A theory is developed for the analysis of composite systems consisting of steel wide flange sections reinforced with GFRP plates connected to one of the flanges through a layer of adhesive. The theory is based on an extension of the Gjelsvik theory and thus incorporates local and global warping effects but omits shear deformation effects. The theory captures the longitudinal transverse response through a system of three coupled differential equations of equilibrium and the lateral-torsional response through another system of three coupled differential equations. Closed form solutions are developed and a super-convergent finite element is formulated based under the new theory. A comparison to 3D FEA results based on established solid elements in Abaqus demonstrates the validity of the theory when predicting the longitudinal-transverse response, but showcases its shortcomings in predicting the torsional response of the composite system. The comparison sheds valuable insight on means of improving the theory. A more advanced theory is subsequently developed based on enriched kinematics which incorporates shear deformation effects. The shear deformable theory captures the longitudinal-transverse response through a system of four coupled differential equations of equilibrium and the lateral-torsional response through another system of six coupled differential equations. A finite difference approximation is developed for the new theory and a new finite element formulation is subsequently to solve the new system of equations. A comparison to 3D FEA illustrates the validity of the shear deformable theory in predicting the longitudinal-transverse response as well as the lateral-torsional response. Both theories are shown to be computationally efficient and reduce the modelling and running time from several hours per run to a few minutes or seconds while capturing the essential features of the response of the composite system.

Le comportement poussant fait référence au phénomène de grande déformation différée et souvent anisotrope observée lors de l'excavation du tunnel en terrain tectonisé. Il est à l'origine de difficultés d'avancement ce qui exige une adaptation de la méthode de creusement et de la conception des soutènements. Le présent travail vise à étudier le comportement des tunnels en terrain poussant en portant une attention particulière à l'anisotropie du massif rocheux par des approches à la fois analytique et numérique. Après un état de l'art sur le creusement des tunnels en terrain poussant, on interprète les données d'auscultation récoltées pendant l'excavation de la descenderie de Saint-Martin-La-Porte dans la cadre du projet Lyon-Turin. Des solutions analytiques pour tunnel creusés en milieu anisotrope sont ensuite développées en prenant en compte la complexité géométrique de la section, l'interaction entre deux tunnels parallèles, l'interaction terrain-soutènement et aussi les grandes déformations. Enfin, un modèle différé anisotrope qui comprend des joints rocheux avec une orientation fixe, imbriqués dans une matrice viscoplastique est proposé et implémenté dans FLAC3D. Les résultats de la simulation numérique réalisée avec ce modèle sont comparés aux mesures de convergence réalisées pendant l'excavation du tunnel. De plus, l'approche numérique a été étendue pour analyser le comportement d'un soutènement déformable en prenant en compte l'effet de l'anisotropie de la masse rocheuse / Squeezing behavior is characterized by large time-dependent and often anisotropic deformation during and well after excavation of tunnel and may lead to tremendous operational difficulties. The present thesis aims to deal with tunneling in squeezing ground with a special emphasis on the anisotropic behavior combining analytical and numerical approach. Following an overview on the squeezing behavior, the attention moves on the interpretation of the data monitored during the excavation of Saint-Martin-La-Porte within the Lyon-Turin railway project. The closed-formed solutions for tunnel excavated in anisotropic ground are then developed considering the complexity of tunnel cross-section, the interaction between two tunnels, the interaction ground/support and also the large strain calculation. Finally, an anisotropic creep model which includes weak planes of specific orientation embedded in a viscoplastic medium is proposed and implemented in FLac3D in order to back analyze the convergence data of Saint-Martin-La-Porte access gallery. The numerical model is also applied to the analysis of the behavior of the yield-control support systems taking account the effect of anisotropy of rock mass

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

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The objective of this research is to demonstrate the impact of interconnect process variations, line-edge roughness and size effects on interconnect effective resistivity and ultimately chip performance. The investigation is accomplished through five tasks. In Task I, a new closed-form effective resistivity model, which is a function of line-edge roughness (LER), surface specularity and grain boundary reflectivity, is derived. In Task II, a critical path model is enhanced by including interconnect parasitics using the model in Task I. This enhancement also involves an extensive survey of foundry process data to shed light on the device resistance estimation used in the critical path model in Task II. Task III develops a Monte Carlo (MC) simulation framework called the Fast Interconnect Statistical Simulator (FISS). Using the latest International Technology Roadmap for Semiconductors (ITRS) projections, the FISS projects the impact of interconnect process variations and size effects onto high performance microprocessor units (HP-MPUs). Task IV fabricates metallic interconnect test structures with sub-100nm line-widths. The fifth task statistically calibrates the model from Task I using resistivity data measured from the test structures in Task IV.

Le traitement des données massives, communément connu sous l’appellation “Big Data”, constitue l’un des principaux défis scientifiques de la communauté STIC.Plusieurs domaines, à savoir économique, industriel ou scientifique, produisent des données hétérogènes acquises selon des protocoles technologiques multi-modales. Traiter indépendamment chaque ensemble de données mesurées est clairement une approche réductrice et insatisfaisante. En faisant cela, des “relations cachées” ou des inter-corrélations entre les données peuvent être totalement ignorées.Les représentations tensorielles ont reçu une attention particulière dans ce sens en raison de leur capacité à extraire de données hétérogènes et volumineuses une information physiquement interprétable confinée à un sous-espace de dimension réduite. Dans ce cas, les données peuvent être organisées selon un tableau à D dimensions, aussi appelé tenseur d’ordre D.Dans ce contexte, le but de ce travail et que certaines propriétés soient présentes : (i) avoir des algorithmes de factorisation stables (ne souffrant pas de probème de convergence), (ii) avoir un faible coût de stockage (c’est-à-dire que le nombre de paramètres libres doit être linéaire en D), et (iii) avoir un formalisme sous forme de graphe permettant une visualisation mentale simple mais rigoureuse des décompositions tensorielles de tenseurs d’ordre élevé, soit pour D > 3.Par conséquent, nous nous appuyons sur la décomposition en train de tenseurs (TT) pour élaborer de nouveaux algorithmes de factorisation TT, et des nouvelles équivalences en termes de modélisation tensorielle, permettant une nouvelle stratégie de réduction de dimensionnalité et d'optimisation de critère des moindres carrés couplés pour l'estimation des paramètres d'intérêts nommé JIRAFE.Ces travaux d'ordre méthodologique ont eu des applications dans le contexte de l'analyse spectrale multidimensionelle et des systèmes de télécommunications à relais. / Massive and heterogeneous data processing and analysis have been clearly identified by the scientific community as key problems in several application areas. It was popularized under the generic terms of "data science" or "big data". Processing large volumes of data, extracting their hidden patterns, while preforming prediction and inference tasks has become crucial in economy, industry and science.Treating independently each set of measured data is clearly a reductiveapproach. By doing that, "hidden relationships" or inter-correlations between thedatasets may be totally missed. Tensor decompositions have received a particular attention recently due to their capability to handle a variety of mining tasks applied to massive datasets, being a pertinent framework taking into account the heterogeneity and multi-modality of the data. In this case, data can be arranged as a D-dimensional array, also referred to as a D-order tensor.In this context, the purpose of this work is that the following properties are present: (i) having a stable factorization algorithms (not suffering from convergence problems), (ii) having a low storage cost (i.e., the number of free parameters must be linear in D), and (iii) having a formalism in the form of a graph allowing a simple but rigorous mental visualization of tensor decompositions of tensors of high order, i.e., for D> 3.Therefore, we rely on the tensor train decomposition (TT) to develop new TT factorization algorithms, and new equivalences in terms of tensor modeling, allowing a new strategy of dimensionality reduction and criterion optimization of coupled least squares for the estimation of parameters named JIRAFE.This methodological work has had applications in the context of multidimensional spectral analysis and relay telecommunications systems.

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Structure learning of Bayesian Networks (BNs) is an NP-hard problem, and the use of sub-optimal strategies is essential in domains involving many variables. One of them is to generate multiple approximate structures and then to reduce the ensemble to a representative structure. It is possible to use the occurrence frequency (on the structures ensemble) as the criteria for accepting a dominant directed edge between two nodes and thus obtaining the single structure. In this doctoral research, it was made an analogy with an adapted one-dimensional random-walk for analytically deducing an appropriate decision threshold to such occurrence frequency. The obtained closed-form expression has been validated across benchmark datasets applying the Matthews Correlation Coefficient as the performance metric. In the experiments using a recent medical dataset, the BN resulting from the analytical cutoff-frequency captured the expected associations among nodes and also achieved better prediction performance than the BNs learned with neighbours thresholds to the computed. In literature, the feature accounted along of the perturbed structures has been the edges and not the directed edges (arcs) as in this thesis. That modified strategy still was applied to an elderly dataset to identify potential relationships between variables of medical interest but using an increased threshold instead of the predict by the proposed formula - such prudence is due to the possible social implications of the finding. The motivation behind such an application is that in spite of the proportion of elderly individuals in the population has increased substantially in the last few decades, the risk factors that should be managed in advance to ensure a natural process of mental decline due to ageing remain unknown. In the learned structural model, it was graphically investigated the probabilistic dependence mechanism between two variables of medical interest: the suspected risk factor known as Metabolic Syndrome and the indicator of mental decline referred to as Cognitive Impairment. In this investigation, the concept known in the context of BNs as D-separation has been employed. Results of the carried out study revealed that the dependence between Metabolic Syndrome and Cognitive Variables indeed exists and depends on both Body Mass Index and age. / O aprendizado da estrutura de uma Rede Bayesiana (BN) é um problema NP-difícil, e o uso de estratégias sub-ótimas é essencial em domínios que envolvem muitas variáveis. Uma delas consiste em gerar várias estruturas aproximadas e depois reduzir o conjunto a uma estrutura representativa. É possível usar a frequência de ocorrência (no conjunto de estruturas) como critério para aceitar um arco dominante entre dois nós e assim obter essa estrutura única. Nesta pesquisa de doutorado, foi feita uma analogia com um passeio aleatório unidimensional adaptado para deduzir analiticamente um limiar de decisão apropriado para essa frequência de ocorrência. A expressão de forma fechada obtida foi validada usando bases de dados de referência e aplicando o Coeficiente de Correlação de Matthews como métrica de desempenho. Nos experimentos utilizando dados médicos recentes, a BN resultante da frequência de corte analítica capturou as associações esperadas entre os nós e também obteve melhor desempenho de predição do que as BNs aprendidas com limiares vizinhos ao calculado. Na literatura, a característica contabilizada ao longo das estruturas perturbadas tem sido as arestas e não as arestas direcionadas (arcos) como nesta tese. Essa estratégia modificada ainda foi aplicada a um conjunto de dados de idosos para identificar potenciais relações entre variáveis de interesse médico, mas usando um limiar aumentado em vez do previsto pela fórmula proposta - essa cautela deve-se às possíveis implicações sociais do achado. A motivação por trás dessa aplicação é que, apesar da proporção de idosos na população ter aumentado substancialmente nas últimas décadas, os fatores de risco que devem ser controlados com antecedência para garantir um processo natural de declínio mental devido ao envelhecimento permanecem desconhecidos. No modelo estrutural aprendido, investigou-se graficamente o mecanismo de dependência probabilística entre duas variáveis de interesse médico: o fator de risco suspeito conhecido como Síndrome Metabólica e o indicador de declínio mental denominado Comprometimento Cognitivo. Nessa investigação, empregou-se o conceito conhecido no contexto de BNs como D-separação. Esse estudo revelou que a dependência entre Síndrome Metabólica e Variáveis Cognitivas de fato existe e depende tanto do Índice de Massa Corporal quanto da idade.