Mechanical Behavior of Damaged Laminated Composites Plates and Shells: Higher-Order Shear Deformation Theories

A higher-order structural model based on a Unified Formulation is employed to investigate the mechanical behavior of laminated composite plates and shells with variable elastic properties. The variability in hand is obtained by means of peculiar mathematical laws that allow to describe linear, sine-wave, and exponential variations of the mechanical properties. In addition, two-dimensional functions are also introduced to define more complex variations. For instance, by choosing the Gaussian function is possible to model a damage that can affect a shell structure. In fact, a generic damage within the reference domain can be modeled by setting properly the parameters of the distribution at issue and imposing an abrupt deterioration of the engineering elastic constants. In particular, the size and intensity damage effects on the structural response are investigated through a set of parametric analyses. Similar considerations can be extended to the case of an ellipse shaped function introduced for the same purpose. Since a numerical analysis is performed, the governing equations are solved by the Generalized Differential Quadrature (GDQ) method due to its accuracy and stability features. The same numerical approach is used to evaluate the geometric properties of the doubly-curved surfaces in hand, which denote the reference domains. In addition, it should be specified that the differential geometry provides all the analytical definitions for an accurate description of these shells with variable radii of curvature.