The frictionless axial interaction of a rigid disk with a two-layered functionally graded transversely isotropic medium

Abstract

A rigorous formulation is presented for the frictionless axisymmetric interaction of a rigid disk with a two-layered inhomogeneous medium. The materials are considered to be linearly elastic transversely isotropic materials and the exponential variation of properties along the depth of each layer is assumed in order to model the effect of inhomogeneity. The disk is considered to be at the top of the coating layer or embedded at the interface of the two media. By satisfying the boundary conditions, the problem leads to a dual integral equation and is reducible to a Fredholm integral equation of the second kind which is solved numerically. The numerical solutions survey the effect of material inhomogeneity through two special cases: a functionally graded coating on a homogeneous transversely isotropic half-space and a homogeneous transversely isotropic coating on an inhomogeneous half-space. The accuracy of the numerical solutions is verified by comparison with the corresponding solution for homogeneous material in the literature.

Three-dimensional dynamic Green’s functions in exponentially graded transversely isotropic tri-material composites

“…Akbari et al [31] examined the static response of exponentially graded transversely isotropic substrate-coating system composed of an exponentially graded transversely finite layer perfectly bonded to exponentially graded transversely isotropic half-spaces. Shahmohamadi et al [32] investigated the smooth interaction of a rigid circular disk with an exponentially graded transversely isotropic coating-substrate system. In the context of functionally graded coating-substrate composite systems, several studies may be found in the literature [33][34][35][36][37].…”

Rocking forced displacement of a rigid disc embedded in a functionally graded transversely isotropic half-space

“…It is assumed that the shear modulus of the graded interfacial layer varies as exponential function along the thickness direction. Shahmohamadi et al [19] presented a rigorous formulation for the frictionless axisymmetric interaction of a rigid disk with a two-layered inhomogeneous medium under vertical load. They considered materials are linear elastic transversely isotropic, and the exponential variation of properties along the depth of each layer was assumed in order to model the effect of inhomogeneity.…”