Three-Dimensional Exact Analysis of Functionally Graded Laminated Composite Plates

A paper focuses on the implementation of the method of sampling surfaces (SaS) to three-dimensional (3D) exact solutions for functionally graded (FG) laminated composite plates. According to the SaS method, we introduce inside the nth layer I-n not equally spaced SaS parallel to the middle surface of the plate in order to choose the displacements of these surfaces as basic plate variables. This permits the presentation of the proposed FG laminated plate formulation in a very compact form. It is important that the SaS are located inside each layer at Chebyshev polynomial nodes. This fact allows one to uniformly minimize the error due to Lagrange interpolation, i.e. the use of Lagrange polynomials of high degree becomes possible. As a result, the SaS method can be applied efficiently to 3D exact solutions of elasticity for FG laminated plates with a specified accuracy utilizing the sufficient number of SaS.