Asymmetric Green's functions for a functionally graded transversely isotropic tri-material

Abstract

• A set of analytical Green's functions for a cross anisotropic inhomogeneous tri-material solid is given. • The response of a graded solid sandwiched between two homogenous transversely isotropic layers is studied numerically. • The analysis of an finite bi-material layer has been given in terms of Green's functions and analyzed numerically. • The results may be used as benchmarks for numerical studies or developing numerical methods like boundary element methods . This paper considers the elastic analysis of a functionally graded transversely isotropic tri-material solid under the arbitrary distribution of applied static loads. Using two displacement potential functions, for three-dimensional point-load and patch-load configurations, Green's functions for displacement and stress components are generated in the form of infinite line-integrals. These solutions are shown to be analytically reducible to the special cases of exponentially graded bi-material, exponentially graded half-space and homogeneous tri-material Green's functions. It also encompasses a functionally graded finite layer on a rigid base with surface loading with two cases of interfacial conditions, rigid-bonded and rigid-frictionless. Finally, for the special case of a functionally graded layer sandwiched between two homogeneous layers, using several numerical displays, the effect of material inhomogeneity on the responses is studied and the accuracy of numerical scheme is verified.