The Contact Problem for a Rigid Inclusion Pressed Between Two Dissimilar Elastic Half Planes

Paper concerns the plane-strain problem of a rigid, thin, rounded inclusion pressed between two isotropic elastic half planes with different elastic constants. Required to find the extents of the contact regions between each plane and the inclusion, and the contact stress distributions. The governing integral equations are solved approximately by using Chebyshev expansions. Numerical results are presented.

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

Journal of Applied Mechanics ◽

10.1115/1.3422789 ◽

1972 ◽

Vol 39 (3) ◽

pp. 786-790 ◽

Cited By ~ 4

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.

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Axisymmetric stress-transfers from an embedded elastic cylindrical shell to a half-space

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1993.0059 ◽

1993 ◽

Vol 441 (1912) ◽

pp. 237-259 ◽

Cited By ~ 9

Keyword(s):

Cylindrical Shell ◽

Integral Equations ◽

Half Space ◽

Contact Stress ◽

Mathematical Formulation ◽

Numerical Procedure ◽

Fredholm Integral Equations ◽

Elastic Cylindrical Shell ◽

Stress Distributions ◽

Axisymmetric Stress

Within the framework of three-dimensional classical elastostatics and thin shell theories, a rigorous mathematical formulation is presented for the torsionless axisymmetric stress-transfer problem of a cylindrical shell of finite length embedded in a semi-infinite solid. By virtue of a set of ring-load Green’s functions for the shell and a group of fundamental solutions for the half-space, the mechanical interaction problem is shown to be reducible to a pair of Fredholm integral equations. Through the analysis of an auxiliary set of Cauchy integral equations, the singularities of the resultant contact stress distributions are rendered explicit, the results of which are incorporated in a numerical procedure. Typical solutions for the axial and radial load-transfers, contact stress distributions, as well as other related responses are included as illustrations. In addition to furnishing results of direct relevance to a number of engineering applications, the present treatment is apt to be useful as a basis of assessment for various approximate methods for this class of contact problems.

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The Problem of Minimizing Stress Concentration at a Rigid Inclusion

Journal of Applied Mechanics ◽

10.1115/1.3169031 ◽

1985 ◽

Vol 52 (1) ◽

pp. 83-86 ◽

Cited By ~ 10

Author(s):

L. Wheeler

Keyword(s):

Stress Concentration ◽

Variational Problem ◽

Plane Strain ◽

Rigid Inclusion ◽

Elastic Matrix ◽

Optimum Shape ◽

Plane Strain Problem ◽

Elementary Problem ◽

Conventional Methods

With the objective of minimizing stress concentration, the plane-strain problem of the optimum shape for a rigid inclusion in an elastic matrix of unbounded extent is investigated. It is shown rigorously that the underlying variational problem is reducible to a more elementary problem which can be solved by conventional methods to arrive at the optimum shape, which is a suitably proportioned ellipse.

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The Affine Transformation for Orthotropic Plane-Stress and Plane-Strain Problems

Journal of Applied Mechanics ◽

10.1115/1.4011198 ◽

1956 ◽

Vol 23 (1) ◽

pp. 1-6

Author(s):

H. A. Lang

Keyword(s):

Shear Modulus ◽

Plane Strain ◽

Elastic Constants ◽

Plane Stress ◽

Affine Transformation ◽

Orthotropic Material ◽

Elastic Symmetry ◽

Concentrated Load ◽

Plane Strain Problem ◽

Orthotropic Plane

Abstract It is demonstrated that a single affine transformation of the type x = ax′, y = by′ immediately extends the solution of any isotropic plane-stress or plane-strain problem to the solution of an orthotropic plane problem where the orthotropic material is characterized by three independent constants. Since orthotropy, defined as elastic symmetry with respect to two orthogonal axes, implies four independent elastic constants, the affine transformation introduces a restriction upon the orthotropic shear modulus. The orthotropic shear modulus differs from that used by previous investigators. This difference alters the equation which the orthotropic stress function must satisfy and, therefore, directly affects the solution to every plane-stress or plane-strain problem. Some arguments are advanced to favor the shear modulus, as here defined, whenever orthotropy must be restricted to three elastic constants. The two solutions of the orthotropic half plane subjected to a normal concentrated load are contrasted to illustrate the effect of the two definitions of orthotropic shear modulus.

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Effective Elastic Constants for Thick Perforated Plates With Square and Triangular Penetration Patterns

Journal of Engineering for Industry ◽

10.1115/1.3428087 ◽

1971 ◽

Vol 93 (4) ◽

pp. 935-942 ◽

Cited By ~ 54

Author(s):

T. Slot ◽

W. J. O’Donnell

Keyword(s):

Plane Strain ◽

Elastic Constants ◽

Plane Stress ◽

Numerical Results ◽

Exact Formulation ◽

Perforated Plates ◽

Effective Elastic Constants ◽

Wide Range ◽

The Relationship ◽

Generalized Plane Strain

An exact formulation is presented of the relationship between the effective elastic constants for thick perforated plates (generalized plane strain) and thin perforated plates (plane stress). Extensive numerical results covering a wide range of ligament efficiencies and Poisson’s ratios are given for plates with square and triangular penetration patterns.

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Wave propagation in micropolar monoclinic thermoelastic half space

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2013-0063 ◽

2013 ◽

Vol 18 (4) ◽

pp. 1013-1023

Author(s):

R.R. Gupta

Keyword(s):

Wave Propagation ◽

Quality Factor ◽

Plane Strain ◽

Half Space ◽

Numerical Results ◽

Plane Strain Problem ◽

Phase Velocities ◽

Propagation Of Waves

Abstract Propagation of waves in a micropolar monoclinic medium possessing hermoelastic properties based on the Lord- Shulman (L-S),Green and Lindsay (G-L) and Coupled thermoelasticty (C-T) theories is discussed. The investigation is divided into two sections, viz., plane strain and anti-plane strain problem. After developing the solution, the phase velocities and attenuation quality factor have been derived and computed numerically. The numerical results have been plotted graphically.

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