A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

This paper presents a layerwise finite element formulation for dynamic analysis of functionally graded material (FGM) sandwich shell in thermal and non-thermal environments. The layerwise theory used in this work is based on the first-order shear deformation theory (FSDT) for each layer satisfying the displacement continuity at layer interface. Two configurations of FGM sandwich shells are considered, the first with FGM facesheet and homogenous core, and the second having homogenous facesheets and FGM core. Effective material properties of the FGM are estimated according to two micromechanical models, namely, Voigt's rule of mixture (ROM) and Mori-Tanaka (MT) scheme. For the shells in thermal environment, a nonlinear temperature distribution in thickness direction is considered and the elastic properties are assumed to be temperature dependent. The results obtained from the proposed formulation are validated with those available in the literature. Natural frequencies obtained from Sanders', Love's and Donnell's shell theories for different geometric and boundary conditions are compared to assess the performance of different shell theories for FGM sandwich shells under non-thermal environment. The effects of volume fraction index, core thickness and temperature gradient on natural frequencies of FGM sandwich shells are investigated. The present formulation is simple, accurate and computationally efficient.