A contact problem for a nonhomogeneous half-space

A solution of a contact problem for a non-homogeneous half-space is given. The analysis is based on the assumption that the shearing displacement is prescribed within the band $\text{y = 0, ¦x¦<1, ¦z¦< ∞}$ and shearing stress is zero in the outside area $\text{|x|> 1, y = 0, ¦z¦<∞}$. The shear modulus of the non-homogeneous half-space is assumed in the following form μ = μ₀(1 + α₁x)² (1 + β₁y)², where α₁, β₁ and μ₀ are constants. Here x, y and z are referred to a rectangular coordinates system.