scholarly journals An Elastic Half Space with a Moving Punch

2021 ◽  
Vol 16 ◽  
pp. 245-249
Author(s):  
Sandip Saha ◽  
Vikash Kumar ◽  
Apurba Narayan Das
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Integral Transform ◽  
Contact Region ◽  
Stress Component ◽  
Static Problem ◽  
Fourier Integral ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Dual Integral Equations

The dynamic problem of a punch with rounded tips moving in an elastic half-space in a fixed direction has been considered. The static problem of determining stress component under the contact region of a punch has also been solved. Fourier integral transform has been employed to reduce the problems in solving dual integral equations. These integral equations have been solved using Cooke’s [1] result (1970) to obtain the stress component. Finally, exact expressions for stress components under the punch and the normal displacement component in the region outside the punch have been derived. Numerical results for stress intensity factor at the punch end and torque applied over the contact region have been presented in the form of graph.

Interaction between a Rigid Cylinder with a Piezoelectric Half-Space with Partial Adhesion

2008 ◽  
Vol 33-37 ◽  
pp. 333-338 ◽  
Author(s):  
Zuo Rong Chen ◽  
Shou Wen Yu
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Piezoelectric Materials ◽  
Contact Region ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Dual Integral Equations ◽  
Slip Region

An axisymmetric problem of interaction of a rigid rotating flat ended punch with a transversely isotropic linear piezoelectric half-space is considered. The contact zone consists of an inner circular adhesion region surrounded by an outer annular slip region with Coulomb friction. Beyond the contact region, the surface of the piezoelectric half-space is free from load. With the aid of the Hankel integral transform, this mixed boundary value problem is formulated as a system of dual integral equations. By solving the dual integral equations, analytical expressions for the tangential stress and displacement, and normal electric displacement on the surface of the piezoelectric half-space are obtained. An explicit relationship between the radius of the adhesion region, the angle of the rotation of the punch, material parameters, and the applied loads is presented. The obtained results are useful for characterization of piezoelectric materials by micro-indentation and micro-friction techniques.

Torsion of a Cylindrical Rod Welded to an Elastic Half Space

1967 ◽  
Vol 34 (3) ◽  
pp. 687-692 ◽  
Author(s):  
N. J. Freeman ◽  
L. M. Keer
Keyword(s):  
Integral Equation ◽  
Stress Distribution ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Cylinder ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Dual Integral Equations ◽  
Single Integral

A solution is given for the problem of the torsion of an elastic cylinder welded to an elastic half space. The problem was formulated so as to involve coupling between dual-integral equations and Dini series. These equations were reduced to a single integral equation. Numerical results are given and functions found that approximate the stress distribution.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

scholarly journals Dynamic Behavior of an Embedded Foundation under Horizontal Vibration in a Poroelastic Half-Space

2019 ◽  
Vol 9 (4) ◽  
pp. 740 ◽  
Author(s):  
Yang Chen ◽  
Wen Zhao ◽  
Pengjiao Jia ◽  
Jianyong Han ◽  
Yongping Guan
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Mixed Boundary ◽  
Fredholm Integral Equations ◽  
Wave Forces ◽  
Dual Integral Equations ◽  
Horizontal Vibration ◽  
Embedded Foundation ◽  
Embedded Foundations ◽  
Caisson Foundations

More and more huge embedded foundations are used in large-span bridges, such as caisson foundations and anchorage open caisson foundations. Most of the embedded foundations are undergoing horizontal vibration forces, that is, wind and wave forces or other types of dynamic forces. The embedded foundations are regarded as rigid due to its high stiffness and small deformation during the forcing process. The performance of a rigid, massive, cylindrical foundation embedded in a poroelastic half-space is investigated by an analytical method developed in this paper. The mixed boundary problem is solved by reducing the dual integral equations to a pair of Fredholm integral equations of the second kind. The numerical results are compared with existing solutions in order to assess the accuracy of the presented method. To further demonstrate the applicability of this method, parametric studies are performed to evaluate the dynamic response of the embedded foundation under horizontal vibration. The horizontal dynamic impedance and response factor of the embedded foundation are examined based on different embedment ratio, foundation mass ratio, relative stiffness, and poroelastic material properties versus nondimensional frequency. The results of this study can be adapted to investigate the horizontal vibration responses of a foundation embedded in poroelastic half-space.

Axisymmetric contact with friction of a rigid sphere with an elastic half-space

2009 ◽  
Vol 465 (2108) ◽  
pp. 2565-2588 ◽  
Author(s):  
O. I. Zhupanska
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Integral Transform ◽  
Elastic Half Space ◽  
Rigid Sphere ◽  
Analytical Treatment ◽  
Normal Contact ◽  
Exact Analytical Solutions ◽  
Single Integral ◽  
Toroidal Coordinates

The problem of normal contact with friction of a rigid sphere with an elastic half-space is considered. An analytical treatment of the problem is presented, with the corresponding boundary-value problem formulated in the toroidal coordinates. A general solution in the form of Papkovich–Neuber functions and the Mehler–Fock integral transform is used to reduce the problem to a single integral equation with respect to the unknown contact pressure in the slip zone. An analysis of contact stresses is carried out, and exact analytical solutions are obtained in limiting cases, including a full stick contact problem and a contact problem for an incompressible half-space.

A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Wei Zhang
Keyword(s):  
Half Space ◽  
Power Law ◽  
Contact Region ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Abel Transformation ◽  
Numerical Solution Methods ◽  
Special Cases

In the present paper, axisymmetric frictionless adhesive contact between a rigid punch and a power-law graded elastic half-space is analytically investigated with use of Betti's reciprocity theorem and the generalized Abel transformation, a set of general closed-form solutions are derived to the Hertzian contact and Johnson–Kendall–Roberts (JKR)-type adhesive contact problems for an arbitrary punch profile within a circular contact region. These solutions provide analytical expressions of the surface stress, deformation fields, and equilibrium relations among the applied load, indentation depth, and contact radius. Based on these results, we then examine the combined effects of material inhomogeneities and punch surface morphologies on the adhesion behaviors of the considered contact system. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials and the Gibson soil as special cases and, therefore, can also serve as the benchmarks for checking the validity of the numerical solution methods.

THREE-DIMENSIONAL SURFACE CRACK ANALYSIS OF ELASTIC HALF-SPACE UNDER ROLLING CONTACT LOAD

2009 ◽  
Vol 06 (02) ◽  
pp. 317-332 ◽  
Author(s):  
MENG-CHENG CHEN ◽  
HUI-QIN YU
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Rolling Contact ◽  
Contact Load ◽  
Hypersingular Integral ◽  
Space Body ◽  
Planar Crack

In this work a three-dimensional planar crack on the surface of elastic half-space was analyzed under rolling contact load. The stresses interior to an elastic half-space body under rolling contact load and those produced by an infinitesimal displacement jump loop for the elastic half-space body were used to reduce the planar crack problem to the solution of a system of two-dimensional hypersingular integral equations with unknown displacement jump. The ideas of finite element discretization were employed to construct numerical solution schemes for solving the integral equations. An appropriate treatment of the associated hypersingular integral in the numerical solution to the integral equations was proposed in Hadamard's finite-part integral sense. The numerical results showed that the present procedure yields solutions with high accuracies. The stress intensity factors near the crack front edge under rolling contact load were indicated in graphical form with varying the crack shape, the radius of rolling contact zone and the friction coefficients, respectively. In addition, the influence of the lubricant infiltrating the crack surfaces on the crack propagation was also discussed in the paper.

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