Static and Dynamic Analyses of Doubly-Curved Composite Thick Shells with Variable Radii of Curvatures

Shell structures have an important role in many engineering fields. A shell is a 3D solid that can be studied with the classical theory of elasticity. Some simplifications have to be introduced to reduce the computational cost. There are three different ways to deal with anisotropic shell structures: 3D elasticity, Equivalent Single Layer (ESL) and Layer Wise (LW) approaches. The last two theories have their own roots in the Carrera Unified Formulation (CUF), which is capable of studying several higher-order displacement fields taking the kinematic expansion order as a free parameter for the representation of any higher order formulation [1-4]. These theoretical models allow to consider variable mechanical properties on the shell surface and variable thickness. The geometric description of the shells is carried out using differential geometry. Thus, the geometry of the structure is described mathematically through certain predefined parameters that depend on the geometry under consideration. In this study innovative materials, such as Functionally Graded (FG) and Carbon Nanotube (CNT) reinforced composites, are investigated. Moreover, a new class of fiber reinforced laminated composites defined by a curvilinear path of the fibers is examined. The so-called Variable Angle Tow (VAT) placement permits to design composite structures with the desired stiffness. Different loads are taken into account. Several surface load distributions, the effect of the Winkler-Pasternak foundation, seismic actions, as well as concentrated forces, can be included in the proposed approach. The mathematical problem, governed by a partial differential system of equations, is solved using a strong formulation approach, named Generalized Differential Quadrature (GDQ) method [1-4]. Both the free vibration analysis and the static analysis with the recovery procedures for estimating strains and stresses at each point of the 3D solid shells, are worked out. Several applications and numerical results to exhibit the accuracy of the present technique are shown.