Justification and refinement of Winkler–Fuss hypothesis
Zeitschrift für angewandte Mathematik und Physik, 2018•Springer
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.
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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