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By L. I. Sedov, J. R. M. Radok

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Additional info for A course in continuum mechanics, vol. 1: Basic equations and analytical techniques

Example text

34) represents the governing integral equation of the frictionless contact problem for two elastic layers bonded to slightly curved rigid substrates, where the substrate shapes are taken into account through the gap function ϕ(y), and the curvature effect on the integral operator on the right-hand side is neglected. 2 Distributional Asymptotic Analysis In this section, we develop an alternative for the perturbation approach to the contact problem in the thin-layer approximation considered in Sects.

The boundary conditions of unilateral contact are considered in detail, including the refined contact condition with allowance for tangential displacements on the contact interface. The contact problem is formulated as an integral equation over the contact area, which in turn should be determined by the positiveness condition imposed on the contact pressure. 1 Geometry of Surfaces in Contact Let us consider two thin elastic layers (n = 1, 2), each of uniform thickness h n , ideally bonded to rigid substrates with slightly curved surfaces (see Fig.

Math. Mech. 41, 320–328 (1977) 22. : Asymptotic analysis of a thin interface: the case involving similar rigidity. Int. J. Eng. Sci. 48, 473–486 (2010) 23. : Theory of Elasticity of an Anisotropic Body. Mir publishing, Moscow (1981) 18 1 Deformation of a Thin Bonded Transversely Isotropic Elastic Layer 24. : Mode III interface crack lying at thin nonhomogeneous anisotropic interface. Asymptotics near the crack tip. B. ) IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, pp.

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A course in continuum mechanics, vol. 1: Basic equations and analytical techniques by L. I. Sedov, J. R. M. Radok

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