A General Formulation Based Based on Higher-Order Theories for the Static and Dynamic Analysis of Doubly-Curved Structures with Variable Mechanical and Geometrical Properties

The need of a specific static or dynamic behavior has led to the study of doubly-curved structures with specific mechanical configurations. In fact, this kind of structures, which are already well-known for their excellent performances, can show considerably different structural responses, in terms of both natural frequencies and stress and strain profiles along the thickness, when a mechanical property variation is taken into account. Such variations can be obtained by assuming variable engineering constants or by altering the fiber orientation, if an orthotropic fiber-reinforced composite is considered. In particular, the Variable Angle Tow placement concept allows to arrange the reinforcing fibers along curvilinear paths. In the same way, the geometric parameters are assumed variable in each point of the domain. In fact, by using the differential geometry is possible to study several structures with variable radii of curvature and variable thickness. In addition, the mechanical behavior of doubly-curved structures can be considerably different if one layer with variable properties is combined with other orthotropic plies or with a softer core. Nevertheless, the well-known first-order shell theories cannot represent correctly the mechanical behavior of such laminated composite structures. Hence, higher-order formulations have to be introduced for this aim. The validation of this approach is performed through several applications. In particular, the numerical solution obtained by using the Generalized Differential Quadrature appears to be accurate and stable.