Antiplane Eigenstrain Problem of an Elliptic Inclusion in an Anisotropic Half Space

1982 ◽  
Vol 49 (1) ◽  
pp. 52-54 ◽  
Author(s):  
R. A. Masumura ◽  
Y. T. Chou
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Elastic Energy ◽  
Infinite Medium ◽  
Elliptic Inclusion ◽  
Image Field ◽  
Line Force ◽  
Force Concept

The antiplane eigenstrain problem of an elliptic inclusion in an anisotropic semi-infinite medium is investigated. Expressions for the stresses and elastic energy have been developed using the line force concept and superposition of the image field. It is shown that in the presence of a free surface the stresses inside the inclusion are not constant. In addition, the elastic energy of the system is reduced as the inclusion approaches the free surface.

Analysis of Two Cracks Vertical to the Isotropic Plane in Transversely Isotropic Bimaterials

2011 ◽  
Vol 90-93 ◽  
pp. 307-310
Author(s):  
Bing Jun Wang ◽  
Hong Tian Xiao
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Interaction Effect ◽  
Crack Surface ◽  
Crack Opening ◽  
Transversely Isotropic ◽  
Infinite Medium ◽  
Isotropic Plane ◽  
Effect Factor ◽  
Distributed Load

This paper analyzed the interaction between two parallel vertical cracks in a transversely isotropic half space by using the boundary element method (DBEM). The crack surface is perpendicular to the free surface and isotropic plane subjected to normal and tangential uniform distributed load respectively. The stress intensity factor (SIF) values of the crack are calculated from the crack opening displacements. And the interaction effect factor of SIF values is employed to quantitatively describe the interaction between two cracks. The variations of interaction effect factor are investigated with the distances between cracks, the side ratios and free surface. Results show that the existence of the free surface exerts more obvious influence on the SIF values of the crack close to free surface in half space than those in infinite medium. But the free surface has almost no influence on the interaction between two cracks.

Antiplane Eigenstrain Problem of an Elliptic Inclusion in a Two-Phase Anisotropic Medium

1985 ◽  
Vol 52 (1) ◽  
pp. 87-90 ◽  
Author(s):  
H. T. Zhang ◽  
Y. T. Chou
Keyword(s):  
Anisotropic Medium ◽  
Strain Energy ◽  
Homogeneous Medium ◽  
Stress Singularity ◽  
Elliptic Inclusion ◽  
Two Phase ◽  
Line Force ◽  
Elastic Inhomogeneity ◽  
Inhomogeneity Factor ◽  
Force Concept

An antiplane eigenstrain problem of an elliptic inclusion in a two-phase anisotropic medium is analyzed based on the line-force concept. Explicit expressions for the stress field and strain energy are obtained under a given symmetry. The results are used to determine the stress singularity coefficient for a flat inclusion. When the tip of the inclusion is located at the interface boundary, the stress singularity coefficient S′ varies according to the formula S′ = (1 + K) S° where K is the elastic inhomogeneity factor and S° is the stress singularity coefficient for a homogeneous medium (K = 0).

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

scholarly journals Benchmarking the invariant embedding method against analytical solutions in model transport problems

2006 ◽  
Vol 21 (2) ◽  
pp. 3-13
Author(s):  
Malin Wahlberg ◽  
Imre Pázsit
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Length Distribution ◽  
Infinite Medium ◽  
Scattering Medium ◽  
Embedding Method ◽  
Invariant Embedding ◽  
Invariant Embedding Method ◽  
Transport Problems ◽  
Energy Dependent

The purpose of this paper is to demonstrate the use of the invariant embedding method in a few model transport problems for which it is also possible to obtain an analytical solution. The use of the method is demonstrated in three different areas. The first is the calculation of the energy spectrum of sputtered particles from a scattering medium without absorption, where the multiplication (particle cascade) is generated by recoil production. Both constant and energy dependent cross-sections with a power law dependence were treated. The second application concerns the calculation of the path length distribution of reflected particles from a medium without multiplication. This is a relatively novel application, since the embedding equations do not resolve the depth variable. The third application concerns the demonstration that solutions in an infinite medium and in a half-space are interrelated through embedding-like integral equations, by the solution of which the flux reflected from a half-space can be reconstructed from solutions in an infinite medium or vice versa. In all cases, the invariant embedding method proved to be robust, fast, and monotonically converging to the exact solutions.

A note on disturbances in a layered medium containing a magnetic field

1964 ◽  
Vol 54 (6A) ◽  
pp. 1771-1777
Author(s):  
D. K. Sinha
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Layered Medium ◽  
Present Note ◽  
Infinite Medium ◽  
The Other ◽  
Time Dependent ◽  
The Earth ◽  
Propagation Of Waves ◽  
Initial Magnetic Field

abstract In recent years, Kaliski has contributed a series of papers on the interaction of elastic and magnetic fields and some of them, [1], [2], [3] are concerned with the propagation of waves in a semi-infinite medium either loaded or conditioned otherwise, at its free surface. Such problems, as Kaliski [1] has remarked, may have relevance in the practical seismic problem of detecting the mechanical explosions inside the earth. Moreover, their geophysical implications have also been examined by Knopoff [4[, Cagniard [5], Banos [6], and Rikitake [7]. The present note seeks to investigate disturbances in a medium consisting of two layers (one finite and the other infinite) of elastic medium intervened by a thin layer of vacuum. The vacuum is traversed by an initial magnetic field. The disturbances in the medium are assumed to have been produced by a time-dependent load on the free surface of the medium. The method of Laplace transform has been used to facilitate the solution of the problem.

Stress relaxation in a semi-infinite viscoelastic earth model

1973 ◽  
Vol 63 (6-1) ◽  
pp. 2145-2154
Author(s):  
Martin Rosenman ◽  
Sarva Jit Singh
Keyword(s):  
Free Surface ◽  
Stress Relaxation ◽  
Half Space ◽  
Epicentral Distance ◽  
Strike Slip ◽  
Strike Slip Fault ◽  
Earth Model ◽  
Contour Maps ◽  
Surface Stresses ◽  
Stress Components

Abstract Expressions for quasi-static surface stresses resulting from a finite, rectangular, vertical, strike-slip fault in a Maxwellian viscoelastic half-space are derived. Variation of the stresses with time and epicentral distance is studied. Contour maps are obtained in some representative cases. It is found that all nonvanishing stress components at the free surface die exponentially with time. This is in contrast to the behavior of the displacements and strains which, in general, do not vanish for large times.

scholarly journals Dynamic Stress and Displacement in an Elastic Half-Space with a Cylindrical Cavity

2011 ◽  
Vol 18 (6) ◽  
pp. 827-838 ◽  
Author(s):  
İ. Coşkun ◽  
H. Engin ◽  
A. Özmutlu
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Circular Cross Section ◽  
Elastic Half Space ◽  
Least Square ◽  
Polar Coordinates ◽  
Wave Number ◽  
Forcing Function

The dynamic response of an elastic half-space with a cylindrical cavity in a circular cross-section is analyzed. The cavity is assumed to be infinitely long, lying parallel to the plane-free surface of the medium at a finite depth and subjected to a uniformly distributed harmonic pressure at the inner surface. The problem considered is one of plain strain, in which it is assumed that the geometry and material properties of the medium and the forcing function are constant along the axis of the cavity. The equations of motion are reduced to two wave equations in polar coordinates with the use of Helmholtz potentials. The method of wave function expansion is used to construct the displacement fields in terms of the potentials. The boundary conditions at the surface of the cavity are satisfied exactly, and they are satisfied approximately at the free surface of the half-space. Thus, the unknown coefficients in the expansions are obtained from the treatment of boundary conditions using a collocation least-square scheme. Numerical results, which are presented in the figures, show that the wave number (i.e., the frequency) and depth of the cavity significantly affect the displacement and stress.

MATHEMATICAL ANALYSIS OF ELASTIC SURFACE WAVES IN TOPOGRAPHIC WAVEGUIDES

1999 ◽  
Vol 09 (05) ◽  
pp. 755-798 ◽  
Author(s):  
A. S. BONNET-BEN DHIA ◽  
J. DUTERTE ◽  
P. JOLY
Keyword(s):  
Free Surface ◽  
Half Space ◽  
Guided Waves ◽  
Transverse Energy ◽  
Eigenvalue Problems ◽  
Low Frequency ◽  
Elastic Half Space ◽  
High Frequencies ◽  
Guided Mode ◽  
Adjoint Operators

We present here a theoretical study of the guided waves in an isotropic homogeneous elastic half-space whose free surface has been deformed. The deformation is supposed to be invariant in the propagation direction and localized in the transverse ones. We show that finding guided waves amounts to solving a family of 2-D eigenvalue problems set in the cross-section of the propagation medium. Then using the min-max principle for non-compact self-adjoint operators, we prove the existence of guided waves for some particular geometries of the free surface. These waves have a smaller speed than that of the Rayleigh wave in the perfect half-space and a finite transverse energy. Moreover, we prove that the existence results are valid for arbitrary high frequencies in the presence of singularities of the free boundary. Finally, we prove that no guided mode can exist at low frequency, except maybe the fundamental one.

scholarly journals Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Pramod Kumar Vaishnav ◽  
Santimoy Kundu ◽  
Shishir Gupta ◽  
Anup Saha
Keyword(s):  
Porous Medium ◽  
Dispersion Relation ◽  
Initial Stress ◽  
Half Space ◽  
Love Wave ◽  
Separation Of Variables ◽  
Infinite Medium ◽  
Type Wave ◽  
Bounded Below ◽  
Irregular Interface

Propagation of Love-type wave in an initially stressed porous medium over a semi-infinite orthotropic medium with the irregular interface has been studied. The method of separation of variables has been adopted to get the dispersion relation of Love-type wave. The irregularity is assumed to be rectangular at the interface of the layer and half-space. Finally, the dispersion relation of Love wave has been obtained in classical form. The presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves in porous medium bounded below by an orthotropic half-space. The scientific effect of porosity, irregularity, and initial stress in the phase velocity of the Love-type wave propagation has been studied and shown graphically.

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