PERIOD: JUNE - JULY The aerospace structures sector is increasingly oriented towards the use of complex geometries and laminations where innovative materials, such as composites and Functionally Graded Materials (FGMs), are employed. An effective design of these elements is strictly connected to the use of structural models able to capture the different effects due to the complexity of these structures. The present course, after providing an overview on the various numerical and analytical 3D, 2D and 1D models for the analysis of multilayer structures, provides all the necessary tools for the development of 3D shell models for static and free vibration analyses of sandwich, composite and FGM structures. In this regard, the conditions of interlaminar continuity for anisotropic multilayer structures are discussed. Elements of geometry, geometrical relations, constitutive equations and undefined equilibrium equations for the multilayer shells, in the 3D version and for orthogonal mixed curvilinear coordinates, are provided. The proposed exact 3D shell models will also be extended to the thermal and hygrometric stress analyses, taking into account temperature and moisture content profiles that can be a priori assumed as linear or can be appropriately calculated. In the case of calculated profiles, the Fourier conductivity and Fick diffusion equations will be written and solved in the 1D and 3D versions (in this last case the orthogonal mixed curvilinear coordinates will be used). Several results will be proposed and discussed in the case of free frequencies (and related vibration modes) and static analyses (with combinations of mechanical loads and equivalent thermal and hygroscopic loads). These results, in terms of frequencies, vibration modes, displacements, strains, stresses, heat fluxes and temperature and humidity profiles, will be compared with those deriving from classic 2D numerical models, trying to highlight the critical issues related to the effects linked to the load conditions, boundary conditions, degrees of freedom, free edges and cylindrical bending.

- Meaning of 3D, 2D and 1D analytical and numerical modeling of composite, sandwich and FGM (Functionally Graded Material) structures. - C0z requirements, interlaminar continuity, equilibrium and congruency conditions for multilayer anisotropic structures. - Geometry, geometrical relations, 3D constitutive equations and 3D equilibrium equations for shells in orthogonal curvilinear mixed coordinates. - Exact 3D shell model for the free frequency analysis (and related vibration modes) and for the static analysis (combined transverse normal and transverse shear loads) for composite, sandwich and FGM structures. - Overview and discussion of different 3D results about free frequencies (and related vibration modes) for composite, sandwich and FGM plates and shells. How to carry out possible comparisons with classical 2D numerical models. Discussion about the effects of boundary conditions, cylindrical bending, degrees of freedom and free edges on the aforementioned comparisons. - Overview and discussion of different 3D results about static analysis of composite, sandwich and FGM plates and shells. Visualization of displacements, strains and stresses trough the thickness and verification of loading boundary conditions and interlaminar continuity conditions. Possible comparisons with classical 2D numerical models. - Exact 3D shell model for thermal stress and hygroscopic stress analyses of composite, sandwich and FGM structures. Temperature and moisture content profiles can be: a priori assumed as linear, calculated by solving the 1D Fourier heat conduction equation and the 1D Fick moisture diffusion law, calculated by solving the 3D Fourier heat conduction equation and the 3D Fick moisture diffusion law (both written using orthogonal mixed curvilinear coordinates). - Overview and discussion of different 3D results about thermal stress and hygroscopic stress analyses of composite, sandwich and FGM plates and shells (in terms of displacements, stresses, strains, temperature profiles, heat fluxes and moisture content profiles). The final evaluation will be based on a short written report about a course topic previously agreed with the teacher.

Inizio corso: 01/07/2019, ORE 09:00, SALA FERRARI DIMEAS

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Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.