Assessment of the sampling surfaces formulation for thermoelectroelastic analysis of layered and functionally graded piezoelectric shells

ABSTRACT The article focuses on the implementation of the sampling surfaces (SaS) concept for the three-dimensional (3D) coupled steady-state thermoelectroelastic analysis of layered and functionally graded (FG) piezoelectric shells subjected to thermal loading. The SaS formulation is based on choosing inside the nth layer In, not equally spaced SaS parallel to the middle surface, in order to introduce the temperatures, electric potentials, and displacements of these surfaces as basic shell variables. Such choice of unknowns with the consequent use of Lagrange polynomials of degree In − 1 in the assumed distributions of the temperature, electric potential, displacements, and mechanical properties through the thickness of the layer leads to the robust FG piezoelectric shell formulation. The SaS are located inside each layer at Chebyshev polynomial nodes, which permits one to minimize uniformly the error due to the Lagrange interpolation. As a result, the SaS formulation can be applied efficiently to deriving the analytical solutions for FG piezoelectric shells, which asymptotically approach the 3D exact solutions of thermoelectroelasticity as the number of SaS tends to infinity.