Contact problem of a graded layer supported by two rigid punches

This paper considers the frictionless contact plane problem of an infinitely graded layer supported by two rigid cylindrical punches and subjected to a concentrated normal force by means of a rigid cylindrical punch. The layer is made of non-homogeneous material with an isotropic stress–strain law with exponentially varying properties. Rather than assuming vanishing displacements or stresses at the bottom of the geometry, this study examines the effect of supports on the graded layer. Using standard Fourier transform and the related boundary conditions, the plane elasticity equations are converted analytically to a system of singular integral equations in which the unknowns are the contact stresses and areas. Gauss–Chebyshev integration formulas are then employed to discretize and solve numerically the derived integral equations. Numerical results for the contact stresses and areas are provided for various dimensionless quantities including material inhomogeneity, distance between the punches, external load and upper and lower punch radii.