Higher-Order Formulations for the Mechanical Analysis of Doubly-Curved Shell Structures Made of Advanced and Innovative Materials

Doubly-curved shells represent the most intriguing elements of the structural and solid mechanics, due to their unique shapes and outstanding mechanical behavior. Nevertheless, the difficulties that can be encountered during their structural analysis are related to these aspects as well. Therefore, the study of structures characterized by variable radii of curvature is still an open topic, as proven by the huge number of papers published in the last decades. For this purpose, many scientists and engineers developed more and more refined approaches able to investigate their mechanical behavior in an accurate manner. The need of advanced methods of analysis is even more evident if innovative constituents and materials are employed. Laminates, Functionally Graded Materials (FGMs), Carbon Nanotubes (CNTs) reinforced media, Variable Angle Tow (VAT) composites, are only few examples of these advanced materials that could require specific structural models to be properly analyzed. A theoretical framework based on Higher-order Shear Deformation Theories (HSDTs) is developed to this aim. The same approach is used to deal efficiently with several kinds of external forces, such as seismic actions, point and line loads, the effect of an elastic foundation, and arbitrary angular velocities. It should be noted that the governing equations cannot be solved analytically, thus a numerical tool based on the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods is developed to obtain and solve the strong and weak formulations of the fundamental systems in hand. This methodology allows obtaining accurate and reliable results, and is employed to solve different kinds of structural issues, such as the evaluation of the natural frequencies, the achievement of the through-the-thickness profiles of stresses and strains, the transient dynamic responses caused by time-depending loads, and the computation of the critical rotating velocities.