Determination Of Potential Function In
Contact Problems
Author(s)
F. Sharafbafi & S. Adibnazari
Abstract
In this paper, a relation is introduced that simplifies the determination of the
Muskhelishvili’s potential function in plane contact problems. The relation is
)] ( ) ( [ 2 / 1 ) ( z iq z p z − = Φ , which is correct for all uncoupled-elastic contact
problems. This relation is proved in a mathematical way and utilized to obtain
the potential function in several contact problems. A complete agreement has
been observed between our results and the potential functions that have been
obtained from complicated methods in the past. Utilization of the relation
simplifies the solution of contact problems and analytical calculation of the stress
and displacement fields, which is helpful in the analytical studies of contact
mechanics. It also may lead to the design of better cutting tools or fretting fatigue
test pads.
Keywords: contact mechanics, uncoupled-elastic plane contacts, analytical
solution, Muskhelishvili’s potential function, a simple relation.
1 Introduction
A routine procedure for solving analytically plane contact problems is the
following: find pressure and shear distributions from the contact fundamental
equations and substitute those into the Muskhelishvili’s integral equation to
obtain the contact potential function. The contact stress and displacement fields
are achievable through the determined potential function [1–3]. Since the
Muskhelishvili’s integral equation is a complex singular integral equation,
calculation of the potential function, in this way, is not so simple. Therefore, the
closed-form potential function of a few contact problems has been obtained. For
a contact problem with complicated geometry, there are other procedures to
Keywords
contact mechanics, uncoupled-elastic plane contacts, analytical
solution, Muskhelishvili’s potential function, a simple relation.
Related Book
Other papers in this volume
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