Contact mechanics of a functionally graded orthotropic layer

In this study, the continuous contact problem of a functionally graded (FG) orthotropic layer resting on a rigid foundation is investigated while neglecting frictional effects. A point load is applied to the FG orthotropic layer through a rigid punch from its top surface. The weight effects of the FG orthotropic layer are also considered in the solutions. Orthotropic material parameters and density are assumed to vary exponentially in the direction of the layer height. Stress and displacement expressions are derived using elasticity theory and integral transformation techniques. A singular integral equation is formulated based on the boundary conditions of the problem. This integral equation is numerically solved for cylindrical and flat punch profiles using the Gauss-Chebyshev integration method. The study's results include dimensionless contact stresses under the punch, contact lengths, the critical separation load, and the critical separation point where the first separation occurs between the FG orthotropic layer and the rigid foundation. Additionally, normal stresses along the symmetry axis in the FG orthotropic layer, shear stresses along a selected section near the symmetry axis, and normal stresses along the x-axis on the bottom surface of the FG orthotropic layer are obtained, depending on various parameters and different orthotropic material types.