Three-dimensional vibration analysis of layered and functionally graded plates through sampling surfaces formulation

The paper deals with a recently developed method of sampling surfaces (SaS) and its implementation for the three-dimensional (3D) free vibration analysis of layered plates with embedded functionally graded (FG) layers. The SaS method is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the plate in order to introduce the displacements of these surfaces as basic plate variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In-1 in the assumed distributions of the displacements and mechanical properties through the thickness of the layer leads to the robust FG plate formulation. The SaS are located inside each layer at Chebyshev polynomial nodes that makes it possible to minimize uniformly the error due to the Lagrange interpolation. As a result, the SaS formulation can be applied efficiently to obtaining the analytical solutions for layered and FG plates, which asymptotically approach the 3D exact solutions of elasticity as the number of SaS tends to infinity.