Inverse Problems Of Plane Elasticity For The
Determination Of Contact Stresses
Author(s)
A. N. Galybin
Abstract
This article presents some results of numerical experiments on the reconstruction
of contact stresses by using synthetic data on displacement monitoring on a
traction-free surface. The corresponding boundary value problem is ill-posed
therefore a regularisation procedure based on the SVD decomposition is
employed. Statistical analysis of results has been performed.
Keywords: contact problem, plane elasticity, boundary value problems, inverse
problems, SVD regularisation.
1 Introduction
There are many applications where data on stresses or displacements may not be
available on the entire boundary of a body (including internal boundaries). Such
problems appear in strain-stress measurements, interferometry, rock mechanics,
monitoring the fracture development in strength tests etc. They require the
consideration of a specific boundary value problem, BVP, which is overspecified
on a part of the boundary and underspecified on the rest of it.
The theory of classical BVPs of plane elastostatics is fully presented in the
classical monograph by Muskhelishvili [1], it assumes that two scalar boundary
conditions are given on the entire boundary of a domain. In contact mechanics
the BVPs are usually formulated as the mixed type problems when
displacements are given in the contact zone and tractions on the rest of the
surface. Other formulations of contact conditions are discussed in detail in
Johnson [2]. In all these cases the boundary value problem is well posed,
therefore it possesses a unique and stable solution.
Despite classical boundary conditions describe a wide class of mechanical
phenomena there is still the necessity to use additional assumptions in
Keywords
contact problem, plane elasticity, boundary value problems, inverse
problems, SVD regularisation.
Related Book
Other papers in this volume
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