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The Hertz contact problem, coupled Volterra integral equations and a linear complementarity problem

Gauthier, A. and Knight, P.A. and McKee, S. (2007) The Hertz contact problem, coupled Volterra integral equations and a linear complementarity problem. Journal of Computational and Applied Mathematics, 206 (1). pp. 322-340. ISSN 0377-0427

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Abstract

This paper is concerned with the indentation of an elastic half-space by an axisymmetric punch under a monotonically applied normal force and under the assumption of Coulomb friction with coefficient μ in the region of contact. Within an inner (unknown) circle the contact is adhesive, while in the surrounding annulus the surface moves inwards with increasing load. In this paper it is shown how this problem is equivalent to two coupled Abel's equations with an unknown free point, the inner circumference of the annulus. It is further shown that a product integration finite difference approximation of those integral equations leads to a mixed linear complementarity problem (mixed LCP). A method based on Newton's method for solving non-smooth nonlinear equations is demonstrated to converge under restrictive assumptions on the physical parameters defining the system; and numerical experimentation verifies that it has much wider applicability. The method is also validated against the approach of Spence. The advantage of the mixed LCP formulation is that it provides the radius of the inner adhesive circle directly using the physical parameters of the problem.

Item type: Article
ID code: 25767
Keywords: Hertz contact problem, Abel's integral equations, Linear complementarity problem, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Faculty of Science > Mathematics and Statistics > Mathematics
Related URLs:
    Depositing user: Mrs Carolynne Westwood
    Date Deposited: 02 Jul 2010 14:24
    Last modified: 04 Oct 2012 13:19
    URI: http://strathprints.strath.ac.uk/id/eprint/25767

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