A general solution for the receding contact problem of a functionally graded layer resting on a Winkler foundation

TLDR: In this paper, the receding contact problem of functionally graded (FG) layer resting on a Winkler foundation is considered and a general formulation is obtained using elasticity theory and Fourier integral transform.

Abstract: In this paper, the receding contact problem of functionally graded (FG) layer resting on a Winkler foundation is considered. It is assumed that the shear modulus of the layer change functionally along the depth whereas Poisson ratio remains constant. Arbitrary concentrated loads by means of arbitrary rigid punches are applied to the top of the layer. The problem is considered as a plain strain problem. A general formulation is obtained using elasticity theory and Fourier integral transform. Obtained formulation is valid for both symmetric and asymmetric systems. A parametric study is carried out to investigate the effect of material properties and loading on contact distances and contact pressures. It is found that, increasing rigidity of the bottom of the FG layer compared to the top of the FG layer, the contact distances between the circular punch and FG layer contact surface decreases whereas maximum contact pressure increases. In addition, placement of the rigid punches has an effect on the contact distances and contact pressures.