Higher-Order Theories for Structural Analysis of Doubly-Curved Shells with Variable Mechanical Properties

The static and dynamic behavior of several shell structures is affected by their mechanical properties. In particular, the natural linear frequencies can be subjected to a considerable variation by placing the reinforcing fibers along curvilinear paths or assuming variable thickness in the whole domain. Similarly, if a static problem is considered, the stress and strain profiles along the thickness of the structure, as well as the three-dimensional displacements, can show different trend varying the fiber orientation. Therefore, the mechanical behavior of doubly-curved structures shows more and more changes combining this kind of layers, characterized by variable properties, with classic orthotropic plies or with a soft-core. Nevertheless, the use of such laminated composite materials does not allow to employ the well-known first-order shear deformation shell theories anymore due to the strong anisotropic behavior. Hence, higher-order Equivalent Single Layer formulations and Layer-Wise models have to be introduced for this purpose. In the same way, the geometric parameters are assumed variable in each point of the domain. The study of doubly-curved shells with variable radii of curvature and variable thickness can take place once the geometric description is performed accurately by using the differential geometry principles. In order to solve numerically all these problems, the Generalized Differential Quadrature method is introduced. Several applications and numerical results are shown to exhibit the accuracy of the present technique.