The variational-asymptotic method (VAM) [1] is a powerful tool for reducing the dimensionality of structural problems, particularly those involving complex geometries or material gradations. In this study, VAM is employed to derive an accurate two-dimensional (2D) theory for functionally graded piezoelectric shells from the full three-dimensional (3D) piezoelectricity theory [2]. The error estimate of the constructed 2D theory is provided, ensuring its reliability and accuracy. Additionally, the study demonstrates the construction of refined theories for intelligent structures, incorporating shear deformation and rotatory inertia effects (FSDT) [3]. These refined theories enhance the accuracy of predictions for structural behavior, especially in cases involving high frequencies or significant shear effects. The effectiveness of the developed theory is showcased through several analytical solutions to complex problems. The first example involves the forced vibration of a functionally graded piezoceramic cylindrical shell, which is fully covered by electrodes and excited by a harmonic voltage. The second example addresses the forced vibration of a circular elastic plate partially covered by two piezoceramic patches. These analytical solutions provide valuable insights into the behavior of intelligent structures under dynamic loading conditions. Finally, the problem of wave propagation in sandwich structures is investigated to validate the asymptotic accuracy of the refined theory for functionally graded plates. The findings confirm the reliability and accuracy of the VAM-based approach for analyzing complex structures.