A study of Greens functions for three-dimensional problem in thermoelastic diffusion media

Abstract

The purpose of the present paper is to study the three-dimensional general solution and Green’s functions in transversely isotropic thermoelastic diffuson media for static problem. With this objective, two displacement functions are introduced to simplify the basic equation and a general solution is then obtained by using the operator theory. Based on the obtained general solution, the three- dimensional Green’s functions for a study point heat source on the apex of a transversely isotropic thermoelastic cone are constructed by four newly introduced harmonic functions. The components of displacement, stress, temperature distribution and mass concentration are expressed in terms of elementary functions and are convenient to use. When the apex angle equals to , then we obtain the solution for semi-infinite body with a surface point. From the present investigation, a special case of interest is deduced to depict the effect of diffusion on components of stress and temperature distribution. Key words: Thermoelastic diffuson media, Green’s function, transversely isotropic.