Green's Functions for a Steady Heat Source in a Semi-Infinite Transversely Isotropic Elastic Solid : The Case of 2-ple and 3-ple Roots for the Characteristic Roots of the Governing Differential Equations

Abstract

Green's functions reported in the previous paper were the solutions for single root in the characteristic equation of a semi-infinite transversely isotropic thermoelastic solid with a steady heat source. The functions were expressed in a Cartesian coordinate system. In this paper, Green's functions for 2-ple and 3-ple roots in the characteristic equation of a semi-infinite transversely isotropic thermoelastic solid with a steady heat source are presented. A different term from the functions for single root in the characteristic equation appears in these solutions. For thermal boundary conditions, both cases of adiabatic condition and the temperature prescribed on the boundary plane are treated, and for the stress and the displacement boundary conditions the following three cases are treated ; (1) stresses are free, (2) all components of displacement are fixed, (3) only displacement in the normal direction is fixed.