A tri-material elastodynamic solution for a transversely isotropic full-space

Abstract

A linear elastic full-space composed of an upper half-space, a lower half-space and a layer of three different transversely isotropic materials under an internal load is considered. The axes of symmetry of the different regions are assumed to be normal to the planar interfaces of the regions and are thus parallel. An arbitrary load in the frequency domain is allowed on a finite patch located at the interface of the upper half-space and the adjacent layer. By means of the complete displacement potentials, the displacements and stresses in the three regions are determined in Fourier–Hankel space in the form of line integrals. The solution can be degenerated to the solution for (i) a full-space under an arbitrary buried load, (ii) a half-space contain a layer bonded to the top of it under an arbitrary surface force, (iii) a half-space under an arbitrary surface load, (iv) a two layer half-space under an arbitrary force applied at the interface of two regions, (v) a half-space under an arbitrary buried force, (vi) a layer of finite thickness fixed at the bottom and under an arbitrary surface load, and (vii) a bi-material full-space under an arbitrary load at the interface of two materials. Examples of the displacements and stresses are obtained numerically and compared to existing solutions.