Showing papers on "Half-space published in 1989"
TL;DR: In this article, the propagator matrix method is used to solve the static deformation of a transversely isotropic and layered elastic half-space under the action of general surface loads.
115 citations
TL;DR: In this article, the static deformation problem of a transversely isotropic and layered half-space by general dislocation sources is solved in the Cartesian system and the cylindrical system of vector functions using multiplications of matrices.
72 citations
TL;DR: In this article, the force-displacement relationship associated with the vertical vibration of a circular rigid disk resting on a saturated layered half-space is derived using Biot's two-phased linear theory.
Abstract: The force-displacement relationship associated with the vertical vibration of a circular rigid disk resting on a saturated layered half-space is derived using Biot’s two-phased linear theory. The analysis relies on the use of integral transform techniques in conjunction with axisymmetric potential theory by means of which Green’s functions are derived. Using the latter, the determination of the force-displacement relationship of the disk is reduced to the evaluation of a stress function that satisfies a Fredholm integral equation of the second kind similar to that obtained in relative studies involving uniform or layered dry media. Plots of vertical stiffness and damping coefficients in terms of frequency and saturation depth-to-risk radius ratio are given. Comparisons are also presented with results from the corresponding dry case. Numerical results obtained from a representative range of parameters show that the effect due to the saturation on the impedence functions is generally not significant. Specifically, at low dimensionless frequencies (i.e., less than 3), this effect is practically negligible, while at higher dimensionless frequencies (i.e., between 3 and 6), the departure from the dry case was about 30%.
63 citations
TL;DR: In this article, a hybrid approach is used to obtain the dynamic response of rigid square foundations embedded in an elastic half-space, where the response of an embedded square foundation can be approximated by that of a cylindrical foundation with an equivalent circular base and the same embedment depth.
45 citations
TL;DR: In this paper, an indirect boundary integral equation (IBE) method was used to analyze the effect of plane harmonic waves by three-dimensional surface irregularities in a non-axisymmetric canyons.
41 citations
TL;DR: In this article, the elastic fields around a hemispherical inhomogeneity at the free surface of a semi-infinite elastic body were analyzed using Boussinesq's displacement potentials and the solution was expressed in terms of five sets of spherical harmonics.
Abstract: This paper analyses the elastic fields around a hemispherical inhomogeneity at the free surface of a semiinfinite elastic body. The loading is either all-around tension at infinity, perpendicular to the axis of symmetry of the inhomogeneity or uniform eigenstrains introduced in the inhomogeneity. The interface between the inclusion and the matrix assumes perfect bonding, shear-traction-free sliding or intermediate between them. A spring-type resistance mode) is used to investigate this intermediate stage. The method of Boussinesq's displacement potentials is used in the analysis and the solution is expressed in terms of five sets of spherical harmonics. Numerical calculations are performed to illustrate the results. It was found that the non-vanishing stress components at the free surface of the inclusion are constant for equal Poisson's ratios.
25 citations
TL;DR: In this paper, the authors considered the time-harmonic vertical vibratios of an elastic annular plate resting in smooth contact with a homogeneous isotropic viscoelastic half space.
Abstract: The time‐harmonic vertical vibratios of an elastic annular plate resting in smooth contact with a homogeneous isotropic viscoelastic half space is considered. The plate is subjected to a vertical distributed loading, or it may be excited by specified displacements or stress resultants applied along the plate edges. The response of the plate is goverried by classical thin‐plate theory and its vertical displacement is represented by an admissible function containing a set of generalized coordinates. A representation for contact stresses is obtained through the solution of a flexibility equation based on an exact displacement Green's function of the half space. The equation of motion of the plate in terms of generalized coordinates are established through the application of Lagrange's equation of motion. The plate edge boundary conditions are incorporated into the plate Lagrangian function as constraint terms through a set of Lagrange multipliers. Selected numerical results for displacement and contact stres...
25 citations
TL;DR: The dispersion relation for surface waves on the corrugated boundary (periodic in one direction and constant in the other) of an elastic half-space is derived using a modal approach, and the result is shown to be equivalent to that derived by the null-field approach as discussed by the authors.
Abstract: The dispersion relation for surface waves on the corrugated boundary (periodic in one direction and constant in the other) of an elastic half‐space is derived using a modal approach, and the result is shown to be equivalent to that derived by the null‐field approach. The dispersion relation is solved numerically for roots on all Riemann sheets for varying corrugation heights, frequencies, and angles of propagation. Many of the roots move on several sheets, and this leads to zero, one, or two roots residing on the physical sheet.
13 citations
13 citations
TL;DR: In this article, a method based on the theory of singular integral equations (SIE) is presented for treating analytically scattering by perfectly conducting infinitely long strips in the presence of a magnetically uniaxial half-space.
Abstract: A method based on the theory of singular integral equations (SIE) is presented for treating analytically scattering by perfectly conducting infinitely long strips in the presence of a magnetically uniaxial half-space. A uniform plane wave, polarized parallel to the strip axis, is incident from the isotropic region. As a prerequisite to this approach, the E-mode scalar Green's function of the structure is developed. Use of the reciprocity theorem then leads to a SIE for the current density induced on the scatterer's surface. The solution of the SIE is carried out in the case of a strip parallel or perpendicular to the interface, either located above or embedded in the anisotropic space. Numerical results for the induced current density and for the scattered far field in a variety of cases are presented in graphical form. >
13 citations
TL;DR: In this article, the authors compared ADINA with an exact solution obtained by the use of integral transforms, in the case of an elastic half-space loaded by a step of pressure applied uniformly over a circular area at the surface.
TL;DR: In this paper, the stability of materials with cracks where compressive loads are applied parallel to the crack planes is considered and critical loads are obtained for small and large distance between the cracks and compared with those for a half space with and without cracks.
TL;DR: In this article, the integral equation for the current induced on a thin, perfectly conducting strip of infinite length above a homogeneous conducting half-space is examined for an incident field with E parallel to the strip axis.
Abstract: The integral equation for the current induced on a thin, perfectly conducting strip of infinite length above a homogeneous conducting half-space is examined for an incident field with E parallel to the strip axis A closed form quasi-static solution is obtained for the case when the width and elevation of the strip are small compared to the skin depth (or wavelength for a lossless medium) in the lower region Results are presented which compare the quasi-static solution with a numerical solution of the exact integral equation
Journal Article•
TL;DR: In this paper, the generalized reflection-transmition coefficient matrix method for calculating synthetc se-ismograms is extended to deal with the static problems, from which a method to calculate the static displacement field of a stratified half space by dislocation source is developed.
Abstract: The generalized reflection-transmition coefficient matrix method for calculating synthetc se-ismograms is extended to deal with the static problems,from which a method to calculate the static displacement field of a stratified half space by dislocation source is developed.The advantages of the original reflection-transmition coefficient matrix method are retained.By comparing the numerical results with the analytical solutions,it is shown that this is an effective method for the investigation of the static deformation produced by seismic faulting process.From careful analysis we find there are both similarities and differences between the wave propagation and static problems.
TL;DR: The main result of as mentioned in this paper states that if m k is even, then every embedding of m k into R2m-k can be isotopically deformed into R 2m k-1, and specifies which embeddings of M into M k can be deformed in case m k k is odd.
Abstract: Let M be a closed, k-connected, m-dimensional PL submanifold of R2m-k-1 (1 < k < m 4). The main result of this paper states that if m k is even, then every embedding of M into R2m-k can be isotopically deformed into R2m-k-1 , and specifies which embeddings of M into R2m-k can be deformed into R2m-k -1 in case m k is odd.
TL;DR: In this paper, the flexural interaction of a rectangular thin elastic plate resting in smooth contact with an isotropic homogeneous elastic half space is analyzed by using constraint variational schemes.
TL;DR: In this paper, a mode III loaded Griffith-type strip crack situated parallel to the free-surface of a semi-infinite isotropic elastic solid is considered and a singular integral equation satisfied by the proposed density function is derived, and then solved in closed-form.
TL;DR: In this article, a distorted-wave Born approximation is introduced to calculate the space-time acoustic wave motion generated by an impulsive point source in a horizontally layered configuration, where the source and the receiver are located in the upper half-space.
Abstract: A new approximate method to calculate the space-time acoustic wave motion generated by an impulsive point source in a horizontally layered configuration is presented. The configuration consists of a stack of fluid layers between two acoustic half-spaces where the source and the receiver are located in the upper half-space. A distorted-wave Born approximation is introduced; the important feature of the method is the assumption of a background medium with vertical varying root-mean-square acoustic wave speed. A closed-form expression for the scattered field in space and time as a function of the contrast parameters is deduced. The result agrees closely with rigorously calculated synthetic seismograms. In the inverse scheme the wave speed and mass density can be reconstructed within a single trace. Results of the inversion scheme applied to synthetic data are shown.
TL;DR: In this article, an asymmetric steady-state structure-media interaction due to obliquely incident body waves is investigated via a version of the global local finite element method, which involves full displacement and traction continuity along the boundary between the local and the exterior regions and satisfaction of the traction-free requirement on the surface of the half-space beyond the discretized region by virtue of a sequence of integral constraints of the nonzero weighted surface tractions of the spherical harmonics.
Abstract: Asymmetric steady-state structure-media interaction due to obliquely incident body waves is investigated via a version of the global local finite element method. In the present version, a local region that houses an axisymmetric structure is modelled by conventional finite elements, while the behaviour in the remaining portion of the homogeneous semi-infinite medium is presented by the spherical harmonics that are the eigensolutions of the entire space problem. The solution scheme involves (1) full displacement and traction continuity along the boundary between the local and the exterior regions and (2) satisfaction of the traction-free requirement on the surface of the half-space beyond the discretized region by virtue of a sequence of integral constraints of the non-zero weighted surface tractions of the spherical harmonics. The numerical results presented are for a perfectly bonded rigid circular foundation resting on the surface of the half-space and subjected to obliquely incident body waves. Dependence of the displacement response of the footing upon incident angles and dimensionless wave numbers is thoroughly studied.
01 Jan 1989
TL;DR: In this article, the closed form expressions for the stresses caused by a two-dimensional shear line load acting on the boundary of a semi-infinite medium consisting of a homogeneous elastic layer lying over a homogenous elastic half-space are derived.
Abstract: The closed form expressions for the stresses caused by a two-dimensional shear line load acting on the boundary of a semi-infinite medium consisting of a homogeneous elastic layer lying over a homogeneous elastic half-space are first derived. The correspondence principle of viscoelasticity is then used to obtain the quasi-static response when the elastic half-space is replaced by a Maxwell viscoelastic half-space. Numerical calculations performed indicate that the quasi-static stresses differ significantly from the corresponding static stresses when the medium is purely elastic.
TL;DR: The dislocation layer method combined with a technique of images is used to study a mode III loaded Griffith-type elastic strip crack situated parallel to the free-surface of a semi-infinite orthotropic crystal as discussed by the authors.
Abstract: The dislocation layer method combined with a technique of images is used to study a mode III loaded Griffith-type elastic strip crack situated parallel to the free-surface of a semi-infinite orthotropic crystal. The density function of the proposed distribution of dislocations is shown to satisfy a complex singular integral equation. Its closed-form solution provides a compact expression for an appropriate combination of the resulting stress field components. Some representative numerical results are presented in tabular form and discussed.
TL;DR: In this article, the scattering of transient elastodynamic waves by a semi-infinite void crack in an isotropic, perfectly elastic half-space is investigated theoretically, and closed-form analytic expressions for the wave quantities are obtained through the application of the Wiener-Hopf technique and the Cagniard-de Hoop technique; they hold in a finite time window.
Abstract: The scattering of transient elastodynamic waves by a semi-infinite void crack in an isotropic, perfectly elastic half-space is investigated theoretically. Closed-form analytic expressions for the wave quantities are obtained through the application of the Wiener-Hopf technique and the Cagniard-de Hoop technique; they hold in a finite time window. The scheme presented is well suited for a first-arrival analysis of the wave field.
Journal Article•
TL;DR: In this paper, a propagator matrix method is used in the system of cylindrical vector functions to solve the problem of the static deformation of a transversely isotropic and layered half-space by internal point dislocation sources.
Abstract: The propagator matrix method is used in the system of cylindrical vector functions to solve the problem of the static deformation of a transversely isotropic and layered half-space by internal point dislocation sources. The source functions in transversely isotropic medium are obtained for the six elementary displacement dislocations by the use of body force equivalents. The explicit integrand expressions for surface displacements are given for an arbitrary shear dislocation source within the layered medium, which can be calculated to investigate the effects of earth layering, and especially transverse isotropy on earthquake displacement, strain and tilt fields.
01 Jan 1989
TL;DR: In this article, the problem of a rectangular footing or a strip footing on a nonhomogeneous elastic half space is studied and the necessary conditions for a footing to be considered rigid, both rigid and flexible footings have been studied.
Abstract: The problem of a rectangular footing or a strip footing on a nonhomogeneous elastic half space is studied in this paper. The medium is assumed to be isotropic with a variable shear modulus G(z) = G 0 + mz and a constant Poisson's ratio equal to 1/3. An important feature of this model is that either the Winkler foundation or the elastic homogeneous half space can be made special cases by letting G 0 or m equal zero, respectively. In order to investigate the necessary conditions for a footing to be considered rigid, both rigid and flexible footings have been studied. Numerical results are presented to illustrate the effects of various parameters over the contact pressure and deflection.
TL;DR: The theory of generalized ray integrals is applied to analyzing transient P- and SV-waves subjected to multiple reflection and refraction when propagating in a dipping layer from a line source to a receiving point fixed in space as discussed by the authors.
Abstract: The theory of generalized ray integrals is applied to analyzing transient P- and SV-waves subjected to multiple reflection and refraction when propagating in a dipping layer from a line source to a receiving point fixed in space Ray integrals are sorted by arrival times and their time signatures are presented
TL;DR: The generalized ray integrals for the propagation of spherical acoustic waves from a point source to a (fixed) receiving point, following various paths of reflection and refraction are derived in this article.
Abstract: The generalized ray integrals for the propagation of spherical acoustic waves from a point source to a (fixed) receiving point, following various paths of reflection and refraction are derived The phase functions in the Weyl-Sommerfeld representation are constructively developed in terms of the apparent local slowness in two coordinate systems, one for each surface Inversion of the Laplace-integrals requires the simultaneous transformation of time into two planes of complex slowness to render a pair of finite integrals for numerical evaluation
TL;DR: In this article, an analytic solution is constructed for the refraction of a wave having the shape of a step of finite length in both the active plastic loading domain and in the unloading zone.
TL;DR: In this paper, the vertical displacement due to a vertical point excitation with non-dimensional frequency changing is studied. But the solutions are derived by a transfer matrix method using a vector-matrix which is obtained by double Fourier transformation.
Abstract: This paper deals with dynamic displacement solutions of a fluid-saturated poroelastic half-space due to a vertical point excitation in the interior of the medium. The solutions are derived by a transfer matrix method using a vector-matrix which is obtained by double Fourier transformation. As numerical examples, this paper shows results of the vertical displacement due to a vertical point excitation with nondimensional frequency changing.
TL;DR: In this paper, the response of an elastic anisotropic half space to an electric excitation by a metallic interdigital transducer is studied for Y-cut quartz crystals with transducers on both sides of the plate.
Abstract: We study the response of an elastic anisotropic half space to an electric excitation by a metallic interdigital transducer. The Fourier integral for the mechanical displacement is first computed at the geometrical approximation : waves inside and near the boundary are studied for singly rotated quartz crystal cuts. This ray approximation fails when the dispersion curve of any propagation mode exhibits an inflexion point. Caustics formation is demonstrated and the field on both sides of the caustic is computed by means of the Airy integral. The theoretical analysis is illustrated by new experiments performed on Y-cut quartz crystals with transducers on both sides of the plate.