Electroelastic analysis of functionally graded piezoelectric material beams

A general two-dimensional solution is proposed for functionally graded piezoelectric material beams with arbitrary graded material properties along the beam thickness direction. The beam is subjected to normal and shear tractions of polynomial form on the top and bottom surfaces, while the end boundary conditions can be cantilever, simply supported or rigidly clamped. The Airy stress function and the electric potential are expressed in a finite power series, and the corresponding recurrence-governing equations are obtained. Explicit expressions of analytical solution to a specific example for a cantilever beam are obtained to demonstrate the usefulness of the proposed general solution technique. The proposed solution method will be useful in analyzing functionally graded piezoelectric structures with arbitrary variations of material properties, and the obtained results can serve as a basis for establishing simplified theories and numerical methodology of functionally graded piezoelectric material beams.