On the axisymmetric Mindlin problem for a semi-space of granular material
The methods of images and Hankel transforms are used to construct solution to an axisymmetric boundary value problem of a semi-space of transversely isotropic (granular) material due to a point force applied at a distance h beneath its stress free plane boundary \(z=0\). Exact closed form expressions are determined for the components of displacements and stresses throughout the interior of the granular semi- space. The solution is then used to derive the surface displacements due to a uniformly distributed force over a circle of radius 'a' with centre at (0,0-h) in the plane \(z=-h\) of the semi-space. By a suitable choice of material constants and through a limit process as \(\alpha_ 1,\alpha_ 2\) approach 1, the granular semi-space becomes isotropic and the corresponding results derived in this particular case agree with those presented by \textit{I. Sneddon} [Fourier transforms (1951; Zbl 0038.268)].
components of displacements and stresses
scientific article; zbMATH DE number 3980592
scientific article