Analytical solutions of stresses in functionally graded piezoelectric hollow structures

Analytical studies for piezoelastic behaviors in functionally graded piezoelectric material (FGPM) hollow cylindrical and spherical structures, subjected to mechanical loading and electric excitation, are presented. For the case that the mechanical, piezoelectric and dielectric properties of the material obey an identical power law in the radial direction, analytical solutions for displacement, stresses and electric potential in the FGPM hollow cylindrical and spherical structures are determined by using the infinitesimal theory of piezoelasticity. Some useful discussions and numerical examples are also presented to show the significant influence of material inhomogeneity, and adopting a certain value of the inhomogeneity parameter β can optimize the piezoelastic responses. This will be of particular importance in modern engineering design.