Displacements and Stresses in Nonhomogeneous Solid

An analysis is described for determining the displacements and stresses in an isotropic nonhomogeneous elastic solid whose modulus of rigidity varies with the depth. The solid, which is assumed to occupy a semi-infinite region, is deformed by the application of normal load symmetrically distributed over a circular portion of the horizontal surface. The physical quantities of interest (e.g., surface displacement, maximum normal and shear stresses, and stress isobars) are computed and the results are displayed graphically. Comparison with the known solution for homogeneous solid suggests that variations in the stiffness exponent, α, could have important influence on the contact settlement and the stress field in the solid.