Thermo-electro-elastic analysis of functionally graded piezoelectric shells of revolution: Governing equations and solutions for some simple cases

In this article, the three-dimensional multi-field equations of functionally graded piezoelectric (FGP) shells of revolution under thermo-mechanical loading are derived. First, the heat conduction equation for an FGP is derived and then, the displacement equations are developed considering thermal effects. The coupling is one-way, i.e. the temperature field affects the displacements and stresses while the back influence of the displacement on the temperature is disregarded. The Hamilton's principle is used to derive the governing equations of motion, in presence of system rotation effects, for thick shells of revolution with variable thickness and arbitrary curvature. Material properties are assumed to vary in various directions according to an arbitrary function. For the sake of simplicity and verification of derivation, the heat conduction and governing equations of motion have been reduced for a functionally graded piezoelectric cylindrical shell under thermal loading. In order for the general equations to be verified, two simple examples are investigated, i.e. thermal stresses in hollow cylinder and sphere. Correctness and generality of the present results can be justified given the capability of these equations for different geometries and material properties.