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

Abstract

This paper presents an analytical formulation for deriving the three-dimensional (3D) elastodynamic Green’s functions of functionally graded transversely isotropic tri-material composite under time-harmonic loading. With the aid of a complete set of displacement potentials, Fourier expansions, and Hankel integral transforms, displacement and stress components of 3D point-load, patch-load, and ring-load are obtained in the form of complex-plane infinite line-integrals. By virtue of a reliable and fast numerical scheme, i.e., the contour integration method, they are numerically treated, and its accuracy is achieved by comparison with some special cases. Finally, some numerical results are selected to demonstrate the influences of the material inhomogeneity and vibration frequency on the displacement and stress components. Particularly, the dependency of the stress transfer process at the interface of the mediums on the degree of inhomogeneity is presented, which is of high importance in evaluating the performance of composite materials.