Analytical and numerical methods of solution of three-dimensional problem of elasticity for functionally graded coated half-space

In the present paper, a three-dimensional problem of elasticity for homogeneous half-space with gradient coating is considered. Poisson's ratio of the layer is constant and its Young's modulus is a power function of the distance from the surface of the half-space. The surface of non-homogeneous half-space is under tangential loading applied in circular area. Analytical solution is obtained using Fourier integral transform technique. The analytical solution of the problem in continuous dependence of the Young modulus is compared with the solution of the problem in which the inhomogeneous layer is modeled by the package of homogeneous layers. In sub-layers of a package and in substrate is constructed an analytical solution satisfying the conditions of ideal mechanical contact at interlines. Good agreement between results is obtained.

► Three-dimensional problem of elasticity for half-space with gradient coating. ► Young modulus in coating is graded through the thickness by power function. ► We obtain analytical and numerical solution and compare results with good agreement.