Justification and refinement of Winkler–Fuss hypothesis

J Kaplunov, D Prikazchikov, L Sultanova - Zeitschrift für angewandte …, 2018 - Springer
Zeitschrift für angewandte Mathematik und Physik, 2018Springer
Two-parametric asymptotic analysis of the equilibrium of an elastic half-space coated by a
thin soft layer is developed. The initial scaling is motivated by the exact solution of the plane
problem for a vertical harmonic load. It is established that the Winkler–Fuss hypothesis is
valid only for a sufficiently high contrast in the stiffnesses of the layer and the half-space. As
an alternative, a uniformly valid non-local approximation is proposed. Higher-order
corrections to the Winkler–Fuss formulation, such as the Pasternak model, are also studied.
Abstract
Two-parametric asymptotic analysis of the equilibrium of an elastic half-space coated by a thin soft layer is developed. The initial scaling is motivated by the exact solution of the plane problem for a vertical harmonic load. It is established that the Winkler–Fuss hypothesis is valid only for a sufficiently high contrast in the stiffnesses of the layer and the half-space. As an alternative, a uniformly valid non-local approximation is proposed. Higher-order corrections to the Winkler–Fuss formulation, such as the Pasternak model, are also studied.
Springer
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