Les travaux de cette thèse concernent l'homogénéisation d'équations de Maxwell harmoniques tridimensionnelles, modélisant la propagation d'une onde électromagnétique issue de la foudre, de l'air dans le matériau composite. La problématique des composites étant, par exemple en aéronautique, l'évacuation de la foudre et la protection contre les agressions électromagnétiques. Nous considérons une structure constituée de fibres de carbone incluses dans une résine époxy qui sera elle-même nano chargée. Rendant ainsi le composite électriquement conducteur. Afin d'obtenir le problème homogénéisé nous utilisons l'analyse asymptotique à deux échelles. Puis nous justifions mathématiquement le résultat par la convergence à deux échelles. La solution du champ électrique est approchée par l'addition du champ électrique moyen et le champ correcteur, dépendant de la microstructure, et solution des problèmes de cellule. Dans la deuxième partie, nous proposons une validation numérique du modèle simplifié en 2D via des simulations avec le logiciel libre d'éléments finis Freefem ++. Trois cas tests seront présentés avant de valider la méthode d'homogénéisation. Enfin, en guise d'illustration du modèle, deux exemples d'agressions électromagnétiques : l'arc en retour de foudre de type A et une impulsion électromagnétique nucléaire seront testées dans le domaine fréquentiel. / The work of this thesis concerns the homogenization of three-dimensional harmonic Maxwell equations, modeling the propagation of an electromagnetic wave originating from lightning, from air in the composite material. The problem of composites being, for example in aeronautics, the evacuation of the lightning and the protection against the electromagnetic aggressions. We consider a structure made of carbon fibers included in an epoxy resin which will itself be nano- charged. Thus rendering the composite electrically conductive. In order to obtain the homogenized problem, we use asymptotic analysis at two scales. Then we mathematically justify the result by two-scale convergence. The solution of the electric field is approximated by the addition of the average electric field and the correct field, depending on the microstructure, and solution of the cell problems. In the second part, we propose a numerical validation of the simplified model in 2D via simulations with the free finite element software Freefem ++. Three test cases will be presented before validating the homogenization method. Finally, as an illustration of the model, two examples of electromagnetic aggression: the Type A lightning bolt and a nuclear electromagnetic pulse will be tested in the frequency domain.

Orientador: Renato Pavanello / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-28T11:58:24Z (GMT). No. of bitstreams: 1 Calixto_TainanKhalilLeite_M.pdf: 15775150 bytes, checksum: e5e4d45becc32f922a1fd31b8f9bd3ab (MD5) Previous issue date: 2015 / Resumo: A utilização de materiais de alta performance se tornou uma realidade em diversos campos da engenharia, como na indústria automotiva e aeroespacial, devido aos avanços nas técnicas de manufatura aditiva. Por outro lado, sabe-se que a otimização topológica estrutural é uma ferramenta de desenvolvimento de estruturas com ampla aplicação industrial. Dentre os vários métodos de otimização topológica existentes, a otimização estrutural evolucionária tem se destacado pela sua versatilidade, podendo ser utilizada em diversos tipos de problemas de engenharia. Na tentativa de combinar esses campos, este trabalho consiste no estudo do método de otimização evolucionária BESO (Bi-directional Evolutionary Structural Optimization) aplicado a sistemas bidimensionais multiescala a fim de se projetar as topologias ótimas, em ambas as escalas, de uma estrutura. A análise do modelo multiescala é feita através do método da homogeneização, onde o padrão do material microestrutural é considerado periódico. O algoritmo implementado pode buscar dois objetivos distintos: a minimização da flexibilidade média, que resulta na maximização da rigidez global; ou a maximização da frequência fundamental. Resultados numéricos do algoritmo são apresentados para o projeto de materiais, onde apenas a microestrutura é otimizada, e de estruturas, na qual otimiza-se as topologias nas duas escalas. Para a análise do desempenho do método de otimização multiescala, são propostos um índice de eficiência estrutural e uma metodologia de fabricação de estruturas periódicas / Abstract: High-performance materials utilization became a reality in many fields of actual engineering, such as in automotive and aerospace industries, due to advances in additive manufacturing techniques. In the other hand, structural topology optimization is a powerful tool for the structure development with wide industrial application. Among the various optimization methods, evolutionary structural optimization stands out for its versatility and it can be used in many engineering problems. As an attempt to combine these fields, this work intends to study the Bi-directional evolutionary Structural Optimization method applied to two-dimensional multi-scale systems in order to design the optimal topologies of structures in both scales. The analysis of multi-scale model is made using the homogenization method, where the pattern of the micro-structural material is considered periodic. The implemented algorithm can use two different objective function: mean compliance minimization, which results in maximizing the global stiffness; or fundamental frequency maximization. Numerical results are presented for material design, where only the micro structure is optimized, and for structural design, in which the topologies in both scales are optimized. Deepening the study in multiscale optimization, it is proposed an index to analyse the structural efficiency and also a manufacturing methodology of periodic structures / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

In this research, the homogenization relations for elastic properties in isotropic and anisotropic materials are studied by applying two-point statistical functions to composite and polycrystalline materials. The validity of the results is investigated by direct comparison with experimental results. In todays technology, where advanced processing methods can provide materials with a variety of morphologies and features in different scales, a methodology to link property to microstructure is necessary to develop a framework for material design. Statistical distribution functions are commonly used for the representation of microstructures and also for homogenization of materials properties. The use of two-point statistics allows the materials designer to consider morphology and distribution in addition to properties of individual phases and components in the design space. This work is focused on studying the effect of anisotropy on the homogenization technique based on two-point statistics. The contribution of one-point and two-point statistics in the calculation of elastic properties of isotropic and anisotropic composites and textured polycrystalline materials will be investigated. For this purpose, an isotropic and anisotropic composite is simulated and an empirical form of the two-point probability functions are used which allows the construction of a composite Hull. The homogenization technique is also applied to two samples of Al-SiC composite that were fabricated through extrusion with two different particle size ratios (PSR). To validate the applied methodology, the elastic properties of the composites are measured by Ultrasonic methods. This methodology is then extended to completely random and textured polycrystalline materials with hexagonal crystal symmetry and the effect of cold rolling on the annealing texture of near- Titanium alloy are presented.

Orientador: Olivâine Santana de Queiroz / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-20T15:36:39Z (GMT). No. of bitstreams: 1 Almeida_FernandaPereiradaSilva_M.pdf: 1905299 bytes, checksum: 26428236d161990046f1d1f982482fe1 (MD5) Previous issue date: 2012 / Resumo: Na dissertação foi estudado um problema elíptico em um domínio limitado com bordo Lipschitz. Parte da fronteira deste domínio está em movimento e oscila rapidamente na variável que representa o espaço, caracterizando-se assim como um problema de fronteira livre com multi escala. Este problema tem aplicações, por exemplo, na construção de filmes semicondutores, levando-se em consideração que a superfície do filme se altera pela deposição de vapor químico. O estudo de tal modelo nos remete a questões de existência e unicidade para um sistema elíptico com condições de bordo do tipo misto acoplado à uma equação hiperbólica através de uma condição de fronteira livre. Além disso, um resultado de aproximação por homogeneização é demonstrado. De fato, provamos uma estimativa na norma H1 para o erro que se comete ao aproximar a fronteira livre real por uma fronteira livre homogeneizada / Abstract: In this dissertation we study an elliptic problem in a bounded Lipschitz domain. Part of the boundary is moving and oscillates rapidly in the variable representing the space. Thus, we have a multi-scale free boundary problem. This problem has applications, for instance, in the construction of semiconductor films taking into account that the surface of the film is changing by chemical vapor deposition. The study of such a model leads us to questions of existence and uniqueness for a system involving an elliptic equation with mixed boundary conditions coupled to a hyperbolic equation by means of a free boundary condition. Furthermore, a result on approximation by homogenization is shown. In fact, an estimate in terms of the H1-norm of the error committed by to approximate the real free boundary problem by the homogenized one is proved / Mestrado / Matematica / Mestre em Matemática