scholarly journals Surface Displacements due to a Steadily Moving Point Force

1996 ◽  
Vol 63 (2) ◽  
pp. 245-251 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Point Force ◽  
Two Dimensional ◽  
Normal Surface ◽  
Displacement Fields ◽  
Linear Superposition ◽  
Surface Displacements ◽  
Stress And Displacement Fields

Closed-form expressions are obtained for the normal surface displacements due to a normal point force moving at constant speed over the surface of an elastic half-space. The Smirnov-Sobolev technique is used to reduce the problem to a linear superposition of two-dimensional stress and displacement fields.

Penetration of a Half Space by a Rectangular Cylinder

1979 ◽  
Vol 46 (3) ◽  
pp. 587-591 ◽  
Author(s):  
A. Cemal Eringen ◽  
F. Balta
Keyword(s):  
Half Space ◽  
Stress Singularity ◽  
Elastic Solid ◽  
Interatomic Interaction ◽  
Elastic Half Space ◽  
Rigid Block ◽  
Field Equations ◽  
Displacement Fields ◽  
Rectangular Cylinder ◽  
Stress And Displacement Fields

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.

scholarly journals Reconstruction of round voids in the elastic half-space: Antiplane problem

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Mezhlum A. Sumbatyan ◽  
Vincenzo Tibullo ◽  
Vittorio Zampoli
Keyword(s):  
Half Space ◽  
Finite Length ◽  
Boundary Surface ◽  
Elastic Half Space ◽  
Point Force ◽  
Good Stability ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Numerical Examples ◽  
Antiplane Problem

We study the reconstruction of geometry (position and size) of round voids located in the elastic half-space, in frames of antiplane two-dimensional problem. We assume that a known point force is applied to the boundary surface of the half-space, and we can measure the shape of the surface over a certain finite-length interval. Then, if the geometry of the defect is unknown, we construct an algorithm to restore its position and size. Some numerical examples demonstrate a good stability of the proposed algorithm.

EFFECT OF IRREGULARITY ON STATIC DEFORMATION OF ELASTIC HALF-SPACE

2008 ◽  
Vol 22 (14) ◽  
pp. 2241-2253
Author(s):  
M. M. SELIM
Keyword(s):  
Fourier Transform ◽  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Static Deformation ◽  
Horizontal Distance ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Rectangular Shape

In the present paper, the problem of two-dimensional static deformation of an isotropic elastic half-space of irregular thickness has been studied using the eigenvalue approach, following a Fourier transform. The irregularity is expressed by a rectangular shape. As an application, the normal line-load acting inside an irregular isotropic half-space has been considered. Further, the results for the displacements have been derived in the closed form. To examine the effect of irregularity, variations of the displacements with horizontal distance have been shown graphically for different values of irregularity size, and they are compared with those for the medium with uniform shape. It is found that irregularity affects the deformation significantly.

Asymmetric Mixed Boundary-Value Problems of the Elastic Half-Space

1965 ◽  
Vol 32 (2) ◽  
pp. 411-417 ◽  
Author(s):  
R. A. Westmann
Keyword(s):  
Boundary Value Problems ◽  
Half Space ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Elastic Half Space ◽  
Integral Solution ◽  
Displacement Fields ◽  
Dual Integral Equations ◽  
Mixed Boundary Value Problems ◽  
Stress And Displacement Fields

Solutions are presented, within the scope of classical elastostatics, for a class of asymmetric mixed boundary-value problems of the elastic half-space. The boundary conditions considered are prescribed interior and exterior to a circle and are mixed with respect to shears and tangential displacements. Using an established integral-solution form, the problem is reduced to two pairs of simultaneous dual integral equations for which the solution is known. Two illustrative examples, motivated by problems in fracture mechanics, are presented; the resulting stress and displacement fields are given in closed form.

Continuous Bond Failure Due to a Moving Force

1973 ◽  
Vol 40 (2) ◽  
pp. 541-545 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Half Space ◽  
Stationary Solution ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Bond Failure ◽  
Moving Force ◽  
Line Force

Within the framework of the two-dimensional theory of elastodynamics a closed-form, quasi-stationary, solution is given to the problem of continuous failure of bond between an elastic half space and a rigid body. The bond failure is due to a line force moving at the interface.

Numerical Modeling of Partial Slip Contact Involving Inhomogeneous Materials

2012 ◽  
Author(s):  
Zhanjiang Wang ◽  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Partial Slip ◽  
Inhomogeneous Materials ◽  
Displacement Fields ◽  
Homogeneous Solutions ◽  
Equivalent Inclusion Method ◽  
Equivalent Inclusion ◽  
Stress And Displacement Fields

When solving the problems involving inhomogeneous materials, the influence of the inhomogeneity upon contact behavior should be properly considered. This research proposes a fast and novel method, based on the equivalent inclusion method where inhomogeneity is replaced by an inclusion with properly chosen eigenstrains, to simulate contact partial slip of the interface involving inhomogeneous materials. The total stress and displacement fields represent the superposition of homogeneous solutions and perturbed solutions due to the chosen eigenstrains. In the present numerical simulation, the half space is meshed into a number of cuboids of the same size, where each cuboid is has a uniform eigenstrain. The stress and displacement fields due to eigenstrains are formulated by employing the recent half-space inclusion solutions derived by the authors and solved using a three-dimensional fast Fourier transform algorithm. The partial slip contact between an elastic ball and an elastic half space containing a cuboidal inhomogeneity was investigated.

scholarly journals Surface waves in multilayered elastic media I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space

1964 ◽  
Vol 54 (2) ◽  
pp. 627-679
Author(s):  
David G. Harkrider
Keyword(s):  
Surface Waves ◽  
Frequency Domain ◽  
Half Space ◽  
Rayleigh Waves ◽  
Elastic Half Space ◽  
Love Waves ◽  
Displacement Fields ◽  
Matrix Formulation ◽  
Total Displacement ◽  
Rayleigh And Love Waves

ABSTRACT A matrix formulation is used to derive integral expressions for the time transformed displacement fields produced by simple sources at any depth in a multilayered elastic isotropic solid half-space. The integrals are evaluated for their residue contribution to obtain surface wave displacements in the frequency domain. The solutions are then generalized to include the effect of a surface liquid layer. The theory includes the effect of layering and source depth for the following: (1) Rayleigh waves from an explosive source, (2) Rayleigh waves from a vertical point force, (3) Rayleigh and Love waves from a vertical strike slip fault model. The latter source also includes the effect of fault dimensions and rupture velocity. From these results we are able to show certain reciprocity relations for surface waves which had been previously proved for the total displacement field. The theory presented here lays the ground work for later papers in which theoretical seismograms are compared with observations in both the time and frequency domain.

Exact Analysis of Dynamic Sliding Indentation at any Constant Speed on an Orthotropic or Transversely Isotropic Half-Space

2002 ◽  
Vol 69 (3) ◽  
pp. 340-345 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Space ◽  
Contact Zone ◽  
Transversely Isotropic ◽  
Exact Formula ◽  
Constant Speed ◽  
Displacement Fields ◽  
Rigid Indentor

A plane-strain study of steady sliding by a smooth rigid indentor at any constant speed on a class of orthotropic or transversely isotropic half-spaces is performed. Exact solutions for the full displacement fields are constructed, and applied to the case of the generic parabolic indentor. The closed-form results obtained confirm previous observations that physically acceptable solutions arise for sliding speeds below the Rayleigh speed, for a single critical transonic speed, and for all supersonic speeds. Continuity of contact zone traction is lost for the latter two cases. Calculations for five representative materials indicate that contact zone width achieves minimum values at high, but not critical, subsonic sliding speeds. A key feature of the analysis is the factorization that gives, despite anisotropy, solution expressions that are rather simple in form. In particular, a compact function of the Rayleigh-type emerges that leads to a simple exact formula for the Rayleigh speed itself.

A TWO-DIMENSIONAL STATIC DEFORMATION OF AN IRREGULAR INITIALLY STRESSED MEDIUM

2008 ◽  
Vol 22 (20) ◽  
pp. 3473-3485
Author(s):  
M. M. SELIM
Keyword(s):  
Closed Form ◽  
Initial Stress ◽  
Half Space ◽  
Static Deformation ◽  
Initial Stresses ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Notable Effect ◽  
Approach Method

The paper discusses the problem of a two-dimensional static deformation as the result of normal line-load acting inside an irregular initially stressed isotropic half-space. The eigenvalue approach method has been used. The irregularity is expressed by a rectangle shape. Further, the results for the displacements and stresses have been derived in the closed form. The effect of initial stress and irregularity are shown graphically. It was found that the initial stresses as well as irregularity have a notable effect on this deformation.

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