A Hermitian Cⁿ finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

Abstract

Within the framework of the consistent couple stress theory (CCST), we develop a Hermitian Cn (n = 1, 2) finite cylindrical layer method (FCLM) for carrying out the three‐dimensional (3D) analysis of the size‐dependent buckling and free vibration behaviors of simply supported, functionally graded (FG) piezoelectric cylindrical sandwich microshells. The microshells of interest are placed under closed‐circuit surface conditions and subjected to axial compression and electric voltages. We derive a 3D weak formulation based on Hamilton's principle for this study. In the resulting formulation, the microshell is artificially divided into nl microlayers, with the elastic displacement components and the electric potential selected as the primary variables. By incorporating a layer‐wise kinematic model into our weak formulation, we develop a Hermitian Cn FCLM, which can be used for analyzing FG piezoelectric cylindrical sandwich microshells. Each primary variable is expanded as a double Fourier series in the in‐surface domain and is interpolated in the thickness direction using Hermitian Cn polynomials. The accuracy and the convergence rate of our Hermitian Cn FCLMs are validated by comparing the solutions they produce for FG piezoelectric cylindrical macroshells and FG elastic cylindrical microshells with the relevant exact and approximate 3D solutions which have been reported in the literature. The material length scale parameter of our FCLMs is set at zero in the comparison made with the FG piezoelectric macroshells. In contrast, the piezoelectric and flexoelectric effects are ignored in the comparison made with the FG elastic microshells. The impact of some essential factors on the critical load, critical voltage, and natural frequency of simply supported FG piezoelectric cylindrical sandwich microshells is assessed. The important factors are identified as piezoelectricity, flexoelectricity, the material length scale parameter, the inhomogeneity index, the radius‐to‐thickness ratio, the length‐to‐radius ratio, and the magnitude of the applied voltage and the applied load.