Cette thèse est consacrée au développement d'outils pour FreeFem++ destinés à faciliter la résolution des problèmes d'optimisation. Ce travail se compose de deux parties principales. La première consiste en la programmation, la validation et l'exploitation d'interfaces permettant l¿utilisation de routines d'optimisation directement dans le logiciel. La seconde comprend le développement de solutions pour le calcul automatisé des dérivées, toujours au sein de FreeFem++, en exploitant les paradigmes de la différentiation automatique. FreeFem++ est un environnement de développement intégré dédié à la résolution numérique d¿équations aux dérivées partielles en dimension 2 et 3. Son langage ergonomique permet à l'utilisateur d'exploiter aisément ses nombreux outils de création de maillages, de résolution de systèmes linéaires, ainsi que ses bibliothèques d'éléments finis, etc... Nous introduisons les nouvelles routines d'optimisation désormais accessibles depuis la bibliothèque de modules du logiciel. En particulier, le logiciel libre d'optimisation sous contraintes IPOPT, qui implémente une méthode de points intérieurs très robuste pour l¿optimisation en grande dimension. Nous appliquons avec succès ces algorithmes à une série de problèmes concrets parmi lesquels la résolution numérique de problèmes de sur- faces minimales, la simulation de condensats de Bose-Einstein, ou encore un problème de positionnement inverse en mécanique des fluides. Une version prototypique de FreeFem++ contenant les outils de différentiation automatique est présentée, après avoir exposé les principes fondamentaux de cette méthode de calcul de dérivées pour le calcul scientifique. / The goal of this Ph.D. thesis was the development of tools for the FreeFem++ software in order to make optimization problems easier to deal with. This has been accomplished following two main directions. Firstly, a set of optimization softwares is interfaced and validated before making use of them. Then, we analyse the field of automatic differentiation as a potential mean of simplification for the users. FreeFem++ is an integrated development environment dedicated to numerically solving partial differential equations. Its high level language allows the user for a comfortable experience while using its mesh generation capabilities, linear system solvers, as well as finite elements capabilities. We describe the newly available optimization features, with a certain emphasis on the open source software IPOPT, which implements a state of the art interior points method for large scale optimization. These optimization tools are then used in a set of quite successful applications, among which minimal surfaces, Bose-Einstein condensate simulation, and an inverse positioning problem in the context of computational fluid dynamics. Finally, after an introduction to the techniques of algorithmic differentiation, we also present an unstable prototype version of FreeFem++ including automatic differentiation features.

This master's thesis deals with stress analysis and optimalization frame of the self- loading package transporter. It consists the analysis of original frame, the proposed changes and analysis of new frame.

This master’s thesis deals with VUT 081 Kondor composite fuselage design and control system layout design. Load computation and selection of critical load cases are made. Principal inner surfaces of the fuselage are designed with respect to basic ergonomic requirements of the crew. Construction materials are chosen and a layup of composite materials is performed. Fuselage FEM model is made in MSC Patran/Nastran system and the structure-strength analysis is given for chosen load cases.

This Master´s thesis describes the design of composite horizontal tail of VUT 100 aircraft. Load calculation and selection of the critical load cases is performed. Internal structure of stabilizer and right elevator is designed. Construction materials are chosen and the structure of the composite materials is proposed. FEM models of stabilizer and the right elevator are created in MSC Patran system and consequently the strength test of the models for the selected load cases is executed using MSC Nastran software and COMPOST.

The presented Master Thesis is focused on the structural analysis of the proximal femur on which the Proximal Femoral Nail (PFN) and Proximal Femoral Tele-Screw (PFT) systems are applied. These systems are used for a treatment of the intertrochanteric and femoral neck fractures. However, in some cases a loss of stability of the systems may be expected. The presented thesis describes a development of numerical models in which stress distribution of implants and strain distribution of bone tissue are compared. Numerical models were created from real objects. The model of femur geometry was created by using the Computed Tomography (CT). Boundary conditions of the model were estimated from the force equilibrium of the lower limb. All numerical models were processed in the commercial package ANSYS Workbench v15.0. It is shown that the hip screws of the PFN system result in lower equivalent stresses than the screws of the PFT system. Maximal strains of the bone tissue, when using the PFN system, are situated near the fracture, close the hip screw thread. For the PFT system, the maximal strains are only near the area of fracture.

No description available.

L'interaction fluide structure est présente dans beaucoup de problèmes industriels, dans les domaines d'ingénierie mécanique, civile ou biomécanique. Même si les performances informatiques s'améliorent considérablement et que les méthodes en mécanique numérique gagnent en maturité, certaines difficultés ne permettent pas encore de réaliser des simulations numériques précises. Actuellement deux méthodes numériques gagnent en popularité pour la simulation numérique d'interactions fluide structure: la méthode de partitionnement et la méthode monolithique. Des résultats de la littérature montrent que la première est efficace et précise mais qu'elle peut rencontrer des problèmes d'instabilité si les ratios de densité sont élevés ou que les géométries sont complexes. Les méthodes d'immersion sont de plus en plus utilisées par la communauté scientifique. Différentes approches ont été développées, dont la Méthode d'Immersion de Volume. Cette méthode permet de faciliter la mise en place des calculs. Ainsi il n'est pas nécessaire de construire des maillages concordant avec la géométrie des objets, et le couplage entre les fluides et les solides se fait naturellement. C'est sur cette analyse qu'a été développé le logiciel Thost. Il permet de simuler des procédés industriels tels que le chauffage de pièces métalliques dans les fours industriels ou la trempe sans caractériser expérimentalement des coefficients de transfert. Le but d'un tel logiciel est de permettre une meilleure compréhension des procédés et ainsi de les optimiser. Cependant les coûts de calcul restant élevés, le but de la thèse est de les diminuer en s'appuyant sur des méthodes numériques innovantes tels que l'adaptation dynamique de maillage anisotrope, des méthodes éléments finis stabilisées ou l'immersion directe des objets à partir de la Conception Assistée par Ordinateur. / Fluid-Structure Interaction (FSI) describes a wide variety of industrial problems arising in mechanical engineering, civil engineering and biomechanics. In spite of the available computer performance and the actual maturity of computational fluid dynamics and computational structural dynamics, several key issues still prevent accurate FSI simulations.Two main approaches for the simulation of FSI problems are still gaining attention lately: partitioned and monolithic approaches. Results in the literature show that the partitioned approach is accurate and efficient but some instabilities may occur depending on the ratio of the densities and the complexity of the geometry. Monolithic methods are still of interest due to their capability to treat the interaction of the fluid and the structure using a unified formulation. In fact it makes the build up of a FSI problem easier as the mesh do not have to fit the geometry of the solids and the transfers are treated naturally.The software Thost has been created based on these analyzes. Thost is a 3D aerothermal numerical software. It has been developped for the numerical simulation of industrial processes like the heating in industrial furnaces as well as quenching. Its target is to model numericaly the thermal history of the industrial pieces in their environment without using any transfer coefficient. However the computational costs are still high and therefore the software is not fully efficient from an industrial point of view to simulate, analize and improve complex processes. All the work in this PhD thesis has been done to reduce the computational costs and optimize the accuracy of the simulations in Thost based on innovatives numerical methods such as dynamic anisotropic mesh adaptation, stabilized finite elements methods and immersing the objects directly from their Computer Aided Design files.

Dans le cadre des opérations de perçage, les billettes en acier subissent un réchauffage de la température ambiante à une température d’environ 1250°C. Au cours de ce réchauffage, le gradient de température dans les billettes entraîne la détérioration de la santé axiale de celles-ci et est à l’origine de l’apparition de défauts sur le tube formé. Une méthodologie d’analyse des mécanismes à l’origine de ces défauts a été mise en place. Elle se base sur la caractérisation de la santé axiale par essais rhéologiques permettant d’établir des indicateurs de ductilité et par des examens métallurgiques identifiant les défauts internes.L'étude de la sollicitation thermomécanique induite par le réchauffage du produit est analysée à l’aide de simulations numériques par éléments finis et les zones de sollicitations critiques associées au procédé sont identifiées. La caractérisation des anomalies observées sur les billettes est ensuite faite à partir d’essais de fissuration et de simulations numériques X-FeM. L’implémentation d’un critère de rupture en contrainte dans la simulation du cycle de chauffe a permis de définir les valeurs de gradient thermique limite et les courbes de chauffe optimales. Les analyses montrent que les conditions de chauffe en début de cycle thermique ont une forte influence sur la santé axiale des billettes. Les résultats de ces travaux conduisent à des solutions concrètes pour l’amélioration de la productivité. / As part of the piercing operations, billets undergo a reheating process from room temperature to a temperature of about 1250°C. During this heating, the thermal gradient in the billet leads to a deterioration of the axial health and is responsible of the initiation ofdefects on the formed tube.A methodology for the analysis of the mechanisms at the origin of these defects has been established. It is based on first, the characterization of the axial health with hot rheological tests to establish some indicators of ductility and second, on metallurgical analyses to identify the internal defects.Then finite element simulations have been performed to study the thermo-mechanical loadings induced by heating. Critical solicitation zones of the product during the processes have been identified.Finally a characterization of the observed defects into the billets has been led coupling cracks growth tests and X-FeM numerical simulations. The implementation of the experimental stress failure criterion, in the simulation of the heating cycle allows to obtain good values of thermal gradient boundary curves and leads to optimal heating curves.The analysis shows that the conditions at the beginning of the reheating process have a strong influence on the axial health of the billets. The results of these studies lead to friendly industrial solutions for improving productivity.

As deformações derivadas da retração e da fluência estão entre os principais fatores que afetam a integridade e facilidade de manutenção das estruturas de concreto a longo prazo. Outro fator que corrobora para a deterioração do concreto é a Reação Álcali-Agregado (RAA), que devido à sua característica expansiva é considerada uma manifestação patológica de difícil tratamento, sendo necessário medidas mitigadoras para evitar sua ocorrência. A retração, a fluência e a RAA são deformações expressivas em estruturas com grandes volumes de concreto, em que as deformações devido à retração e à fluência potencializam o efeito da RAA, criando um ciclo de degradação do concreto de difícil controle. Deste modo, este trabalho tem como objetivo a análise numérica que possibilite a previsão do comportamento da retração e da fluência quando associadas à RAA. O código computacional é baseado no Método de Elementos Finitos Posicional considerando o elemento de chapa com elementos triangulares de ordem cúbica e utilizando a lei constitutiva de Saint-Venant-Kirchhoff. Para a modelagem da RAA utiliza-se o estudo desenvolvido por Carrazedo & Lacerda (2008). A fluência e a retração são modeladas implementando-se os modelos FIB, JSCE e B4. Os resultados deste trabalho demonstram a eficiência da modelagem e da análise numérica para a previsão do comportamento das deformações do concreto sujeito à RAA, considerando os efeitos de retração e fluência. / Shrinkage and creep strains are among the main factors that affect the integrity and serviceability of concrete structures in long term. Another corroborating factor for the concrete deterioration is the Alkali-Aggregate Reaction (AAR), which due to its expansive characteristic is considered a pathological manifestation of difficult treatment, and mitigating measures are necessary to avoid its occurrence. Shrinkage, creep and AAR are expressive strains in structures with large volumes of concrete, in which strains due shrinkage and creep enhance the effect of AAR, creating a concrete degradation cycle that is difficult to control. Thus, this work has the aim of numerical analysis that allows the prediction of the shrinkage and creep behavior when associated with AAR. The computational code is based on the Positional Finite Elements Method considering the element of plate with triangular elements of cubic order and using the constitutive law of Saint-Venant-Kirchhoff. For the modeling of AAR is used the study developed by Carrazedo & Lacerda (2008). The creep and shrinkage are modeled by implementing the FIB, JSCE and B4 models. The results of this work demonstrate the efficiency of modeling and numerical analysis for the prediction of the strains behavior of concrete subject to AAR, considering the effects of shrinkage and creep.

Os tubos flexíveis são amplamente utilizados na produção de petróleo offshore, para transporte de petróleo bruto, óleo e gás natural. Pelo fato de operarem em um ambiente muito agressivo e estarem sujeitos a diversos tipos de carregamentos como pressão interna, pressões externas, tração, compressão, flexão e torção, eles possuem uma estrutura bastante complexa composta por diversas camadas concêntricas, com finalidades estruturais diversas, que interagem entre si. Em termos de carregamento, a compressão, em especial, seja ela dinâmica ou estática representa um problema para estes tubos. Embora eles sejam projetados para suportar altas cargas de tração, por meio de armaduras metálicas helicoidais, têm resistência limitada para cargas de compressão. A presença de tais esforços pode causar falhas por instabilidade radial das armaduras de tração. Este modo de falha, conhecido há mais de duas décadas, é denominado birdcaging, devido à forma característica assumida pelas armaduras. Além dessa instabilidade radial, as armaduras podem sofrer uma instabilidade lateral, a qual é igualmente catastrófica para os tubos flexíveis. Este trabalho consiste em uma investigação destes modos de falha com base em modelos numéricos, usando o Método dos Elementos Finitos. Com tais ferramentas, objetiva-se estudar a mecânica dos fenômenos de instabilidade de armadura de tração, juntamente com os efeitos causados pela alteração de parâmetros construtivos e ambientais nestes modos de falha. / Flexible pipes are widely employed in offshore oil production. Their functions include transporting of crude oil, natural gas, chemicals and water injection. Since they operate in aggressive environments and are subjected to loads such as internal and external pressure, tension, compression, bending and torsion, these pipes are built with a complex multilayered structure. In terms of loading, compression, specially, dynamic or static, present a problem to these pipes. Their tensile armor layers are particularly designed to withstand high levels of tension, but not for compression. The presence of such loads may cause radial instability failure on the armor layers. This failure mode, known for almost three decades, is called birdcaging, due to the peculiar shape assumed by the armor tendons at the post-buckling. Besides radial instability, the tensile armor layers may also suffer from lateral instability, which is equally catastrophic in the operation of flexible pipes. This work consists on an investigation of these failure modes based on numerical models, using the Finite Element Method. With these tools, the mechanism that governs these instability phenomena can be understood, along with the effects caused by the alteration of design and environmental parameters on the failure modes.