Analysis of Transversely Isotropic Half-Spaces under the Effect of a Rigid Circular Plate Using  Ring Load Green’s Functions

Ardeshir-Behrestaghi, Azizolah; Eskandari-Ghadi, Morteza

doi:10.22067/fum-mech.v22i1.9021

Analysis of Transversely Isotropic Half-Spaces under the Effect of a Rigid Circular Plate Using Ring Load Green’s Functions

Document Type : Original Article

Authors

azizolah Ardeshir-Behrestaghi

morteza Eskandari-Ghadi

10.22067/fum-mech.v22i1.9021

Abstract

The main goal for this research is to analyze a transversely isotropic half-space under the effect of a circular rigid disc attached on the surface of the domain. To do so, the potential method is used to uncouple the Navier’s equilibrium partial differential equations. Utilizing Hu-Nowakii-Lekhnitskii potential functions and both Fourier series and Hankel transform, the displacements and stresses Green’s functions are determined for a surface ring load in a cylindrical coordinate system attached to the domain. Then, the effect of circular rigid disc is seen by applying some ring loads of unknown amplitudes, depends on the direction of displacement of the disc, which may be vertical, horizontal or rocking displacement. The amplitudes of the different ring loads are determined by satisfying the displacement boundary conditions. It is shown that the results are identical to the existing ones for the isotropic case. To assess the effect of anisotropy, the results are numerically evaluated for different transversely isotropic materials and compared.

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