A high order theory for functionally graded piezoelectric shells

A high order theory is presented to examine the electromechanical behavior of piezoelectric generic shells with graded material properties in the thickness direction. Different types of charge equations, depending upon whether the driving signal of piezoelectrics is free charge or electric voltage, have been derived. The obtained equations can be readily reduced to typical structures, such as beams, plates and circular cylindrical shells. The high order theory has been used to study the sensing and actuating behavior of a simply supported inhomogeneous piezoelectric circular cylindrical shell and, for comparison and validation purposes, a homogeneous shell. Comparison between the obtained numerical results to those available exact solutions for homogeneous shell shows that the developed theory is accurate. The effects of graded material properties on the piezoelectrically induced displacements, stresses, electric potential and electric displacements distributions are also quantified, clearly showing the advantage of functionally graded piezoelectrics over homogeneous ones in terms of the usages as sensors and actuators