Dans ce travail de thèse, le comportement des composites stratifiés est étudié en utilisant des développements d'ordres élevés ou de type layer wise. Un modèle layer wise LS1 (et l'élément fini à huit nœuds qui lui est associé) a été développé en premier lieu pour l'analyse spécifique des contraintes entre les couches pour des problèmes de bords libres ou bien pour l'étude des liaisons entre les couches. Il est fondé sur un modèle de type layer wise qui considère le stratifié comme une superposition de plaques de Reissner couplées les unes aux autres par des efforts d'interfaces. Cet élément a 5n degrés de liberté par noeud (n étant le nombre de couches) et donne une prédiction des contraintes d'interface. Les travaux précédents se concentraient sur la précision et l'utilisation de l'estimation de ces contraintes d'interface. Mais le modèle permet aussi de calculer les déplacements et les déflexions ainsi que d'extraire les contraintes dans l'épaisseur avec ou sans post-traitement. Dans ce mémoire, la précision et la validité du calcul des déplacements et des contraintes ont été établies à partir d'un nombre important de benchmarks en flexion de composites et des plaques sandwich. Le but de cette étude est aussi de mieux positionner et de promouvoir cette approche en contraintes issue des travaux de Pagano peu utilisés et mal référencés. Ce modèle est ensuite développé et implémenté dans le code de calcul par éléments finis Abaqus via la routine utilisateur User-Element (UEL). Pour démontrer l'efficacité du modèle et du code de calcul, des exemples qui comprennent des plaques isotropes et anisotropes sont traités / In this document, the behaviour of laminated composite is investigated using several high order or layer wise finite element calculations. A layer wise model and its devoted finite element on C° eight-node layer wise finite element have been originally and specifically developed for an interlaminar stresses analysis in a free edge problem or for a bonding study. This model is the core of the present comparisons. It is based on a typical layer wise model that considers the laminate by a superposition of Reissner plates coupled by interfacial stresses. This element consists of 5n degrees of freedom per node (n is the layer number) and is able to predict interlaminar stresses. These out-of-plane stresses are deduced directly from constitutive equations without post-processing works. The previous papers dealt with the accuracy of these estimated interface stresses. However, the model not only permits to compute displacements and usual deflections but also to compute stresses through the layer thicknesses with or without postprocess. In the present paper, the accuracy and the validity of these computed displacements and stresses have also been established on a large number of important benchmarks of bending examples for composites and sandwich plates. The aim of this research is also to better positioning and promoting of this stress approach deriving from the works of Pagano, which was not generally studied in this way. This model has also been implemented into the ABAQUS finite-element program through a User-Element subroutine interface. To demonstrate the effectiveness of the model and the finite element code, examples which include isotropic and anisotropic plates, the problem of the perforated plate are calculated

A finite element model based on the layer-wise theory and the von Kármán type nonlinear strains is used to analyze damage in laminated composite beams. In the formulation, the Heaviside step function is employed to express the discontinuous interlaminar displacement field at the delaminated interfaces. Two types of the most common damage modes in composite laminates are investigated for cross-ply laminated beams using a numerical approach. First, a multi-scale analysis approach to determine the influence of transverse cracks on a laminate is proposed. In the meso-scale model, the finite element model based on the classical laminate theory provides the material stiffness reduction in terms of the crack density by computing homogenized material properties of the cracked ply. The multiplication of transverse cracks is predicted in a macro-scale beam model under bending loads. In particular, a damage analysis based on nonlinear strain fields in contrast to the linear case is carried out for a moderately large deformation. Secondly, the effect of delamination in a cross-ply laminated beam under bending loads is studied for various boundary conditions with various cross-ply laminate lay-ups. The crack growth of delamination is predicted through investigating the strain energy release rate. Finally, the interactions of a transverse crack and delamination are considered for beams of different configurations. The relationships between the two different damage modes are described through the density of intralaminar cracks and the length of the interlaminar crack. It is found that geometric nonlinearity plays an important role in progression of interlaminar cracks whereas growth of intralaminar cracks is not significantly influenced. This study also shows that the mixture of fracture mode I and II should be considered for analysis of delamination under bending loads and the fracture mode leading delamination changes as the damage develops. The growth of delamination originated from the tip of the transverse crack is found to strongly depend on the thickness of 90- degree layers as well as the transverse crack density. Further, the effect of interfacial crack growth on the transverse cracking can be quatitatively determined by the delamination length, the thickness of 90-degree layers and the transverse crack density.

Dans ce travail de thèse, le comportement des composites stratifiés est étudié en utilisant des développements d'ordres élevés ou de type layer wise. Un modèle layer wise LS1 (et l'élément fini à huit nœuds qui lui est associé) a été développé en premier lieu pour l'analyse spécifique des contraintes entre les couches pour des problèmes de bords libres ou bien pour l'étude des liaisons entre les couches. Il est fondé sur un modèle de type layer wise qui considère le stratifié comme une superposition de plaques de Reissner couplées les unes aux autres par des efforts d'interfaces. Cet élément a 5n degrés de liberté par noeud (n étant le nombre de couches) et donne une prédiction des contraintes d'interface. Les travaux précédents se concentraient sur la précision et l'utilisation de l'estimation de ces contraintes d'interface. Mais le modèle permet aussi de calculer les déplacements et les déflexions ainsi que d'extraire les contraintes dans l'épaisseur avec ou sans post-traitement. Dans ce mémoire, la précision et la validité du calcul des déplacements et des contraintes ont été établies à partir d'un nombre important de benchmarks en flexion de composites et des plaques sandwich. Le but de cette étude est aussi de mieux positionner et de promouvoir cette approche en contraintes issue des travaux de Pagano peu utilisés et mal référencés. Ce modèle est ensuite développé et implémenté dans le code de calcul par éléments finis Abaqus via la routine utilisateur User-Element (UEL). Pour démontrer l'efficacité du modèle et du code de calcul, des exemples qui comprennent des plaques isotropes et anisotropes sont traités

Neural networks are regarded as state of the art within many areas of machine learning, however due to their growing complexity and size, a question regarding their trustability and understandability has been raised. Thus, neural networks are often being considered a "black-box". This has lead to the emersion of evaluation methods trying to decipher these complex networks. Two of these methods, layer-wise relevance propagation (LRP) and sensitivity analysis (SA), are used to generate heatmaps, which presents pixels in the input image that have an impact on the classification. In this report, the aim is to do a usability-analysis by evaluating and comparing these methods to see how they can be used in order to understand a particular classification. The method used in this report is to iteratively distort image regions that were highlighted as important by the two heatmapping-methods. This lead to the findings that distorting essential features of an image according to the LRP heatmaps lead to a decrease in classification score, while distorting inessential features of an image according to the combination of SA and LRP heatmaps lead to an increase in classification score. The results corresponded well with the theory of the heatmapping-methods and lead to the conclusion that a combination of the two evaluation methods is advocated for, to fully understand a particular classification. / Neurala nätverk betraktas som den senaste tekniken i många områden inom maskininlärning, dock har deras pålitlighet och förståelse ifrågasatts på grund av deras växande komplexitet och storlek. Således, blir neurala nätverk ofta sedda som en "svart låda". Detta har lett till utvecklingen  av evalueringsmetoder som ämnar att tolka dessa komplexa nätverk. Två av dessa metoder, layer-wise relevance propagation (LRP) och sensitivity analysis (SA), används för att generera färgdiagram som visar pixlar i indata-bilden som har en påverkan på klassificeringen. I den här rapporten, är målet att göra en användarbarhets-analys genom att utvärdera och jämföra dessa metoder för att se hur de kan användas för att förstå en specifik klassificering. Metoden som används i denna rapport är att iterativt förvränga bilder genom att följa de två färgdiagrams-metoderna. Detta ledde till insikterna att förvrängning av väsentliga delar av bilden, vilket framgick ur LRP färgdiagrammen, tydligt minskade sannolikheten för klassen. Det framkom även att förvrängning av oväsentliga delar, som framgick genom att kombinera SA och LRP färgdiagrammen, ökade sannolikheten för klassen. Resultaten stämde väl överens med teorin och detta ledde till slutsatsen att en kombination av metoderna rekommenderas för att förstå en specifik klassificering.

[pt] Esta dissertação trata da modelagem do comportamento dinâmico de cascas cilíndricas laminadas numa faixa considerada de altas frequências onde o comprimento de onda é menor que a espessura da casca. Nestes casos,as teorias tradicionais de cascas tem problemas para representar com acuracidade a resposta dinâmica destas estruturas. Para superar este inconveniente,empregou-se a teoria discreta de Reddy para compósitos laminados.Esta teoria tem como característica o emprego de funções de interpolação para descrever a variação dos campos de deslocamento ao longo da espessura do laminado. Assim, discretizou-se a espessura da casca em lâminas delgadas na direção radial, impondo condições cinemáticas para cada uma delas. Por isto um estado tridimensional de tensões foi assumido para cada lâmina. Esta técnica permitiu a representação de campos de deslocamentos complexos na espessura do laminado representativos daqueles associados às ondas guiadas em altas frequências. A equação de estado que governa a dinâmica da casca foi então obtida no domínio da frequência a partir da aplicação do principio variacional, sendo empregado o método de Riccati para solucionar a mesma. A validação da metodologia proposta nesta dissertação foi feita comparando o espectro de frequência exato com aquele previsto pela teoria aproximada. Desta forma demonstrou-se que a teoria de Reddy é capaz de representar com precisão o comportamento dinâmico da casca cilíndrica na faixa de alta frequência. Além disso, os resultados obtidos na faixa de baixa frequência foram comparados pelo método dos elementos / [en] This dissertation addresses the problem of modeling the dynamic response of laminated cylindrical shells in the high frequency range -short wavelength-. In this range of frequency, traditional theories fail to provide an accurate result of the vibratory structural response; So, in order to overcome this shortcoming, we employed a model based on Reddys discrete layer-wise theory. In this method the cylindrical shell is discretized in an arbitrary number of layers in the radial direction, and a three dimensional stress state is assumed in each one. Hence, the application of this method let the representation of complexes displacement elds through the thickness of the shell. This characteristic is representative of displacement elds associated to guided waves in the high frequency range. In the frequency domain,the governing equations were written in a state space form by applying a variational principle. The solution of this state equation was obtained by employing an algorithm based on a discrete version of the Ricatti transformation.To validate the method proposed in this dissertation, comparisons of the present work to the exact wave-dispersion spectra were assessed with excellent results. It indicates that the present method can predict an accurate description of the dynamic response in the high-frequency range. In the low frequency range, the results of the theory of Reddy were compared with the nite element method and, again, a good accuracy was obtained.