Coupled thermoelectroelastic stress analysis of piezoelectric shells

The paper deals with the sampling surfaces (SaS) method proposed by the authors and its implementation for the three-dimensional (3D) coupled steady-state thermoelectroelastic analysis of laminated 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 of the shell in order to introduce the temperatures 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 thickness direction for each layer permits the presentation of the laminated piezoelectric shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that allows one to minimize uniformly the error due to the Lagrange interpolation. As a result, the SaS formulation can be applied efficiently to derivation of the analytical solutions for laminated piezoelectric shells, which asymptotically approach the 3D exact solutions of thermoelectroelasticity as the number of SaS goes to infinity.