Static and Vibration Analysis of Laminated Sandwich Hyperbolic and Elliptical Paraboloids

This article uses refined higher-order shell theories to generate higher-order closed-form solutions for the static and vibration analysis of laminated sandwich hyperbolic and elliptical paraboloids, which are scarcely addressed in existing literature. A generalized theory is employed to formulate several equivalent single-layer shell models. Most refined and classical shell theories can be theoretically unified because a theory is independent of the selection of the shearing stress function. The theory generates an appropriate distribution of transverse shear stresses through the thickness of the shell and does not require a problem-dependent shear correction factor. The governing equations of motion and associated boundary conditions are derived using Hamilton’s principle. Higher-order Navier-type closed-form solutions are obtained for simply supported boundary conditions. For laminated composite and sandwich paraboloids, nondimensional results are presented in tabular and graphical forms. The study emphasizes the impact of shell curvature, thickness ratio, and layups on the deflection, stresses, and natural frequencies of laminated and sandwich paraboloids. A comparison is made between the results of several refined shell theories and, if available, with results from previous publications. A major highlight of the present research is the first-time presentation of numerical results for laminated and sandwich paraboloids, establishing new benchmarks.