Three-dimensional analytical elasticity solution for loaded functionally graded coated half-space

• The analytic solution of the three-dimensional problem of elasticity is obtained.
• The loading is applied in elliptical region.
• Elastic body is composed of the homogeneous base and gradient coatings.
• The solution method is based on the two-dimensional integral Fourier transform.
• The shear, first principal stress and tensile stress distribution were analysed.

In the present paper, a three-dimensional problem of elasticity of normal and tangential loading of surface of the functionally graded coated half-space is considered. In case when Poisson's ratio is constant and the Young's modulus is a power or exponential function of the distance from the surface of the half-space, analytical solution using Fourier transform is obtained. Stress field due to Hertz contact pressure in an elliptical region are studied as a function of the parameter b/a (where a and b are axes of the contact ellipse) and coating thickness.