Showing papers on "Half-space published in 2005"
TL;DR: In this article, the authors considered the problem of a half-space with a permeating substance in contact with the bounding plane in the context of the theory of generalized thermoelastic diffusion with one relaxation time.
255 citations
TL;DR: In this article, a transmission and reflection matrices (TRM) method for a layered porous half-space subject to a point force or a fluid point source is developed. But the authors focus on the point force and the point fluid source in both the frequency domain and the time domain.
Abstract: The focus of this contribution is to develop a transmission and reflection matrices (TRM) method for a layered porous half-space subject to a point force or a fluid point source. Applying the Hankel and the Fourier transformation, the general solutions for the displacements, stresses and pore pressure are derived from the potentials for the solid skeleton and the pore fluid as well as the governing equations of Biot’s theory. The transmission and reflection matrices (TRM) for each interface are obtained by using the general solutions as well as the continuity conditions at the interface. The TRM method for the layered porous medium is developed on the basis of the transmission and reflection matrices (TRM) and the boundary conditions as well as the source terms for the point force or the fluid point source. The fundamental solutions of the point force and the point fluid source in both the frequency domain and the time domain are obtained by using the proposed TRM method. Some numerical examples are given in the paper.
86 citations
TL;DR: In this article, a generalized thermo-viscoelastic plane wave model was proposed for a half-space whose surface is subjected to a thermal shock under the effect of rotation with one relaxation time.
Abstract: In this article, we propose a model of generalized thermo-viscoelastic plane waves for a half-space whose surface is subjected to a thermal shock under the effect of rotation with one relaxation time. The normal mode analysis is used to obtain the exact expressions for the considered variables. The resulting formulation is applied to two kinds of boundary conditions. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results predicted by the coupled theory and with the theory of generalized thermo-elasticity with one relaxation time in the absence of rotation.
69 citations
TL;DR: In this paper, the authors considered the non-axisymmetric three-dimensional problem of a penny-shaped crack with permeable electric conditions imposed on the crack surfaces, subjected to a pair of point normal forces applied symmetrically with respect to the crack plane.
Abstract: This paper considers the non-axisymmetric three-dimensional problem of a penny-shaped crack with permeable electric conditions imposed on the crack surfaces, subjected to a pair of point normal forces applied symmetrically with respect to the crack plane. The crack is embedded in an infinite transversely isotropic piezoelectric body with the crack face perpendicular to the axis of material symmetry. Applying the symmetry of the problem under consideration then leads to a mixed–mixed boundary value problem of a half-space, for which potential theory method is employed for the purpose of analysis. The cases of equal eigenvalues are also discussed. Although the treatment differs from that for an impermeable crack reported in literature, the resulting governing equation still has a familiar structure. For the case of a point force, exact expressions for the full-space electro-elastic field are derived in terms of elementary functions with explicit stress and electric displacement intensity factors presented. The exact solution for a uniform loading is also given.
38 citations
TL;DR: In this article, an exact solution to the problem of indentation with friction of a rigid cylinder into an elastic half-space is presented, and the corresponding boundary value problem is formulated in planar bipolar coordinates, and reduced to a singular integral equation with respect to the unknown normal stress in the slip zones.
Abstract: An exact solution to the problem of indentation with friction of a rigid cylinder into an elastic half-space is presented. The corresponding boundary-value problem is formulated in planar bipolar coordinates, and reduced to a singular integral equation with respect to the unknown normal stress in the slip zones. An exact analytical solution of this equation is constructed using the Wiener-Hopf technique, which allowed for a detailed analysis of the contact stresses, strain, displacement, and relative slip zone sizes. Also, a simple analytical solution is furnished in the limiting case of full stick between the cylinder and half-space.
36 citations
TL;DR: In this paper, the steady-state response of displacements and stresses in a half-space subjected to a point sink is modeled as a multilayered poroelastic medium.
Abstract: This paper presents analytical solutions for the steady-state response of displacements and stresses in a half-space subjected to a point sink. The half-space is modeled as a multilayered poroelastic medium with both the permeability and the poroelasticity being cross anisotropic. The basic governing equations are presented in dimensionless style, and the state vector method together with the Hankel transform technique is adopted to solve them and obtain a transfer matrix in a clearly arranged way. Forward and backward transfer matrix techniques are utilized in the analytical formulation of solutions for a multilayered half space. Numerical results are presented to conduct some parametric studies and illustrate the influence of layering and material inhomogeneity on the settlement of the soils. The numerical evaluations of the solutions in the multilayered porous media can be easily achieved with high efficiency and accuracy.
35 citations
TL;DR: In this article, a two-dimensional coupled problem in electromagneto-thermoelasticity for a thermally and electrically conducting half-space solid whose surface is subjected to a thermal shock is considered.
Abstract: A two‐dimensional coupled problem in electromagneto‐thermoelasticity for a thermally and electrically conducting half‐space solid whose surface is subjected to a thermal shock is considered. The problem is in the context of the Lord and Shulman’s generalized thermoelasticity with one relaxation time. There acts an initial magnetic field parallel to the plane boundary of the half‐space. The medium deformed because of thermal shock and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the medium. The Maxwell’s equations are formulated and the electromagneto‐thermoelastic coupled governing equations are established. The normal mode analysis is used to obtain the exact expressions for the considered variables. The distributions of the considered variables are represented graphically. From the distributions, it can be found the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier’s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. Comparisons are made with the results predicted by the coupled theory for two values of time.
29 citations
TL;DR: Theoretically light backscattered by tissues using the radiative transport equation is studied using the theory of Green's functions to solve the one-dimensional problem in which a plane wave is incident normally on the top layer and is the only source of light.
Abstract: We study theoretically light backscattered by tissues using the radiative transport equation. In particular we consider a two-layered medium in which a finite slab is situated on top of a half space. We solve the one-dimensional problem in which a plane wave is incident normally on the top layer and is the only source of light. The solution to this problem is obtained formally by imposing continuity between the solutions for the upper and lower layers. However, we are interested solely in probing the top layer. Assuming that the optical properties in the lower layer are known, we remove it from the problem yielding a finite slab problem by prescribing an alternate boundary condition. This boundary condition is derived using the theory of Green's functions and is exact. Hence, one needs only to solve the transport equation in a finite slab using this alternate boundary condition. We derive an asymptotic solution for the case when the slab is optically thin. We extend these results to the three-dimensional problem using Fourier transforms. These results are validated by comparisons with numerical solutions for the entire two-layered problem.
29 citations
TL;DR: In this article, an analytic solution of two-dimensional scattering and diffraction of plane SV waves by circular cylindrical canyons in a half space of saturated porous media is presented.
27 citations
TL;DR: In this paper, the Lamb's problem for the half-space covered with the pre-stretching layer is studied within the framework of the piecewise homogeneous body model, where the three-dimensional linearized theory of elastic waves in initially stressed bodies is used.
26 citations
TL;DR: In this article, the steady-state displacements and stresses in elastic half-space generated by a surface point load moving with constant speed parallel to the free surface of the half space are analyzed.
TL;DR: In this paper, a class of hyperbolic stochastic partial di®erential equations in Euclidean space is studied, including the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane.
Abstract: We study a class of hyperbolic stochastic partial di®erential equations in Euclidean space, that includes the wave equation and the telegraph equation, driven by Gaussian noise concentrated on a hyperplane. The noise is assumed to be white in time but spatially homogeneous within the hyperplane. Two natural notions of solutions are function-valued solutions and random field solutions. For the linear form of the equations, we identify the necessary and sufficient condition on the spectral measure of the spatial covariance for existence of each type of solution, and it turns out that the conditions di®er. In spatial dimensions 2 and 3, under the condition for existence of a random field solution to the linear form of the equation, we prove existence and uniqueness of a random field solution to non-linear forms of the equation.
TL;DR: In this article, a well-grained representation of a family of partial orders on a given finite set X is presented, where relations in B are represented by regions and cells of a hyperplane arrangement arising from numerical representations of the partial orders in B.
Journal Article•
TL;DR: In this article, the Laplace transform is used to solve the problem of distribution of thermal stresses and temperature in a generalized thermoelastic half-space subjected to sudden heating with constant temperature on the bounding plane under the action of a body force.
Abstract: In this work, we consider a one-dimensional problem of distribution of thermal stresses and temperature in a generalized thermoelastic half-space subjected to sudden heating with constant temperature on the bounding plane under the action of a body force. The Laplace transform technique is used to solve the problem. The inverse transforms are obtained in an approximate manner using asymptotic expansions valid for short times. The temperature, displacement, and stress are obtained and represented graphically.
TL;DR: In this paper, the propagation of ultrasonic waves in a thick plate with a cladding is investigated in the two-dimensional case, where the surfaces of the plate are traction-free except where an ultrasonic probe is attached and emits waves into the plate.
TL;DR: In this article, the authors studied non-negative singular infinity-harmonic functions in the half-space and showed that the blowup rate is of the order of O( √ n −1/n log n).
Abstract: In this work we study non-negative singular infinity-harmonic functions in the half-space. We assume that solutions blow-up at the origin while vanishing at infinity and on a hyperplane. We show that blow-up rate is of the order .
TL;DR: A piezoelectric strip of finite width and thickness is placed on top of an isotropic elastic half space and a time harmonic voltage is thus applied across it, and the problem is solved exactly by Fourier series expansions.
Abstract: A piezoelectric strip of finite width and thickness is placed on top of an isotropic elastic half space. It operates in actuator mode, and a time harmonic voltage is thus applied across it. The piezoelectric material is of type 6 mm oriented so that a two-dimensional (2-D) in-plane (P-SV) problem results. By Fourier series expansions, the problem is solved exactly, and this result is compared to the case when the piezoelectric strip is replaced by an effective boundary condition, which is derived by series expansions in the thickness coordinate in the piezoelectric strip. At low frequencies, the results agree very well, and this corresponds to the situation often met in practice. In general, the effective boundary condition should be much easier to apply, for example when a finite element method (FEM) program is used.
TL;DR: In this paper, an analytical model for the indentation of a smooth cylinder is presented, which takes into account the elastic properties of the cylinders and the elastic then elastoplastic behaviour of the coating.
13 Apr 2005
TL;DR: An algorithm is provided that solves the digital hyperplane recognition problem by reducing it to an integer linear programming problem of fixed dimension within an algebraic model of computation.
Abstract: We consider the following problem. Given a set of points M={p1,p2...pm}⊆ℝn, decide whether M is a portion of a digital hyperplane and, if so, determine its analytical representation. In our setting p1,p2...pm may be arbitrary points (possibly, with rational and/or irrational coefficients) and the dimension n may be any arbitrary fixed integer. We provide an algorithm that solves this digital hyperplane recognition problem by reducing it to an integer linear programming problem of fixed dimension within an algebraic model of computation. The algorithm performs O(mlogD) arithmetic operations, where D is a bound on the norm of the domain elements.
TL;DR: In this paper, the authors provided one-dimensional numerical simulation results of the propagation of plane electromagnetic (EM) pulse onto a dielectric half-space that is constantly moving, and the governing equations are numerically solved using characteristic-based method.
Abstract: This paper provides one-dimensional numerical simulation results of the propagation of plane electromagnetic (EM) pulse onto a dielectric half-space that is constantly moving. The governing equations are numerically solved using characteristic-based method. The medium employed in the one-dimensional model is assumed to be homogeneous, isotropic, lossless, and linear, and moving with a constant velocity of one tenth of the light speed. The velocities of EM pulses inside moving media are investigated by comparing with the analytical values predicted by the theory of relativity. The effects of the moving dielectrics on the reflected and transmitted electric fields are examined by comparing them side-by-side. Also shown are the corresponding spectra.
TL;DR: In this article, the authors adopt two strategies based respectively on the exact electromagnetic solution to the problem, and a more phenomenological approach based on coupled-wave analysis, and find good agreement between the two methods.
Abstract: We analyse electromagnetic radiation normally incident to a structurally chiral half-space. We adopt two strategies based respectively on the exact electromagnetic solution to the problem, and a more phenomenological approach based on coupled-wave analysis. We find good agreement between the two methods.
Journal Article•
TL;DR: In this article, a double Fourier transform was introduced for the analysis of an elastic half space loaded with vertical force, and an integral representation for displacements of the half space was presented.
Abstract: The method of double Fourier transform was introduced for the analysis of an elastic half space loaded with vertical force,and an integral representation for displacements of an elastic half space was presented.The analytic solution of an elastic rectangular plate on an elastic half space was also given by combining the analytic solution of an elastic rectangular plate with four free edges.Some examples were analyzed and the results were compared with those from the literature which used other methods such as finite element method.The agreement was found to be satisfactory which proved the validity of the new method in solving the problem of a rectangular plate on an elastic half space with four free edges.This new method would be feasible in practical applications.
Journal Article•
TL;DR: In this article, an approach is proposed to further develop the said aspects of the theory of rigid-plastic bodies subject to fracture in the case of plane axisymmetric strain.
Abstract: The theory of ideal rigid-plastic bodies is one of the most elaborated branches of solid mechanics. Within the framework of that theory, the main attention has been given to problems of the limiting equilibrium, i.e., the initiation of plastic flow. Only few solutions have been obtained for problems that take into account the geometry of the body and pertain to the plastic flow. In this connection, we mention the following problems: a wedge indented half-space, a flat punch crushing a wedge [1-3]; uniaxial tension of a plane sample [4] or a cylindrical sample [5]; tension of a strip with V-shaped notches [6]. In [7-9], on the basis of these solutions, a class of solutions was obtained for contact problems for bodies of an arbitrary shape; these solutions take into account changes in the geometry of the free surface. When solving such problems, strains were evaluated visually by observing distortions of a rectangular mesh. A more precise description of the deformation process requires the utilization of tensor characteristics as the measure of strain (distortion tensor, Almansi strain tensor, etc.). Solutions that take into account the geometry of the body are especially needed for calculating strains near the surfaces of displacement rate discontinuities or other singularities of the plastic region. Another issue of the theory of rigid-plastic bodies is the nonuniqueness of the position and the shape of the plastic region, and therefore, the nonuniqueness of the displacement rate field that determines the geometrical changes of the body. For practical utilization of theoretical solutions, one requires a criterion for choosing a particular plastic flow and one has to formulate the conditions that determine the change of the plastic region. Fracture of rigid-plastic bodies was studied in [10, 11]. In this paper, an approach is proposed to further development of the said aspects of the theory of rigid-plastic bodies subject to fracture in the case of plane axisymmetric strain.
TL;DR: In this article, the authors studied the influence of the depth of location of the circular crack on the stress intensity factor for a constant temperature (or heat flow) specified on the crack surfaces.
Abstract: The problem of stationary thermal conductivity and thermoelasticity is solved by the method of boundary integral equations for a semiinfinite body containing a circular crack perpendicular to its edge provided that temperature (or a heat flow is specified) on the crack surfaces. The boundary of the body is unloaded and either is thermally insulated or its temperature is equal to zero. We study the influence of the depth of location of the circular crack on the stress intensity factor for a constant temperature (or heat flow) specified on the crack surfaces. Under thermal loading (unlike the case of constant force loading), the stress intensity factors attain their maximum values on the side of the half space opposite to its boundary.
TL;DR: In this article, an analytic solution of three-dimensional scattering of incident plane SV waves by hemispherical canyons in a fluid saturated porous media half space is derived using the Fourier-Bessel series expansion technique.
Abstract: On the basis of the Biot dynamic theory, an analytic solution of three-dimensional scattering of incident plane SV waves by hemispherical canyons in a fluid saturated porous media half space is derived. The Fourier-Bessel series expansion technique is used to get the analytic solution for the first time. The results of surface displacement amplitudes are presented, the effects of frequency and angle of incident waves on the surface displacement amplitudes are discussed. These results are compared with those from the same situation but with an elastic one-phase medium. We conclude that (1) there is a significant difference between the previous single-phase model and the present two-phase model; (2) the normalized displacements on the free surface of alluvial valley are mainly dependent on the incident wave angles, the dimensionless frequency of the incident SV-waves; (3) with the increases of the incident angle, frequency, the displacements become more complicated; and the amplification of the displacement on the free surface of alluvial valley is more prominent than that modeled by single-phase.
DOI•
21 Feb 2005
TL;DR: In this paper, the time domain formulation of the problem is based on simplified reflection and transmission coefficient expressions arising from the modified image theory, and the impulse response of the finitely conducting half-space the reflected and transmitted fields respectively, can be obtained by using a convolution operator.
Abstract: Transient behaviour of plane waves in the presence of a two media configuration is analysed in this work. The time domain formulation of the problem is based on simplified reflection and transmission coefficient expressions arising from the modified image theory. Knowing the impulse response of the finitely conducting half-space the reflected and transmitted fields respectively, can be obtained by using a convolution operator. Some illustrative numerical results for transient earth-reflected waves are presented.
Journal Article•
TL;DR: In this article, the authors considered the plane and axisymmetric contact problems for a three-layer elastic half-space, where the plane problem is reduced to a singular integral equation of the first kind, whose approximate solution is obtained by a modified Multhopp-Kalandiya collocation method.
Abstract: We consider the plane and axisymmetric contact problems for a three-layer elastic half-space. The plane problem is reduced to a singular integral equation of the first kind, whose approximate solution is obtained by a modified Multhopp-Kalandiya collocation method. The axisymmetric problem is reduced to a Fredholm integral equation of the second kind, whose approximate solution is obtained by a specially designed collocation method at the Legendre nodes. For these problems, examples of computation of typical integral characteristics are given.
TL;DR: In this article, the acoustic scattering by a submerged spherical rigid obstacle near an acoustically hard concave corner, which is insonified by plane waves at arbitrary angles of incidence, is studied.
Abstract: The acoustic scattering by a submerged spherical rigid obstacle near an acoustically hard concave corner, which is insonified by plane waves at arbitrary angles of incidence, is studied. The formulation utilizes the appropriate wave-harmonic field expansions and the classical method of images in combination with the translational addition theorems for spherical wave functions to develop a closed-form solution in form of infinite series. The analytical results are illustrated by numerical examples where the spherical object is located near the rigid boundary of a fluid-filled quarterspace and is insonified by plane waves at oblique angles of incidence. Subsequently, the basic acoustic field quantities such as the form function amplitude, the scattered far-field pressure, and the scattered acoustic intensity are evaluated for representative values of the parameters characterizing the system. The limiting case involving a spherical object submerged in an acoustic halfspace is considered and good agreement with a well-known solution is established.
25 Jul 2005
TL;DR: In this paper, the problem of determining the two different shape description of a perfectly conducting cylinder buried in a half-space by the genetic algorithm is investigated, where a cylinder of unknown shape is buried in one half space and scatters the field incident from another half space where the scattered field is measured.
Abstract: The problem of determining the two different shape description of a perfectly conducting cylinder buried in a half-space by the genetic algorithm is investigated. Assume that a cylinder of unknown shape is buried in one half-space and scatters the field incident from another half-space where the scattered field is measured. Based on the boundary condition and the measured scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulated into an optimization problem. As a result, the shape of the scatterer which is described by using cubic-spline can be reconstructed. In such a case, Fourier series expansion will fail.