An improved mathematical model for static and dynamic analysis of functionally graded doubly-curved shells

In the present paper, an improved mathematical model is developed based on a new refined sinusoidal shear deformation theory with only four unknown variables for static bending and dynamic analysis of functionally graded (FG) doubly-curved shell structures. The proposed higher-order shell theory yields an adequate distribution of the transverse shear strains through the thickness by satisfying the tensile-free boundary conditions at the top and bottom surfaces of the shell. The mechanical properties are supposed to change gradually through the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The shell equilibrium equations for this study are derived from Hamilton's variational principle and subsequently solved for simply supported boundary conditions by using the Navier solution methodology. However, this improved model is substantiated by several numerical results for the mechanical behavior of FG shell structures having different geometrical configurations, namely, cylindrical, spherical, hyperbolic paraboloid, and elliptical paraboloid shapes, which were compared, and successfully converged with the corresponding results found by alternative higher-order shear deformation models to validate the accuracy of the proposed theory.