Elastostatic Far-Field Behavior in a Layered Half Space Under Surface Pressure

Abstract

Elastostatic problem of a half space with a layer of possibly distinct mechanical properties under arbitrary normal tractions on the surface is reconsidered to establish far-field asymptotic expansions of the displacements. This work was motivated by application of such far field solutions to problems of the layered half space by Global-Local Finite-Element Method (GLFEM). When the traction is a unit concentrated force, the asymptotic expansion is found to coincide, up to the second term of its inverse power series expansion with respect to the distance from the point at interface below the point of load application, with that of the classical Boussinesq solution with a suitably chosen coordinate system. This agreement between the two solutions is also observed for normal tractions on a bounded surface region. Comparative numerical results are given to demonstrate the modeling capabilities of the far-field asymptotic expansions in a GLFEM example. It’s effectiveness is shown in terms of greater accuracy and computational efficiency over the conventional finite-element method.