-state motion in anisotropic half-spaces and bimaterials

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Deconstructing plane anisotropic elasticity. II: Stroh's formalism sans frills.

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Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems in 3D

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Discussion on the time-harmonic elastodynamic half-space Green's function obtained by superposition

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Dynamic Green's functions for a poroelastic half-space

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3D dynamic Green's functions in a multilayered poroelastic half-space

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Frequency domain fundamental solutions for a poroelastic half-space

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A Method to Evaluate Three-Dimensional Time-Harmonic Elastodynamic Green’s Functions in Transversely Isotropic Media

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Identifiers

zbMATH Open document ID

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10.1016/j.enganabound.2019.04.003

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2420336

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