Vol. 13, No. 4, 2018

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Analytical approach to the problem of an auxetic layer under a spatially periodic load

Henryk Kamiński and Paweł Fritzkowski

Vol. 13 (2018), No. 4, 463–479
Abstract

The problem of an infinite elastic layer under a periodic load is considered. A mathematical model is formulated for the plane strain state. An analytical procedure based on the Fourier integral transformation is discussed. The displacement components are obtained as infinite sums directly via the inverse Fourier transform. Semianalytical results are presented in a nondimensional form for the case of conventional elastic materials (positive Poisson’s ratio) and auxetic materials (negative Poisson’s ratio). The deformation of the loaded boundary and other characteristic surfaces of the layer is analyzed, and the displacement and stress fields are demonstrated. The effect of Poisson’s ratio on the system behavior is studied. The results are compared with the purely numerical solutions obtained using the finite element method.

Keywords
linear elasticity, elastic layer, deformation, auxetic materials, Fourier transform, approximate methods
Milestones
Received: 16 January 2018
Revised: 26 July 2018
Accepted: 19 August 2018
Published: 13 December 2018
Authors
Henryk Kamiński
Institute of Applied Mechanics
Poznan University of Technology
Poznan
Poland
Paweł Fritzkowski
Institute of Applied Mechanics
Poznan University of Technology
Poznan
Poland