Higher-Order Theories for the Structural Analysis of Doubly-Curved Shells and Panels Made of Innovative Materials

The static and dynamic behavior of shell structures is influenced considerably by the use of innovative materials such as functionally graded materials and carbon nanotubes. Similarly, the manufacture of laminated shells with a soft core or reinforced by curvilinear fibers implies remarkable effects both on the free vibrations and on the stresses and strains of these structures. Nevertheless, the First-Order Shear Deformation Theory turns out to be inadequate when the exact mechanical behavior has to be gotten. Therefore, a higher-order displacement field is needed in order to study properly these structures. The present approach is based on the Carrera Unified Formulation (CUF) and allows to consider variable mechanical properties on the shell surface and variable thickness. Both Equivalent Single Layer and Layer-Wise models are taken into account since the classical theory of elasticity is too burdensome from the computational point of view. Several surface load distributions, as well as concentrated forces, can be included in the current approach. The partial differential system of governing equations for laminated composite doubly-curved shells and panels with variable radii of curvature is solved by using the Generalized Differential Quadrature (GDQ) method, whereas the geometry of these structures is described mathematically through the differential geometry. Several numerical applications are presented to show the accuracy of the current technique for the resolution of various dynamic and static problems. In particular, the recovery procedure based on the three-dimensional equilibrium equations is employed to estimate the strain and stress profiles at each point of the 3D solid when the static analysis is performed.