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An effective asymptotic method in the axisymmetric frictionless contact problem for an elastic layer of finite thickness
Author(s) -
Argatov I. I.
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3782
Subject(s) - mathematics , a priori and a posteriori , rotational symmetry , finite element method , asymptotic analysis , radius , mathematical analysis , layer (electronics) , algebraic equation , contact mechanics , geometry , physics , materials science , nonlinear system , computer science , composite material , philosophy , computer security , epistemology , quantum mechanics , thermodynamics
A brief review of asymptotic methods to deal with frictionless unilateral contact problems for an elastic layer of finite thickness is presented. Under the assumption that the contact radius is small with respect to the layer thickness, an effective asymptotic method is suggested for solving the unilateral contact problem with a priori unknown contact radius. A specific feature of the method is that the construction of an asymptotic approximation is reduced to a linear algebraic system with respect to integral characteristics (polymoments) of the contact pressure. As an example, the sixth‐order asymptotic model has been written out. Copyright © 2015 John Wiley & Sons, Ltd.