Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field

This paper presents analytical solutions for hygrothermal stresses in one-dimensional functionally graded piezoelectric media. The media are subjected to an external constant magnetic field and could be rested on a Winkler-type elastic foundation. The material properties are assumed to vary through the thickness according to a power-law with different non-homogeneity indices. The governing equations including the Lorentz force effect are written in a unified form that can be used for one-dimensional functionally graded piezoelectric media in Cartesian, cylindrical, and spherical coordinates. The moisture concentration and temperature distributions along the thickness of one-dimensional media are achieved by solving the steady state Fickian moisture diffusion and Fourier heat conduction equations. The two coupled ordinary differential equations in terms of displacement and electric potential are solved analytically. The numerical results illustrate the effects of hygrothermal loading, medium geometry, non-homogeneity indices, external magnetic field, and elastic foundation on the behavior of one-dimensional piezoelectric media. For a uniform temperature rise, the influence of temperature-dependency of material properties on the electromechanical responses is investigated as well. At last, the results are verified with those reported in the literature.