Concentrated ring loading in a nonlocal elastic medium

Abstract

Assuming an appropriate nonlocal modulus and using the Boussinesq–Galerkin vector representation of the nonlocal stress field the stress distribution in a nonlocal elastic medium has been found under the concentrated ring normal and shear loadings and force dipoles. The nonlocal modulus used in the paper is the Green function of the diffusion equation. To solve the corresponding boundary-value problem the Laplace transform with respect to the nonlocal parameter and the Hankel transform with respect to the radial coordinate are used. The Laplace transform is inverted analytically; inverting the Hankel transform the oscillatory integrals containing products of Bessel functions have been changed into integrands which decay exponentially, thus producing a solution more amenable to numerical quadrature. All classical singularities for stresses are eliminated.