Higher-order static and free vibration analysis of doubly-curved FGM sandwich shallow shells

Plenty of research papers are available on the static and free vibration analysis of single-layer FG shells, however, literature on the analysis of FGM sandwich shells of double curvature is limited. Especially, the authors have not found any paper on the analysis of hyperbolic and elliptical paraboloid FGM sandwich shells. Therefore, FGM sandwich shallow shells with double curvature are analyzed in this study for the static and free vibration conditions. Face sheets of sandwich shells are made up of functionally graded material whereas the core is made up of isotropic material. A functionally graded material considered herein is a combination of alumina and aluminum. Sandwich shallow shells on rectangular planform are modeled using various equivalent single-layer shell theories via unified formulation considering the effects of shear deformation and rotary inertia. Different shell theories recovered from the present unified formulation satisfy the transverse shear stress-free conditions on the lower and upper surfaces of the shell. Hamilton's principle is applied to the present unified formulation for establishing equations of motion. Solutions to free vibration and static problems of simply-supported sandwich shells are obtained using Navier's technique. The numerical results of frequencies, displacements, and stresses are obtained for various types of shells, different sandwich schemes, different values of the power-law factor, and radii of curvature. The results available in the literature are used for the comparison of the present results and found in good agreement with those. However, many new and useful results are also reported in this paper for the reference of readers.