Semi-Analytic Method for a Tri-Material Transversely Isotropic Full-Space in Frequency Domain

A linear elastic transversely isotropic full-space containing three different regions, which are an upper half-space, a lower half-space and a layer in between is considered in such a way, each region contains different material. The axes of symmetry of different regions are assumed to be normal to the interface of the regions and thus parallel. An arbitrary load in frequency domain is applied on an arbitrary patch located at the interface of the upper half-space and its underneath layer. Integral formulations are presented for the determination of the displacements and stresses in all regions. By means of the complete displacement potentials introduced by Eskandari-Ghadi (2005), Fourier series in circumferential direction and Hankel transform in radial direction, the displacements and stresses are determined in Fourier-Hankel space. Then, the displacements and stresses at any point are given in the line integral form. The solution is numerically evaluated for: (i) a half-space under an arbitrary surface load, (ii) a half-space under an arbitrary buried force, (iii) a half-space fixed at the top and under an arbitrary buried force, (iv) a half-space containing a layer bonded to the top of a half-space under an arbitrary force applied at the interface of two regions, (v) a full-space under an arbitrary load in it, (vi) a bi-material full-space under an arbitrary force applied at the interface of two half-space, and (vii) a layer of finite thickness fixed at the bottom and under an arbitrary surface load. To confirm the accuracy of the numerical evaluation of the integrals involved, some of the results are compared with existing solutions.