Engineering assemblies are very frequently subject to fretting fatigue, which is a damage process that results when very small slip displacements arise at nominally stationary frictional interfaces. Fretting accelerates the initiation and early propagation of fatigue cracks, thereby causing significant reductions in the fatigue performance of many critical engineering components. A majority of the previous research on fretting fatigue has focused on incomplete (i.e. smooth-edged) contacts, while complete (i.e. sharp-edged) contacts have received less attention. The aim of this thesis is to contribute to the theoretical understanding of complete contacts, especially when they are subject to fatigue conditions. This problem is addressed in two separate ways. First, because fretting failures almost invariably initiate from the edge of contact, a detailed understanding of the conditions in this region should enable more accurate assessments of fatigue performance to be made. Thus, an asymptotic analysis is presented, which provides an accurate description of the contact edge under many conditions. This is done by using the elasticity solution for a semi-infinite notch to represent the state of stress near the contact edge in an asymptotic sense. Attention is then placed on the fact that cyclically loaded frictional contacts tend toward a steady-state response in which less frictional slip (and energy dissipation) occurs than in the first few load cycles. To investigate this effect, a numerical sub-structuring procedure is described, which significantly reduces the number of degrees of freedom in finite element models of frictional contact. This reduced model is then used to calculate the shakedown limit, i.e. the amplitude of cyclic load above which frictional slip is guaranteed to persist in the steady state. The sensitivity of the steady-state solution to the initial residual displacement state is then investigated, and it is shown that initial conditions can have a large influence on the steady-state behaviour of complete contacts.

Les structures mécaniques complexes résultent de l’assemblage de plusieurs composants, possédant souvent des propriétés mécaniques différentes, reliés à leurs interfaces par différents types de jonctions. L’hétérogénéité des comportements dynamiques de ces sous-structures et leurs sollicitations extérieures vont générer des efforts sur la structure principale et des accélérations importantes au niveau des équipements embarqués, affectant leur fonctionnement, leur fiabilité, leur sécurité. Il est alors nécessaire de les protéger en les isolant du reste de la structure.Ces travaux concernent la maîtrise des niveaux vibratoires et visent à fournir une méthode de caractérisation dynamique des interfaces entre différentes sous-structures. Celle-ci est ensuite intégrée dans une démarche visant à minimiser la puissance transmise entre des sous-structures sources et réceptrices.Une méthode de modes de flux de puissance a été développée, dont les valeurs et efforts propres fournissent, respectivement, des informations quantitatives et qualitatives sur les flux de puissance à l’intérieur d’une structure. Son application à l’étude de la puissance transmise entre deux sous-structures permet d’identifier les directions et les participations des principaux chemins de puissance transitant par les jonctions.Ces résultats ont été appliqués afin de proposer une méthodologie de conception robuste des interfaces de structures. Deux démarches d’optimisation ont été comparées visant à minimiser la puissance transmise par rapport aux paramètres de raideurs des jonctions. L’importance de considérer la robustesse de ces solutions a été soulignée par une approche complémentaire non-probabiliste. / Complex mechanical structures are composed of an assembly of several components, often exhibiting different mechanical properties and joined at their interfaces by different junction types. The various dynamic behaviours of these substructures and the applied external loadings generate important efforts on the main structure, resulting in high acceleration responses of the on-board equipments, affecting their performance, reliability and security. It is therefore necessary to protect them from these harsh conditions by isolating them from the rest of the structure.These researches are related to structural vibration control and aim at proposing a new method to dynamically characterize interfaces between different substructures. This method is then integrated to a robust design approach to minimize the power transmitted between a source and a receiver substructure. A power flow mode method has been developed, which allows determining eigenvalues and eigenvectors respectively representing qualitative and quantitative information on the power flowing inside the structure. This has been further applied to study the power transmitted at the interface, making it possible to identify the direction associated to the dominant power flow pattern and to quantify their contribution.These results have been applied to propose a robust design approach of structural interfaces. Optimization procedures have been implemented and compared to minimize the power transmitted between with respect to the interface stiffness parameters. The importance of considering the robustness of these solutions has been underlined by performing a complementary analysis based on a non-probabilistic approach.

Dans le cadre de l’amortissement passif de structure, les élastomères sont employés dans les industries du transport sous la forme de liaisons amortissantes. Ces matériaux ont un comportement dépendant de la fréquence, de la température et de l’amplitude d’excitation. Les modèles numériques associés peuvent être coûteux en temps de calcul, notamment en phase d’optimisation. Le but de cette thèse est de proposer un modèle réduit efficace de ces liaisons amortissantes, qui prenne en compte la dissipation viscoélastique et les précharges non-linéaires dans les liaisons. La première partie de ce mémoire se concentre sur la représentation de la dissipation par le modèle réduit. Une loi de comportement viscoélastique, basée sur un modèle rhéologique identifié expérimentalement, est utilisée avec la méthode des éléments finis pour obtenir un modèle numérique des liaisons amortissantes. Un premier modèle réduit prédictif, prenant en compte la dissipation en est dérivé en utilisant une extension originale des méthodes de sous-structuration. La deuxième partie traite de l’influence des précharges statiques non-linéaires sur le comportement dynamique et la dissipation dans les liaisons. Pour cela, une loi de comportement hyper-visco-élastique linéarisée autour d’un état précontraint statique non-linéaire est développée. Les méthodes de sous-structuration introduites dans la première partie sont alors enrichies afin de tenir compte de la dissipation et les non-linéarités géométriques dans les liaisons. Finalement, ces modèles réduits à 2 nœuds permettent des gains en temps de calcul d’un facteur 50 à 100 et sont facilement utilisables par l’ingénieur en phase de conception. / In the context of passive damping, various mechanical systems from the space, aeronautic or auto-mobile industry use elastomer components (shock absorbers, silent blocks, flexible joints...).These materials have frequency, temperature and amplitude dependentcharacteristics. The associated numerical models may become computationally too expensive during an optimization process.The aim of this work is to propose an efficient reduced model of rubber devices that account for the viscoelastic damping and the non-linear pre-stress in the dampers.The first part of this thesis is about how to include the viscoelasticdamping in the reduced model. It starts by using a viscoelastic constitutive relation, based on experimental identification, within the frame of the finite element method to obtain a numerical model of the rubber dampers. A first efficient reduced model is then derived from this FE model by using an original extension of sub-structuring methods in the case of viscoelastic damping.In the second part, the influence of non-linear static pre-stress overthe dynamic behavior and the dissipation in the dampers is studied. An hyper-visco-elastic constitutive relation, linearized in the neighbourhood of a pre-stressed state, is developed. The sub-structuring methods presented in the first part are then upgraded to account for the damping and the geometrical non-linearities in the dampers. Finally, these 2-node reduced models give access to greatly reduced computation times (50 to 100 times faster) and are easy to use for the engineer.

Une large classe de méthodes numériques possède une propriété d’échelonnabilité connue comme étant la loi d’Amdahl. Elle constitue l’inconvénient majeur limitatif du calcul parallèle, en ce sens qu’elle établit une borne supérieure sur le nombre d’unités de traitement parallèles qui peuvent être utilisées pour accélérer un calcul. Des activités de recherche sont donc largement conduites à la fois sur les plans mathématiques et informatiques, pour repousser cette limite afin d’être en mesure de tirer le maximum des machines parallèles. Les méthodes de décomposition de domaine introduisent une approche naturelle et optimale pour résoudre de larges problèmes numériques de façon distribuée. Elles consistent en la division du domaine géométrique sur lequel une équation est définie, puis le traitement itératif de chaque sous-domaine, séparément, tout en assurant la continuité de la solution et de sa dérivée sur leur interface de jointure. Dans le présent travail, nous étudions la suppression de la limite d’accélération en appliquant des itérations asynchrones dans différents cadres de décomposition, à la fois de domaines spatiaux et temporels. Nous couvrons plusieurs aspects du développement d’algorithmes asynchrones, de l’analyse théorique de convergence à la mise en oeuvre effective. Nous aboutissons ainsi à des méthodes asynchrones efficaces pour la décomposition de domaine, ainsi qu’à une nouvelle bibliothèque de communication pour l’expérimentation asynchrone rapide d’applications scientifiques existantes. / An important class of numerical methods features a scalability property well known as the Amdahl’s law, which constitutes the main limiting drawback of parallel computing, as it establishes an upper bound on the number of parallel processing units that can be used to speed a computation up. Extensive research activities are therefore conducted on both mathematical and computer science aspects to increase this bound, in order to be able to squeeze the most out of parallel machines. Domain decomposition methods introduce a natural and optimal approach to solve large numerical problems in a distributed way. They consist in dividing the geometrical domain on which an equation is defined, then iteratively processing each sub-domain separately, while ensuring the continuity of the solution and of its derivative across the junction interface between them. In the present work, we investigate the removal of the scalability bound by the application of the asynchronous iterations theory in various decomposition frameworks, both for space and time domains. We cover various aspects of the development of asynchronous iterative algorithms, from theoretical convergence analysis to effective parallel implementation. Efficient asynchronous domain decomposition methods are thus successfully designed, as well as a new communication library for the quick asynchronous experimentation of existing scientific applications.

Fires following earthquake (FFE) have historically produced enormous post-earthquake damage and losses in terms of lives, buildings and economic costs, like the San Francisco earthquake (1906), the Kobe earthquake (1995), the Turkey earthquake (2011), the Tohoku earthquake (2011) and the Christchurch earthquakes (2011). The structural fire performance can worsen significantly because the fire acts on a structure damaged by the seismic event. On these premises, the purpose of this work is the investigation of the experimental and numerical response of structural and non-structural components of steel structures subjected to fire following earthquake (FFE) to increase the knowledge and provide a robust framework for hybrid fire testing and hybrid fire following earthquake testing. A partitioned algorithm to test a real case study with substructuring techniques was developed. The framework is developed in MATLAB and it is also based on the implementation of nonlinear finite elements to model the effects of earthquake forces and post-earthquake effects such as fire and thermal loads on structures. These elements should be able to capture geometrical and mechanical non-linearities to deal with large displacements. Two numerical validation procedures of the partitioned algorithm simulating two virtual hybrid fire testing and one virtual hybrid seismic testing were carried out. Two sets of experimental tests in two different laboratories were performed to provide valuable data for the calibration and comparison of numerical finite element case studies reproducing the conditions used in the tests. Another goal of this thesis is to develop a fire following earthquake numerical framework based on a modified version of the OpenSees software and several scripts developed in MATLAB to perform probabilistic analyses of structures subjected to FFE. A new material class, namely SteelFFEThermal, was implemented to simulate the steel behaviour subjected to FFE events.