The paper is to present an overview of various semi-analytical numerical methods for quasi-three-dimensional (3D) analyses of laminated composite and multilayered (or sandwiched) functionally graded elastic/piezoelectric materials (FGEMs/FGPMs) plates and shells with combinations of simply-supported, free and clamped edge conditions. This review introduces the development of various semi-analytical numerical methods incorporating 3D analytical approaches (i.e., the state space and asymptotic ones) with numerical techniques (i.e., the differential quadrature, meshless reproducing kernel and finite element ones), and their applications to the analyses of plates and shells made of advanced materials, such as the fiber-reinforced composite materials, FGEMs and FGPMs, and carbon nanotube-reinforced composite materials. Two micromechanical schemes (i.e., the rule of mixtures and Mori-Tanaka scheme) used to estimate the effective material properties of functionally graded structures are presented. The strong and weak formulations of the 3D piezoelectricity theory and their corresponding possible edge conditions for circular hollow cylinders are presented for the illustration purposes. A comparative study of the results obtained by using assorted semi-analytical numerical methods is undertaken.
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