Exact solution of a compositionally graded piezoelectric layer under uniform stretch, bending and twisting

Electromechanical responses of compositionally graded piezoelectric layers are analysed. The layers consist of polycrystalline piezoelectric ceramics poled along the thickness direction, and thus exhibit material symmetry of a hexagonal crystal in class 6mm. Two cases for layers (i) covered by surface electrodes and (ii) without surface electrodes are considered. Analytical solutions are exact in Saint Venant's sense for both cases. However, solutions are obtained for layers subjected to uniform mechanical loads, including stretch, bending and twisting. Numerical results to show the effects of different compositional gradients are presented.