Rigid Inclusion in Nonhomogeneous Incompressible Elastic Half‐Space

Abstract

The elastostatic problem of a nonhomogeneous incompressible elastic half‐space containing a partially or fully embedded axially loaded, axisymmetric rigid inclusion is analyzed. The shear modulus of the half‐space is assumed to vary linearly with depth. The rigid inclusion is perfectly bonded to the half‐space. The associated boundary‐value problem is solved by using an indirect boundary integral equation method based on exact displacement and traction Green's functions of the nonhomogeneous elastic half‐space. The general solutions of the nonhomogeneous half‐space can be derived by employing Hankel integral transforms. Green's functions appearing in the boundary integral equation correspond to axisymmetric ring loads in radial and vertical directions acting in the interior of the half‐space. Explicit solutions for Green's functions are presented. Numerical techniques are adopted to solve the integral equation and to evaluate Green's functions. Selected numerical results for rigid cylindrical inclusions are presented to illustrate the influence of degree of nonhomogeneity of the half‐space on the axial stiffness and load transfer curves.