Piezothermoelastic Solutions of Functionally Graded Piezoelectric Shells

The solutions of piezothermoelastic responses of functionally gradient piezoelectric hollow circular cylinders are developed. A functionally gradient piezoelectric shell is divided to a number of layers through its thickness like a composite laminate, each layer with constant material properties. The piezothermoelastic solutions are deduced. The integration constants in the solutions are determined according to the continuity conditions between layers. The solutions are approximate and converge to the exact solutions when the number of layers increases. The solutions can deal with some or all thermo-electro-mechanical multi-fields loadings. This method solved three-fields coupling problems and set up a simple solution, which is independent of the distribution functions of material properties through thickness.