Advanced Applications for Laminated Doubly-Curved Shells with Variable Curvatures

The paper aims to describe laminated composite doubly-curved shells and panels with variable radii of curvatures using differential geometry. In this way the geometry of the shell or panel is described mathematically through certain predefined parameters that depend on the geometry under consideration. The mechanical model is based on the well-known Carrera Unified Formulation (CUF) with the curvature effect included in the formulation. Furthermore, the theoretical model developed by the authors allows to consider variable mechanical properties along the shell surface and variable shell thickness (according to a given smooth function). In addition, complete revolution shells are defined as special cases of panels by enforcing the kinematical and physical compatibility conditions at the closing meridian. The solution is given in terms of displacement parameters using two advanced theoretical approaches: the equivalent single layer and the layer-wise approach. It is a very well-known fact that collocation methods (known also as mesh-less or mesh-free methods) have some limitations in treating special problems in engineering, since they can only deal with regular geometries. At the same time one of the most important features of these techniques is connected to their high accuracy and stability for solving partial differential systems of equations. It could be of interest for some applications to use collocation methods in order to solve a certain numerical problem when distorted geometry and material or load discontinuities are taken into account. Thus, the governing partial differential system of equations for laminated composite doubly-curved shells and panels is solved by using the Generalized Differential Quadrature (GDQ) method and related ones. The authors employ both the free vibration analysis and the static analysis with the recovery procedure for evaluating the through the thickness strain and stresses at each point of the 3D solid shell for these advanced engineering problems. The accuracy of the present technique is verified through several comparisons with analytical and numerical finite element models.