scholarly journals Effects of an axisymmetric rigid punch on a nonhomogeneous transversely isotropic half-space

2003 ◽  
Vol 44 (3) ◽  
pp. 461-474 ◽  
Author(s):  
P. K. Chaudhuri ◽  
Subhankar Ray
Keyword(s):  
Integral Equation ◽  
Half Space ◽  
Fredholm Integral Equation ◽  
Contact Region ◽  
Homogeneous Medium ◽  
Transversely Isotropic ◽  
Elastic Behaviour ◽  
Rigid Punch ◽  
Nonhomogeneous Medium ◽  
Homogeneous Case

AbstractElastic behaviour of a nonhomogeneous transversely isotropic half-space is studied under the action of a smooth rigid axisymmetric indentor. Hankel transforms of different orders have been used. It is observed that in contrast to a homogeneous medium, the pressure distribution in the contact region in a nonhomogeneous medium is not directly available, rather it is obtainable from the solution of a Fredholm integral equation. The integral equation is solved for a flat-ended punch and paraboloidal indentations for various values of the nonhomogeneity parameter, and the effects of nonhomogeneity in elastic behaviour on stresses have been shown graphically. The results of the associated homogeneous case are readily available from the results of the present study.

scholarly journals An Integral Equation Model for a Pile in a Layered Transversely Isotropic Saturated Soil

2018 ◽  
Vol 12 (1) ◽  
pp. 316-339
Author(s):  
Uwiduhaye Fabrice ◽  
Jian-Fei Lu ◽  
Dan-Dan Jin
Keyword(s):  
Integral Equation ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Half Space ◽  
Fredholm Integral Equation ◽  
Transversely Isotropic ◽  
Equation Model ◽  
Saturated Soil ◽  
Soil System ◽  
Transversely Isotropic Saturated Soil

Objective: In this paper, an integral equation model is established to predict the time-dependent response of a vertically loaded pile embedded in a layered Transversely Isotropic Saturated Soil (TISS). Methods: Based on the fictitious pile method, the pile-soil system is decomposed into an extended saturated half-space and a fictitious pile. The extended half-space is treated as a layered TISS, while the fictitious pile is considered as a 1D bar. The pile-soil compatibility is accomplished by requiring that the axial strain of the fictitious pile be equal to the vertical strain of the extended layered TISS along the axis of the pile. The second kind Fredholm integral equation of the pile is then derived by using the aforementioned compatibility condition and the fundamental solution of the layered TISS, which is equivalent to the solution of the layered TISS subjected to a uniformly-distributed load acting vertically over a circular area with the radius equal to that of the pile. The fundamental solution of the layered TISS is obtained via the Reflection-Transmission Matrix (RTM) method for the layered TISS. Applying the Laplace transform to the Fredholm integral equation, and solving the resulting integral equation, the transformed solution is obtained. The time domain solution of the pile-soil system is retrieved via the inverse Laplace transform. Results and Conclusion: Numerical results of this paper agree with existing solutions very well, validating the proposed pile-soil interaction model. A parametric study is carried out to examine the influence of some parameters on the response of the pile-soil system.

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.

A Punch Problem for a Transversely Isotropic Layer

1962 ◽  
Vol 58 (3) ◽  
pp. 539-547 ◽  
Author(s):  
A. H. England
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Transversely Isotropic ◽  
Isotropic Layer ◽  
Rigid Foundation ◽  
Axially Symmetric ◽  
Isotropic Materials ◽  
Transversely Isotropic Materials ◽  
Transversely Isotropic Layer ◽  
Punch Problem

In this note we consider the axially symmetric indentation of a transversely isotropic layer resting on a rigid foundation. The corresponding half-space problems both for isotropic and transversely isotropic materials have been solved previously (see (l), (2), (3), p. 455) and, more recently, the present problem has been solved for isotropic materials in (4) and (5) using methods different from that given in this paper. In § 2 the problem is reduced to the solution of a Fredholm integral equation of the second kind. In § 3 and subsequently the case of incomplete penetration by the punch, when the radius of the circle of contact is less than that of the end face of the punch, is considered. Finally, in §4 the results are illustrated by considering a hemispherically ended punch.

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.

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