Refined and advanced shell models for the analysis of advanced structures.

Structures technology for aerospace systems includes a wide range of component technologies from materials development to analysis, design and testing of the structures. The main improvements in future aircraft and spacecraft could depend on an increasing use of conventional and unconventional multilayered structures. New unconventional materials could be used in the near future: e.g. piezoelectric ones, which are commonly used in the so-called smart structures and functionally graded materials, which have a continuous variation of physical properties in a particular direction. The most of multilayered structures are subjected to different loadings: mechanical, thermal and/or electric loads. This fact leads to the definition of multifield problems. In particular applications, the aforementioned structures appear as two-dimensional and they are known as shells. The advent of new materials in aerospace structures and the use of multilayered configurations has led to a significant increase in the development of refined theories for the modelling of shells. Classical two-dimensional models, which were frequently used in the past, are inappropriate for the analysis of these new structures: their modelling involves complicated effects that are not considered in the hypotheses used in classical models. To overcome these limitations, a new set of two-dimensional models, which employ Carrera’s Unified Formulation (CUF), are presented. The dissertation is organized in three main parts: - the refined and advanced shell models contained in the CUF; - the computational methods used to calculate the solution of differential equations; - the results obtained from the analysis of several problems. In the first part, the different refined and advanced shell models contained in the CUF are presented. The CUF permits to obtain, in a general and unified manner, several models that can differ by the chosen order of expansion in the thickness direction, by the equivalent single layer or layer wise approach and by the variational statement used. These models are here defined directly for the shells, according to different geometrical assumptions. Both the cylindrical and the double-curvature geometries are considered. The constitutive equations of the advanced materials are provided. The constitutive equations for multi-field problems are obtained in a generalized way by employing thermodynamic considerations and they are opportunely rewritten for the case of mixed models. Depending on the variational statement used, one can define the refined theories, that are based on the principle of virtual displacements, and the advanced theories, based upon the Reissner’s mixed variational theorem, in which secondary variables are "a priori" modelled. A complete system of acronyms is introduced to characterize these two-dimensional models. The second part is devoted to the derivation of the governing equations by means of different methods: an analytical method, that is the Navier method, and two approximated numerical methods, that are the Finite Element Method (FEM) and the Radial Basis Functions (RBF) method. The RBF method is based on a meshless approach and it can be considered a good alternative to the FEM. It is demonstrated that the Unified Formulation permits to derive the governing equations in terms of some few basic elements called fundamental nuclei. Expanding them by means of opportune indexes and loops, it is possible to obtain the stiffness matrix of the global structure. The use of such nuclei permits to obtain in a unified manner the different refined and advanced models contained in the CUF. The governing equations can be obtained in weak form for the Finite Element Method or strong form for the Navier method and the Radial Basis Functions method. A review of these solution methods is also provided, with particular attention to the finite element method that is the most common method in literature and it is the main topic of this thesis. In the last part, different problems are analyzed. The thermo-mechanical analysis of FGM shells, the electromechanical analysis of piezoelectric shells and the dynamic analysis of carbon nanotubes are performed by means of the Navier method. The aim of this study is to demonstrate the efficiency of the models contained in the CUF in the analysis of multifield problems in advanced structures. Then, the CUF shell finite element, presented in this thesis, is tested and used for the analysis of composite and FGM shells. The superiority of this element in respect to finite elements based on classical theories is shown. Finally, the RBF method is combined with the CUF for the analysis of composite and FGM shells in order to overcome the numerical problems relative to the mesh that usually affect the finite elements.