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Inverse contact problem for an elastic half-space.pdf
Engineering Analysis with Boundary Elements 68 (2016) 35–41
Contents lists available at ScienceDirect
Engineering Analysis with Boundary Elements
journal homepage: /locate/enganabound
Inverse contact problem for an elastic half-space
A.N. Galybin
The Schmidt Institute of Physics of the Earth, Moscow, Russia
article info
Article history: Received 31 December 2015 Received in revised form 25 February 2016 Accepted 31 March 2016 Available online 7 April 2016
Keywords: Contact problem Inverse problem Integral equations Trefftz approach Regularisation
abstract
This paper presents a system of integral equations for the determination of contact stresses on a part of the boundary of elastic half-space by measured data of displacements on the rest of the stress-free boundary. Inverse problems like this are refereed to as conditionally ill-posed with pronounced dependence of the solution from small perturbations in measured data. The 3D problem formulation is based on spatial harmonic functions. It is proposed to use a Trefftz-type method for the sought harmonic functions based on the radial basis functions to solve the system of integral equations. A synthetic example is presented to illustrate the proposed approach.
2016 Elsevier Ltd. All rights reserved.
1. Introduction
Determination of stresses acting in contact zones between two or more bodies is the primary problem of contact mechanics. The classical approach [1] assumes different types of boundary conditions within contact zones. These can be formulated in terms of stresses for soft punches, displacement for rigid punches or certain linear relationships between stresses and displacements to take friction into account. In all these cases the correspondent boundary value problem is well posed, thus, it possesses a unique and stable solution.
An alternative approach to contact problems deals with socalled, ill-posed problems, in which no boundary conditions are speci?ed in a contact zone but some excessive data are given
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