Static and Free Vibration Analyses of Doubly Curved Composite Sandwich Panels with Soft Core Based on a New Three-Layered Mixed Theory

Abstract

In this paper, a closed-form solution of static problems and free vibrations of a doubly curved sandwich shell with flexible core based on a newly developed three-layered high-order sandwich panel theory (mixed theory) is presented for the first time. In this theory, displacements and transverse stresses at the interface of the core and face sheets are primary unknowns. Linear distribution of transverse normal and shear stresses through the core thickness is considered in the present model. This model accounts for non-linear distribution of displacements through the core thickness. Hamilton's principle is employed to obtain equations of motion. The formulation includes Donnell's shallow shell theory. In the case of static problems and free vibrations, the results of the present model are validated by a three-dimensional elasticity solution and analytical and numerical results published in the literatures. A parametric study is also included in this paper to investigate the effects of radius of curvature, thickness, and flexibility of the core. New results for thin and thick spherical and cylindrical sandwich shells are established, which can be considered as a basic reference for future investigations.