Hygro-thermo-electro-elastic response of a functionally graded piezoelectric cylinder resting on an elastic foundation subjected to non-axisymmetric loads

Abstract

In this paper, the general theoretical analysis of a thick-walled cylinder made of functionally graded piezoelectric materials subjected to a non-axisymmetric hygro-thermo-electro-mechanical loading is presented. The transversely isotropic and non-homogeneous cylinder is rested on a Winkler-type elastic foundation on the outer surface. All mechanical, hygrothermal and electrical properties are assumed to obey a power-law function in the radial direction with different non-homogeneity constants. Non-axisymmetric moisture concentration and temperature distributions are assumed to be a function of radial and circumferential directions and are obtained by solving two-dimensional and steady-state Fourier heat conduction and Fickian moisture diffusion equations. By substituting constitutive equations into electrical and mechanical equilibrium equations, three second-order non-homogeneous partial differential equations in terms of electric potential and mechanical displacements are derived. The separation of variables and complex Fourier series method are employed to solve heat conduction, moisture diffusion and Navier equations. Numerical results clearly illustrate the effects of hygrothermal loading, elastic foundation and non-homogeneity constants on hygro-thermo-electro-elastic behavior of the functionally graded piezoelectric cylinder. It is observed that non-homogeneity constant, hygrothermal loading and elastic foundation have considerable effects on displacements, stresses and electric potential distributions.