Vertical Action of a Concentric Multi-Annular Punch on a Transversely Isotropic Elastic Half-Space

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Morteza Eskandari-Ghadi ◽  
Ronald Y. S. Pak ◽  
Azizollah Ardeshir-Behrestaghi
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Computational Approach ◽  
Mixed Boundary Value Problem ◽  
Contact Conditions ◽  
Degree Of Anisotropy ◽  
Annular Punch ◽  
Vertical Action

In this paper, the response of a transversely isotropic half-space under the punch action of a set of rigid concentric annuli frictionless contacts is considered. By virtue of a compact potential representation and Hankel transforms, a set of ring-load Green’s functions for the axisymmetric equations of equilibrium are derived and shown to be expressible in terms of standard elliptic integrals. With the aid of a rigorous yet highly efficient numerical method, the integral equation is solved for the multi-interval singular mixed boundary value problem. Detailed solutions to illustrate the performance of the computational approach and the influence of the degree of anisotropy and contact conditions on the mechanics problem are presented.

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 Torsional Contact Problem for an Indented Half-Space

1996 ◽  
Vol 63 (1) ◽  
pp. 1-6 ◽  
Author(s):  
R. Y. S. Pak ◽  
F. Abedzadeh
Keyword(s):  
Stress Distribution ◽  
Boundary Value Problem ◽  
Contact Problem ◽  
Half Space ◽  
Contact Stress ◽  
Mixed Boundary ◽  
Elastic Half Space ◽  
Torsional Stiffness ◽  
Mixed Boundary Value Problem ◽  
Contact Stress Distribution

This paper is concerned with the torsion of a rigid disk bonded to the bottom of a cylindrical indentation on an elastic half-space. By virtue of Fourier sine and cosine transforms, the mixed boundary value problem in classical elastostatics is shown to be reducible to a pair of integral equations, of which one possesses a generalized Cauchy singular kernel. With the aid of the theory of analytic functions, the inherent fractional-order singularity in the contact problem is rendered explicit. Illustrative results on the torsional stiffness of the base of the indentation and the corresponding contact stress distribution are presented for engineering applications.

scholarly journals An Asymmetric Mixed Boundary Value Problem of the Elastic Half-Space Subjected to Moment by an Annular Rigid Punch

1978 ◽  
Vol 21 (154) ◽  
pp. 566-571 ◽  
Author(s):  
Toshiaki HARA ◽  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI ◽  
Ichiro NAKAHARA
Keyword(s):  
Boundary Value Problem ◽  
Half Space ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Elastic Half Space ◽  
Rigid Punch ◽  
Mixed Boundary Value Problem

Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space

2020 ◽  
pp. 108128652097935
Author(s):  
Maziar Kalantari ◽  
Naser Khaji ◽  
Morteza Eskandari-Ghadi
Keyword(s):  
Boundary Value Problem ◽  
Integral Equations ◽  
Half Space ◽  
Soil Structure ◽  
Mixed Boundary ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Soil Structure Interaction ◽  
Mixed Boundary Value Problem ◽  
Structure Interaction

Recent studies have confirmed that rockable structures have beneficial effects in earthquakes due to uniform dynamic behavior of the structure. For these kinds of structures, an equivalent static analysis is accurate enough, as the rocking motion is the dominant mode of their interaction with the surrounding soil (i.e. soil–structure interaction problem). In this study, the soil–structure interaction problems are extended to consider the effect of elastic non-homogeneities as well as changing the elasticity constants with depth in an exponential manner for the rocking loads. This paper analytically investigates the mixed boundary value problem regarding the forced rocking interaction of a rigid foundation embedded in a finite depth of an exponentially graded transversely isotropic half-space. The potential function method accompanied by Hankel integral transforms is applied to solve the system of the equations of motion of the media. Due to integral transforms used in the solving procedure, the mixed boundary value problem raised may be apt to be transformed to dual integral equations, which in turn, could be reduced to Fredholm integral equation of the second kind. To evaluate the solution of the integral equations, a robust numerical procedure has been developed for different anisotropic materials. Regarding the complicated integrand functions, the integrals are numerically and graphically presented to cover the effect of degree of change of material properties that plays a key role.

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