Singularities of the stress field in an elastic anisotropic half-plane with a stiffener terminating at the surface

1981 ◽  
Vol 17 (10) ◽  
pp. 944-947
Author(s):  
L. A. Fil'shtinskii
Keyword(s):  
Stress Field ◽  
Half Plane

Asymptotic analysis of the corner-behaviour of a rigid punch bonded to an elastic substrate

2007 ◽  
Vol 42 (5) ◽  
pp. 415-422
Author(s):  
L Bohórquez ◽  
D. A Hills
Keyword(s):  
Stress Field ◽  
Plastic Zone ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Half Plane ◽  
Poisson's Ratio ◽  
Rigid Block ◽  
Rigid Punch ◽  
Oscillatory Behaviour ◽  
Elastic Substrate

The contact between a flat-faced rigid block and an elastic half-plane has been studied, showing that an asymptotic solution correctly captures the stress field adjacent to the contact corners for all values of Poisson's ratio. It is shown that, in practical cases, the plastic zone, which is inevitably present at the contact corners, envelopes the oscillatory behaviour implied locally but is surrounded by an elastic hinterland correctly represented by the asymptote.

A Diffraction Problem and Crack Propagation

1967 ◽  
Vol 34 (1) ◽  
pp. 100-103 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Exact Solution ◽  
Stress Field ◽  
Crack Propagation ◽  
Elastic Medium ◽  
Half Plane ◽  
Diffraction Problem ◽  
Shear Waves ◽  
Stress Waves ◽  
Plane Crack ◽  
Antiplane Strain

The exact solution to the problem of diffraction of plane harmonic polarized shear waves by a half-plane crack extending under antiplane strain is constructed. The solution is employed to study the nature of the stress field associated with an extending crack in an elastic medium excited by stress waves.

Stresses Produced in a Half Plane by Moving Loads

1958 ◽  
Vol 25 (4) ◽  
pp. 433-436
Author(s):  
J. Cole ◽  
J. Huth
Keyword(s):  
Stress Field ◽  
Elastic Medium ◽  
Half Plane ◽  
Load Distribution ◽  
Wave Speed ◽  
Complete Solution ◽  
Moving Loads ◽  
Concentrated Load ◽  
Line Load ◽  
Wave Speeds

Abstract A study is made of stresses and displacements induced in an elastic half plane (plane strain) by a concentrated line load moving at a constant speed along its surface. The stress field for an arbitrary load distribution can be built up by superposition of these concentrated-load solutions. Three cases are considered: (a) The load is moving more slowly than either the longitudinal or transversal wave speeds of the elastic medium (subsonic case). (b) The load speed is between the two wave speeds (transonic case). (c) The load speed is greater than either wave speed (supersonic case). In each of these cases the nature of the singularity caused by the load is examined and the complete solution is given.

The Strength of Some Non-Hertzian Plane Contacts

1986 ◽  
Vol 108 (4) ◽  
pp. 655-658 ◽  
Author(s):  
A. Sackfield ◽  
D. A. Hills
Keyword(s):  
Stress Field ◽  
Half Plane ◽  
Chebyshev Polynomials ◽  
Sliding Contact ◽  
Elastic Contact ◽  
Contact Conditions ◽  
Large Load ◽  
Practical Implications

The problem of plane elastic contact between a symmetrical indentor and a half-plane is addressed. The form of the contacting profile of the indentor is represented in terms of Chebyshev polynomials, and the resulting stress-field is deduced, for both static and sliding contact. It is shown that by making the profile somewhat flatter than a cylinder a large load may be sustained without yielding. Practical implications of the result, including profiles needed to attain optimal contact conditions, are discussed.

scholarly journals Determination of the Stress Field of the Brittle Rock Caused by Quasistatic Load

2016 ◽  
Vol 16 (1) ◽  
pp. 29-32
Author(s):  
Marine Losaberidze ◽  
Mamuka Vazagasvili ◽  
Mikheil Tutberidze
Keyword(s):  
Mathematical Model ◽  
Stress Field ◽  
Half Plane ◽  
Constant Velocity ◽  
Brittle Rock ◽  
Analytical Functions ◽  
The Mathematical Model

Abstract In the paper the mathematical model has been proposed according of which the rock is considered as an orthotropic half-plane. On the boundary of this half-plane the loads, moving at a constant velocity, exert a pressure. The problem was solved by means of the theory of analytical functions.

Explicit equations for the half-plane sub-surface stress field under a flat rounded contact

2014 ◽  
Vol 49 (8) ◽  
pp. 562-570 ◽  
Author(s):  
Jesús Vázquez ◽  
Carlos Navarro ◽  
Jaime Domínguez
Keyword(s):  
Stress Field ◽  
Half Plane ◽  
Surface Stress ◽  
Normal Load ◽  
Elastic Behaviour ◽  
Tangential Load ◽  
Maximum Value ◽  
Interior Stress ◽  
Von Mises ◽  
Flat Section

In this article, the interior half-plane stress field resulting from the contact between a half-plane and a flat rounded punch is obtained in an explicit form. The punch is first subjected to a normal load, N, and later to a tangential load Q =  µN, so a global sliding condition is achieved. The equations presented here are obtained assuming that the contacting bodies exhibit isotropic elastic behaviour and have identical mechanical properties and that both bodies can be modelled as half-planes. In addition to the equations describing the interior stress field, the maximum value of the von Mises parameter and the location of this maximum value are obtained as a function of the b/ a ratio, a and b being the semi-widths of the contact zone and flat section, respectively. Finally, the direct stress, σ txx( x, 0), due to the tangential load is calculated using the formulae developed here.

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