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.
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