A new approach to three-dimensional exact solutions for functionally graded piezoelectric laminated plates

A paper presents the sampling surfaces (SaS) method and its implementation for the three-dimensional (3D) exact analysis of functionally graded (FG) piezoelectric laminated plates. According to this method, we introduce inside the nth layer In not equally spaced SaS parallel to the middle surface of the plate and choose displacement vectors and electric potentials of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the thickness direction for each layer leads to a very compact form of governing equations of the FG piezoelectric plate formulation. This fact gives an opportunity to derive the 3D exact solutions of electroelasticity for thick and thin FG piezoelectric laminated plates with a specified accuracy utilizing a sufficient number of SaS, which are located at interfaces and Chebyshev polynomial nodes.