Two-dimensional steady-state general solutions for isotropic hygrothermoelastic media with applications

Abstract

Five two-dimensional steady-state general solutions for isotropic hygrothermoelastic media are established in this article. Firstly, four general solutions which are expressed in one function can be obtained based on the differential operator theory. Then, because of the Almansi’s theorem and appropriate transformation, the four general solutions can be converted to another four general solutions expressed in two harmonic functions. Finally, the more complete general solution expressed in four harmonic functions is obtained by superposition principle. As a checking example, based on the received complete general solution, the Green’s function for a line heat source combined with moisture source in the interior of infinite hygrothermoelastic plane is obtained. In addition, the Green’s function for a line heat source combined with moisture source on the surface of semi-infinite plane is obtained.