Bending analysis of FGS doubly-curved shallow shells using a new refined kinematic model

This paper focuses on the development of an analytical model based on a new refined parabolic shear deformation theory (RPSDT) to address the static bending behavior of functionally graded sandwich (FGS) shallow shells with double curvature under transverse mechanical loading. The novelty of the proposed theory arises from the introduction of an improved kinematic model in which the transverse displacement is expressed as the sum of bending and shear components. This formulation is designed to reduce the number of unknowns and governing equations, and therefore exactly satisfies the shear stress-free boundary conditions on the upper and lower shell surfaces, thus eliminating the need for any shear correction factors. It provides a unified solution to the bending problems of doubly-curved shallow shells with varying geometrical properties, without the need to adjust the formulations and solution procedures. The sandwich shell structures consist of a homogeneous ceramic core and two FG face sheets, which have broad application in various fields of engineering and defense technology. The mechanical properties of FG layers are assumed to vary gradually through the thickness direction, depending on a simple powerlaw distribution of the volume fractions of the constituents. The shell governing differential equations are derived using the principle of virtual work and are analytically solved by applying the Navier method for simply supported boundary conditions. The accuracy of the proposed theory is confirmed by the good agreement between the present predictions and the corresponding solutions found from the conventional shear deformation shell theories. From this investigation, it can be concluded that the present model, has proven to be computationally efficient and highly accurate in predicting the bending behavior of FGS shells.