The Stresses Induced in a Half-Space by an Arbitrary Axisymmetric Pressure Distribution

1987 ◽  
Vol 109 (4) ◽  
pp. 630-633
Author(s):  
D. A. Hills ◽  
A. Sackfield
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Half Space ◽  
Fourth Order ◽  
Small Area ◽  
Hertz Contact ◽  
Hertz Contact Problem ◽  
General Method

A general method is described for deducing the stresses induced in a half-space by an axisymmetric pressure distribution applied over a small area of the surface. The technique is illustrated by re-evaluating the solution to Hertz’ contact problem, and deducing the stresses induced in a fourth-order contacting pair.

Contact Area Variation in Elastic Indentation Problems

2009 ◽  
Author(s):  
Roman Riznychuk
Keyword(s):  
Contact Problem ◽  
Pressure Distribution ◽  
Half Space ◽  
Analytical Solutions ◽  
Contact Area ◽  
Elastic Half Space ◽  
Exact Expression ◽  
Rigid Punch ◽  
Contact Pressure Distribution ◽  
Area Variation

Contact problem of the frictionless indentation of elastic half-space by smooth rigid punch of curved profile is investigated. An exact expression of the contact pressure distribution for a curved profile punch in terms of integral involving the pressure distribution for sequence of flat punches is derived. The method is illustrated and validated by comparison with some well-known analytical solutions.

Some useful results in the classical Hertz contact problem

1983 ◽  
Vol 18 (2) ◽  
pp. 101-105 ◽  
Author(s):  
A Sackfield ◽  
D A Hills
Keyword(s):  
Stress Field ◽  
Contact Problem ◽  
Hertz Contact ◽  
Hertz Contact Problem

A resumé is given of the results available in the literature for the stresses resulting from frictionless loading by Hertz pressures. The problem is posed formally in tensor notation and new convenient forms are given for the complete stress field, in the general elliptical-patch case.

Asymmetric Contact Problem Including Wear for Nonhomogeneous Half Space

1982 ◽  
Vol 49 (1) ◽  
pp. 43-46 ◽  
Author(s):  
T. S. Sankar ◽  
V. Fabrikant
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Elastic Modulus ◽  
Contact Problem ◽  
Half Space ◽  
Tangential Stresses ◽  
Method Of Solution ◽  
Work Done ◽  
General Method ◽  
Asymmetric Contact

Contact problem with wear for asymmetric rigid die acting on a half space whose elastic modulus is a power function of depth is considered for the case when the die is rotating according to an arbitrary law. Zone of contact is taken to be a circle, and the wear is proportional to the work done by the tangential stresses obeying Coloumb’s law. Integral equation of the problem is derived and an exact solution of the equation is obtained in closed form. The case of inclined flat die is discussed as an illustrative example of the general method of solution that is proposed.

A note on the hertz contact problem: A correlation of standard formulae

1983 ◽  
Vol 18 (3) ◽  
pp. 195-197 ◽  
Author(s):  
A Sackfield ◽  
D Hills
Keyword(s):  
Contact Problem ◽  
Hertzian Contact ◽  
Hertz Contact ◽  
Geometry Problem ◽  
Special Case ◽  
Hertz Contact Problem

The values of stresses resulting from point or line Hertzian contact (including frictional traction) are deduced as a special case of the general elliptical geometry problem, and are compared with known solutions.

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