Cette thèse se focalise sur le développement d’un élément continu de coque axisymétrique raidie de type Reissner/Mindlin. La démarche consiste à utiliser les éléments de coques axisymétriques développés aux LISMMA pour lesquels une méthode de prise en compte de chargements repartis a été définie. L'introduction des raidisseurs longitudinaux est menée à partir d'éléments de poutres droites couplés à la coque. L'introduction des raidisseurs circonférentiels nécessite quant à elle le développement d'éléments de poutres circulaires selon une formulation analogue à celle des coques axisymétriques. Cette formulation appelée méthode des éléments continus est basée,entre autre, sur le développement en série de Fourier des champs inconnus selon la dimension circonférentielle et sur la détermination de la matrice de rigidité dynamique de la structure étudiée.Deux configurations de couplage ont été envisagées: Le couplage de coques axisymétriques avec des éléments d'anneaux circulaires de Timoshenko agissant comme raidisseurs circonférentiels puis avec des poutres droites de Timoshenko agissant comme raidisseurs longitudinaux. Des analyses harmoniques sont ensuite menées de manière à valider les formulations présentées par comparaison avec les résultats issus de modélisations éléments finis. / This thesis focuses on the development of a continuous stiffened axisymmetric shell element of type Reissner/Mindlin. The approach consist in using the axisymmetric shell element developed in LISMMA for which distributed loads were applied on it.The introduction of longitudinal stiffeners is achieved by using a straight beam element coupled to the shell. The introduction of circumferential stiffeners requires the development of circular beam element according to a formulation similar to that used for the axisymmetric shell.In fact, this continuous element method is based on the development of the unknown fields on the Fourier series according to the circumferential dimensions and on the determination of the dynamic stiffness matrix of the studied structure.Two coupling configuration were considered: First of all the coupling of axisymmetric shell with circular Timoshenko beam element acting as circumferential stiffeners, then with straight Timoshenko beam element acting as longitudinal stiffener. Harmonic analyzes are conducted in order to validate the formulations presented in comparison with the results obtained from finite element model.

Cette thèse est consacrée à l'étude du comportement en flexion des renforts textiles et préimprégnés thermoplastiques par des méthodes expérimentales et numériques. Pour préimprégnés thermoplastique, aux températures élevées, la résine est à l'état fondu, et un glissement entre les fibres est possible. En conséquence la rigidité de flexion n'est pas directement liée au module de rigidité de traction dans le plan comme c'est le cas pour les matériaux continus classiques. Par conséquent, il est nécessaire de mesurer sa valeur par l'expérience. Un procédé de test de la rigidité à la flexion a été proposée pour les préimprégnés thermoplastiques. Il est réalisé dans une enceinte thermique. Une caméra CCD a été utilisé pour acquérir le profil de la déformation de flexion à différentes températures élevées en particulier au voisinnage du point de fusion. Le moment de flexion et la courbure ont été calculés le long de la ligne médiane de la profil de la déformation. La pente de la courbe moment-courbure est la rigidité à la flexion. Avec cette méthode, des essais de flexion ont été effectués sur plusieurs préimprégnés thermoplastiques. Pour simuler la déformation de flexion de matériaux fibreux épais, un élément de coque spécifique a été développée. Cet élément est constitué de segments de fibres continues. La rigidité de traction et de flexion de la fibre ont été prise en compte de dans l'énergie de deformation de cet élément. La forme curviligne locale a été construit pour tout segment de fibre a partir des voisins. Il a été utilisé pour caractériser les déformations de traction et de flexion pour le segment de la fibre. Plusieurs tests de simulation de flexion ont été réalisées avec cet élément de coque spécifique et ont été comparés avec les résultats expérimentaux pour montrer l'efficacité de cet élément proposé. Les résultats montrent cet élément de coque spécifique a une bonne capacité à simuler la déformation en flexion des matériaux fibreux épais. / This thesis is devoted to study the bending behaviour of textile reinforcements and thermoplastic prepregs by the experimental and numerical methods. At the high temperature, since the resin is melted, fibers would have the slippage between them, resulting the bending stiffness of thermoplastic prepreg is not directly related to its in-plane tensile modulus as the conventional continuous materials. Consequently, it's necessary to measure its value by the experimental method. A bending stiffness test approach was proposed for thermoplastic prepreg at elevated temperature. It was operated in an environmental chamber and a CCD camera was used to acquire the bending deflection shape. Bending moment and curvature were calculated along the midline of bending deflection shape. The slope of moment-curvature curve is the bending stiffness. With this method, bending tests were conducted for several types of thermoplastic prepregs at a range of high temperatures. In order to simulate the bending deformation of thick fibrous materials, a specific shell element was developed. This element was made of continuous fiber segments. Both the tensile and bending stiffnesses of fibers were taken into account. Local curve was constructed for any fiber segment and its two neighbors, which was used to characterize the tensile and bending deformations of fiber segment. Several bending simulation tests were performed with this specific shell element and were compared with the experimental results to show its efficiency. The results show this specific shell element has good capability to simulate the bending deformation of thick fibrous materials.

Les composites thermoplastiques préimprégnés suscitent un intérêt croissant pour l'industrie automobile grâce à leurs excellentes propriétés mécaniques et leur procédé de fabrication rapide. Dans ce contexte, la modélisation et la simulation numérique des procédées de mise en forme de pièces composites à géométries complexes sont nécessaires pour prédire et optimiser les pratiques de fabrication. Cette thèse est consacrée à la modélisation et à la simulation du comportement de consolidation des composites thermoplastiques préimprégnés lors du processus de mise en forme. Un nouvel élément solide-coque prismatique à sept nœuds est proposé: six situés aux sommets et le septième situé au centre. Le champ de cisaillement transverse est supposé afin de réprimer le verrouillage de cisaillement transversal. La méthode de déformation renforcée supposée par addition d'un DOF de déplacement supplémentaire depuis le nœud central et un schéma d'intégration réduit sont combinées offrant un champ de déformation linéaire le long de la direction d'épaisseur pour contourner le verrouillage. De plus, une procédure de stabilisation de sablier est employée afin de corriger le défaut de rang de l'élément pour le pincement. Cet élément utilise un modèle de relaxation viscoélastique pour modéliser le comportement tridimensionnel de composites thermoplastiques préimprégnés avec effet de consolidation. Un modèle de contact intime est également utilisé pour prédire l'évolution de la consolidation et la microstructure du vide présente au sein du préimprégné. A l’aide d’une loi hyperélastique, plusieurs simulations ont été conduites en combinant le nouvel élément fini et les modèles de consolidation. La comparaison des résultats de simulation avec les essais expérimentaux montre l'efficacité de l’élément solide-coque face aux problèmes de déformations dans le plan et en flexion, mais également pour l'analyse du comportement de consolidation. De plus, le degré de contact intime fournit le degré de consolidation par conditions de procédé appliqué, ce qui est essentiel pour l'apparition de défauts dans la pièce finale de composite. / As the pre-impregnated thermoplastic composites have recently attached increasing interest in the automotive industry for their excellent mechanical properties and their rapid cycle manufacturing process, modelling and numerical simulations of forming processes for composites parts with complex geometry is necessary to predict and optimize manufacturing practices. This thesis is devoted to modelling and simulation of the consolidation behavior during thermoplastic prepreg composites forming process. A new seven-node prismatic solid-shell element is proposed: six located at the apexes and the seventh sited at the center. A shear stain field is assumed to subdue transverse shear locking, the enhanced assumed strain method by addition of an extra displacement DOF from the central node and a reduced integration scheme are combined offering a linear varying strain field along the thickness direction to circumvent thickness locking, and an hourglass stabilization procedure is employed in order to correct the element’s rank deficiency for pinching. This element permits the modelling of three-dimensional constitutive behavior of thermoplastic prepreg with the consolidation effect, which is modelled by a viscoelastic relaxation model. An intimate contact model is employed to predict the evolution of the consolidation which permits the microstructure prediction of void presented through the prepreg. Within a hyperelastic framework, several simulation tests are launched by combining the new developed finite element and the consolidation models. The comparison with conventional shell element and experimental results shows the efficiency of the proposed solid-shell element not only dealing with the in-plan deformation and bending deformation problems, but also in analyzation of the consolidation behavior, and the degree of intimate contact provides the level of consolidation by applied process conditions, which is essential for the appearance of defects in final composite part.

L'objectif de ce travail de thèse est de mettre en place une simulation thermo-mécanique couplée d'une aube revêtue permettant de modéliser l'écaillage de la barrière-thermique qui survient dans les conditions de service de l'aube. La barrière thermique est un revêtement isolant déposé à la surface du substrat monocristallin base Nickel AM1 constitutif de l'aube préalablement recouverte d'une sous-couche. Le mode de dégradation dominant dans ces systèmes est la création de fissures qui résultent de l'accroissement des ondulations hors-plan d'une couche intermédiaire d'oxyde formée en service entre la céramique et la sous-couche. En vue de modéliser ce phénomène d'écaillage, un ensemble d'outils numériques permettant de réaliser un calcul 3D par éléments finis thermo-mécanique couplé de l'aube revêtue est développé au sein du code de calcul par éléments finis Z-set. L'insertion d'éléments de zone cohésive mécanique et thermique au niveau de l'interface barrière-thermique/substrat permet de tenir compte simultanément des changements dans le processus de transert de charge et des variations du flux de chaleur causés par l'amorçage et la propagation d'une fissure interfaciale. L'élément fini d'interface mixte de Lorentz qui repose sur un Lagrangien augmenté, est mis en oeuvre. Afin de tenir compte des propriétés structurelles du revêtement, la modélisation de la barrière thermique est réalisée au moyen d'éléments de coque thermo-mécaniques reposant sur l'approche dite “Continuum Based”. Ces éléments sont développés puis validés dans le cadre de la thèse. La méthode utilisée pour réalier le couplage thermo-mécanique est l'algorithme partitioné CSS (Conventional Serial Staggered) sous-cyclé à pas de couplage fixe dont on montre les limitations dans le cas d'une simulation impliquant la propagation d'une fissure. L'introduction de pas de couplage adaptatifs contrôlés au moyen d'une variable interne du problème mécanique a permis de contourner ces limitations. L'ensemble des briques numériques est validé sur des cas tests de complexité croissante. Des cas d'applications effectués sur des géométries tubulaires à gradient thermique de paroi sont réalisés afin de tester le modèle couplé sur des structures et des chargements proches des conditions de service de l'aube. Enfin, des calculs thermo-mécaniques couplés sur aube revêtue sont présentés. / The purpose of this thesis is to perform a coupled thermomechanical simulation of the failure of thermal barrier coatings for turbine blades under service conditions. The thermal barrier coating is an insulating component applied to the single crystal Nickel-based superalloy AM1 substrate which is covered with a bond coat beforehand. The main degradation mode of those systems is due to the initiation and propagation of cracks caused by the out-of-plane undulation growth of an oxide layer formed in service. A set of numerical tools is implemented into the Finite Element code Z-set in order to perform a 3D thermomechanically coupled simulation of the failure of thermal barrier coatings for turbine blades. Inserting thermomechanical cohesive zone elements at the interface between the coating and the substrate makes it possible to account for the changes in the load transfer and the variations in the heat flux as a consequence of interface degradations. The mixed finite interface element of Lorentz based on an Augmented Lagrangian is used. The thermal barrier coating is modelled by means of thermomechanical shell elements implemented using the Continuum-Based approach to take advantage of the structural properties of the coating layer. Moreover, the partitionned CSS (Conventional Serial Staggered) algorithm used to couple thermal and mechanical problems is assessed. The limitations of sub-cycling with constant coupling time-step are shown through a simulation with crack propagation. The introduction of adaptative time-stepping allows to circumvent that issue. The numerical tools are assessed on test cases with increasing complexity. Numerical simulations on cylindrical tube with a thermal through-thickness gradient are performed with realistic loading sequences. Finally, thermomechanical simulations on turbine blades covered with thermal barrier coating are shown.

At Saab Aerostructures they are manufacturing a lot of parts for Airbus and Boeing. When these components are investigated using finite element analysis four-node Kirchhoff shell elements and a very fine mesh is often used. In order to make the pre-processing easier Saab would like to offset the shell mid surface from the nodal plane (the modeling surface) rather than to extract mid surfaces for the entire component. This would also make it easier to model a component which needs a thickness change later on, this since the original modeling surface could be used but with an offset of the elements in order to represent the new geometry. When offset is used in Nastran multi point constraints are created between the nodes and the shell mid surface points. All loads, which are applied in the nodal plane, are then transformed to the mid surface where the stiffness matrices, displacements and stresses are calculated. In order to be able to use this method more knowledge about its effects are needed, which is the reason for this thesis work. The offset is studied for two simpler cases, thickness variation and a 90°corner, as well as fora more complicated component called a C-bar. This is a hinge connecting the flaps to the wings of an airplane. The simpler cases are modeled using both mid surface and offset models subject to either a transverse load, an in-plane load or a bending moment. These are compared to a solid model in order to determine which is the most accurate. When mid surface modeling is used fort he thickness variation the surfaces are connected using rigid links. The conclusion made from these simulations is that using offset may give different results if the load is an in-plane load. This kind of load leads to the creation of a bending moment, which is linearly dependent on the amount of offset. The severity of this depends on the overall geometry and how this load is applied.

The presented thesis focuses on static analysis of plastic structures, taking into account nonlinear behaviour of the material depending on the stress. The static analysis is performed using the finite element method. The difference between material linear and material nonlinear approach is illustratively described in the introduction. A shell finite element, which is enhanced by the possibility of further delamination into layers and integration points along its thickness, is suitable to be used for a numerical analysis of a plastic structures. Separate chapters are devoted to the integration of the resulting values over the height of the cross-section. The integration of the material stiffness matrix correctly reflects the emergence of eccentricity. A part of the attention is devoted to the numerical quadrature rules. Next chapter is devoted to material nonlinear models. Two approaches are described: a simpler one, using the isotropic nonlinear elastic model, and more general one, using the orthotropic plastic model. The theoretical description is complemented by the graphic interpretation of the criteria according to the individual authors. A significant portion of this work is devoted to the algorithmization of calculation procedures described in the theoretical chapters. The algorithmization itself is implemented in Fortran language into a dynamic-link library which is part of the software program RFEM 5 which is widely used in engineering practice. A part of the work is a study comparing the performance of the different technologies applicable for the algorithmization of the described issues. The agreement of the theoretical analysis of the material models and subsequent implementation within the RFEM 5 is demonstrated on the example of the bent cantilever. The thermoplastic aboveground tank structure is subject of detailed material linear, and nonlinear analysis respectively. The various approaches are compared on the results of stress, deformation an

[pt] A formulação híbrida dos elementos finitos, proposta por Pian, com base no princípio variacional de Hellinger-Reissner, mostrou-se uma ótima alternativa para a construção de elementos finitos eficientes que atendessem a condições tanto de compatibilidade como de equilíbrio. O potencial de Hellinger-Reissner consiste na aproximação de dois campos: um campo tensões que satisfaz, a priori, as equações diferenciais homogêneas de equilíbrio do problema, e um campo de deslocamentos que atende a compatibilidade ao longo do contorno. O conjunto de funções não-singulares que satisfazem as equações governantes de um problema é conhecido como soluções fundamentais ou soluções de Trefftz, e é a base para a interpolação do campo de tensões no método híbrido de elementos finitos. O presente trabalho apresenta uma metodologia geral para a formulação de uma família de elementos finitos híbridos poligonais de membrana para problemas de elasticidade bidimensional, assim como elementos finitos híbridos simples e eficientes a para análise numérica de problemas de placa de Kirchhoff e Mindlin-Reissner. Algumas contribuições conceituais são introduzidas nas soluções fundamentais para a correta concepção dos elementos híbridos em problemas de placa espessa. O desempenho dos elementos é avaliado através de alguns exemplos numéricos, os quais os resultados são confrontados com os de outros elementos encontrados na literatura. / [en] The hybrid finite element formulation, proposed by Pian, on the basis of the Hellinger-Reissner variational principle, has proved to be a good alternative for the development of efficient finite elements that best attend compatibility and equilibrium conditions. The Hellinger-Reissner potential assumes two trial fields: a stress field that satisfies the equilibrium homogenous differential equation in the domain and a displacement field that attends the compatibility along the boundary. The set of nonsingular functions that satisfy the governing equations of the problem is known as Trefftz or fundamental solutions. This work presents a general methodology for the formulation of a family of polygonal hybrid elements for plane strain problems, as well as simple and efficient plate elements for the numerical evaluation of Kirchhoff and Mindlin-Reissner plate problems. Conceptual approaches are introduced for the correct use of fundamental solutions in the plate elements formulation. The performance of the proposed hybrid elements is assessed by means of several numerical examples from the literature.

Utbredningen av en brand inuti en byggnad kan leda till global eller lokal strukturell kollaps, särskilt i stålramkonstruktioner. Faktum är att stålkonstruktioner är särskilt utsatta för termiska angrepp på grund av ett högt värde av stålkonduktivitet och tvärsnitten med små tjockleken. Som en viktig aspekt av konstruktionen bör brandsäkerhetskrav uppnås antingen enligt föreskrivande regler eller enligt antagande av prestationsbaserad brandteknik. Trots möjligheten att använda enkla metoder som involverar membersanalys kombinerat med nominella brandkurvor, är en mer exakt analys av det termomekaniska beteendet hos en stålkonstruktion ett tilltalande alternativ eftersom det kan leda till mer ekonomiska och effektiva lösningar genom att ta hänsyn till möjliga gynnsamma mekanismer. Denna analys kräver vanligtvis utredning av delar av strukturen eller till och med av hela strukturen. För detta ändamål och för att få en djupare kunskap om strukturelementens beteende vid förhöjd temperatur bör numerisk simulering användas. I denna avhandling utvecklades och användes termomekaniska finita element som är lämpliga för analys av stålkonstruktioner utsätta för brand. Relevanta fallstudier utfördes. Utvecklingen av både ett termomekaniskt skal- och 3D balkelement baserade på en korotationsformulering presenteras. De flesta relevanta strukturfall kan undersökas på ett adekvat sätt genom att antingen använda något av dessa element eller kombinera dem. Korotationsformuleringen är väl lämpad för analyser av strukturer där stora förskjutningar, men små töjningar förekommer, som i fallet med stålkonstruktioner i brand. Elementens huvuddrag beskrivs, liksom deras karakterisering i termomekaniskt sammanhang. I detta avseende övervägdes materialnedbrytningen på grund av temperaturökningen och den termiska expansionen av stål vid härledningen av elementen. Dessutom presenteras en grenväxlingsprocedur för att utföra preliminära instabilitetsanalyser och få viktig inblick i efterknäckningsbeteendet hos stålkonstruktioner som utsätts för brand. Tillämpningen av de utvecklade numeriska verktygen ges i den del av avhandlingen som ägnas åt det publicerade forskningsarbetet. Flera aspekter av knäckningen av stålkonstruktionselement vid förhöjd temperatur diskuteras. I Artikel I tillhandahålls överväganden om påverkan av geometriska imperfektioner på beteendet hos komprimerade stålplattor och kolonner vid förhöjda temperaturer, liksom implikationer och resultat av användningen av grenväxlingsprocedur. I Artikel II valideras det föreslagna 3D-balkelementet genom meningsfulla fallstudier där torsionsdeformationer är signifikanta. De utvecklade balk- och skalelementen används i en undersökning av knäckningsmotstånd hos komprimerade vinkel-, Tee- och korsformade stålprofiler vid förhöjd temperatur som presenteras i Artikel III. En förbättrad knäckningskurva för design presenteras i detta arbete. Som ett exempel på tillämpningen av principerna för brandsäkerhetsteknik presenteras en omfattande analys i Artikel IV. Två relevanta brandscenarier identifieras för den undersökta byggnaden, som modelleras och analyseras i programmet SAFIR. / The ignition and the propagation of a fire inside a building may lead to global or local structural collapse, especially in steel framed structures. Indeed, steel structures are particularly vulnerable to thermal attack because of a high value of steel conductivity and of the small thickness that characterise the cross-sections. As a crucial aspect of design, fire safety requirements should be achieved either following prescriptive rules or adopting performance-based fire engineering. Despite the possibility to employ simple methods that involve member analysis under nominal fire curves, a more accurate analysis of the thermomechanical behaviour of a steel structural system is an appealing alternative, as it may lead to more economical and efficient solutions by taking into account possible favourable mechanisms. This analysis typically requires the investigation of parts of the structure or even of the whole structure. For this purpose, and in order to gain a deeper knowledge about the behaviour of structural members at elevated temperature, numerical simulation should be employed. In this thesis, thermomechanical finite elements, suited for the analyses of steel structures in fire, were developed and exploited in numerical simulation of relevant case studies. The development of a shell and of a 3D beam thermomechanical finite element based on a corotational formulation is presented. Most of the relevant structural cases can be adequately investigated by either using one of these elements or combining them. The corotational formulation is well suited for the analyses of structures in which large displacements, but small strains occur, as in the case of steel structures in fire. The main features of the elements are described, as well as their characterization in the thermomechanical context. In this regard, the material degradation due to the temperature increase and the thermal expansion of steel were considered in the derivation of the elements. In addition, a branch-switching procedure to perform preliminary instability analyses and get important insight into the post-buckling behaviour of steel structures subjected to fire is presented. The application of the developed numerical tools is provided in the part of the thesis devoted to the published research work. Several aspects of the buckling of steel structural elements at elevated temperature are discussed. In paper I, considerations about the influence of geometrical imperfections on the behaviour of compressed steel plates and columns at elevated temperatures are provided, as well as implications and results of the employment of the branch-switching procedure. In Paper II, the proposed 3D beam element is validated for meaningful case studies, in which torsional deformations are significant. The developed beam and shell elements are employed in an investigation of buckling resistance of compressed angular, Tee and cruciform steel profiles at elevated temperature presented in Paper III. An improved buckling curve for design is presented in this work. Furthermore, as an example of the application of Fire Safety Engineering principles, a comprehensive analysis is proposed in Paper IV. Two relevant fire scenarios are identified for the investigated building, which is modelled and analysed in the software SAFIR.