An exact solution for functionally graded piezoelectric laminates in cylindrical bending

In the present paper, the exact solutions of a simply supported functionally graded piezoelectric plate/laminate under cylindrical bending are derived. With similar derivation procedure as that used for Stroh formalism, the eigenrelation and general solutions for the problems can be expressed in very concise forms, which are convenient for further treatments of both analytic and numerical studies. The exact solutions can be served as benchmarks to verify and improve various approximate theories and numerical methods. To show the influence of material gradients, numerical examples based on the exact solutions are given, and some properties of the mechanical and electric responses of the plates under mechanical and electrical forces are discussed.