Investigation on the Structural Response of Plates and Shells with Variable Mechanical Properties: Modeling of the Damage

The structural response of plates and shells in terms of static and dynamic behavior is highly affected by the variability of the mechanical properties within the reference domain. It should be noted that in the literature several approaches have been introduced to define variable mechanical properties. For instance, the class of graded materials and of laminated composites reinforced by curvilinear fibers can be taken as a reference. In the current work, an innovative way to describe the variability of the mechanical properties is presented. A proper mathematical formulation is developed to define linear, sine-wave, and exponential variations of the elastic constants of the composites. In particular, two-dimensional laws, such as the Gaussian and the elliptic functions, are taken into account to model the damage of plates and shells. In other words, the damage of a structure can be seen as a rapid and concentrated variation of the mechanical properties of the elastic medium. Several parametric investigations are performed to analyze the effect of the damage parameters (intensity and size) on the structural response. The solution is achieved numerically by means of the Generalized Differential Quadrature (GDQ) method. The structural model is developed in the framework of a Unified Formulation which allows to consider in an efficient manner several higher-order theories. Finally, it should be pointed out that the description of the doubly-curved geometries with variable radii of curvature is obtained by using the well-known differential geometry.