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

Kamiński, Henryk; Fritzkowski, Paweł

doi:10.2140/jomms.2018.13.463

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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

DOI: 10.2140/jomms.2018.13.463

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

Vol. 13, No. 4, 2018

Henryk Kamiński and Paweł Fritzkowski

Abstract

Keywords

Milestones

Authors