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This work aims at dimensional reduction of nonlinear material models in an asymptotically accurate manner. The three-dimensional(3-D) nonlinear material models considered include isotropic, orthotropic and dielectric compressible hyperelastic material models. Hyperelastic materials have potential applications in space-based inflatable structures, pneumatic membranes, replacements for soft biological tissues, prosthetic devices, compliant robots, high-altitude airships and artificial blood pumps, to name a few. Such structures have special engineering properties like high strength-to-mass ratio, low deflated volume and low inflated density. The majority of these applications imply a thin shell form-factor, rendering the problem geometrically nonlinear as well. Despite their superior engineering properties and potential uses, there are no proper analysis tools available to analyze these structures accurately yet efficiently. The development of a unified analytical model for both material and geometric nonlinearities encounters mathematical difficulties in the theory but its results have considerable scope. Therefore, a novel tool is needed to dimensionally reduce these nonlinear material models. In this thesis, Prof. Berdichevsky’s Variational Asymptotic Method(VAM) has been applied rigorously to alleviate the difficulties faced in modeling thin shell structures(made of such nonlinear materials for the first time in the history of VAM) which inherently exhibit geometric small parameters(such as the ratio of thickness to shortest wavelength of the deformation along the shell reference surface) and physical small parameters(such as moderate strains in certain applications). Saint Venant-Kirchhoff and neo-Hookean 3-D strain energy functions are considered for isotropic hyperelastic material modeling. Further, these two material models are augmented with electromechanical coupling term through Maxwell stress tensor for dielectric hyperelastic material modeling. A polyconvex 3-D strain energy function is used for the orthotropic hyperelastic model. Upon the application of VAM, in each of the above cases, the original 3-D nonlinear electroelastic problem splits into a nonlinear one-dimensional (1-D) through-the-thickness analysis and a nonlinear two-dimensional(2-D) shell analysis. This greatly reduces the computational cost compared to a full 3-D analysis. Through-the-thickness analysis provides a 2-D nonlinear constitutive law for the shell equations and a set of recovery relations that expresses the 3-D field variables (displacements, strains and stresses) through thethicknessintermsof2-D shell variables calculated in the shell analysis (2-D). Analytical expressions (asymptotically accurate) are derived for stiffness, strains, stresses and 3-D warping field for all three material types. Consistent with the three types of 2-D nonlinear constitutive laws,2-D shell theories and corresponding finite element programs have been developed. Validation of present theory is carried out with a few standard test cases for isotropic hyperelastic material model. For two additional test cases, 3-Dfinite element analysis results for isotropic hyperelastic material model are provided as further proofs of the simultaneous accuracy and computational efficiency of the current asymptotically-correct dimensionally-reduced approach. Application of the dimensionally-reduced dielectric hyperelastic material model is demonstrated through the actuation of a clamped membrane subjected to an electric field. Finally, the through-the-thickness and shell analysis procedures are outlined for the orthotropic nonlinear material model.

La modélisation numérique des structures bois dans des conditions d’incendie nécessite la connaissance : de la variation des propriétés physiques du bois telles que la conductivité thermique, la chaleur spécifique et la densité en fonction de la température ; de la dégradation thermique du bois au cours des phases de séchage, de pyrolyse et de combustion. En particulier, nous nous sommes intéressés à l’étude du comportement thermomécanique du matériau bois. La loi thermique est décrite par l’équation de la chaleur. Le modèle choisi intègre les trois modes du transfert de chaleur : la conduction, le rayonnement et la convection. La loi mécanique est modélisée dans le cadre de la thermodynamique des processus irréversibles utilisant la notion des variables d’état. Elle tient compte du couplage entre le comportement élastique orthotrope, plastique anisotrope à écrouissage non linéaire isotrope et un endommagement isotrope. L’intégration numérique de la loi mécanique par un schéma implicite itératif combinant la technique du retour radial avec la réduction du nombre des équations est présentée. Le couplage thermomécanique est réalisé, selon l’approche réglementaire de l’Eurocode 5 relatif à la résistance au feu des structures en bois, en appliquant le facteur de réduction Kθ sur la résistance mécanique d’un résineux. Les aspects théoriques et les conditions aux limites associés au modèle thermomécanique sont abordés. L’identification des paramètres du modèle est réalisée sur des données expérimentales obtenues sur des tests réels d’incendie disponibles dans la littérature. À ce titre, plusieurs comparaisons avec différentes applications sont réalisées. Le modèle éléments finis reproduit avec précision la distribution du champ de température dans l’épaisseur des panneaux en bois, la formation du charbon ainsi que l’évolution de la résistance mécanique au cours de l’exposition au feu / Numerical modelling of timber structures in fire conditions requires the knowledge of the variation with temperature of the physical properties of the wood material (the thermal conductivity, the specific heat and the density) in order to take into account the thermal degradation of wood under high temperatures during the drying, pyrolysis and combustion phases, as well as the temperature profiles in the thickness of the surfaces exposed to fire. In particular, this work focusses on the thermomechanical behaviour of timber. The heat transfer analysis is described by the standard equations of heat conduction. It includes the three modes of heat transfer: conduction, radiation and convection. The structural response is modelled within the framework of thermodynamics of irreversible processes using the notion of state variables. It takes into account the coupling between the orthotropic elastic behaviour, the anisotropic plastic behaviour with isotropic nonlinear hardening, and isotropic damage. The numerical integration of the equilibrium equations is carried out with an iterative implicit scheme combining the technique of radial re- turn with the reduction of the number of equations. The thermomechanical coupling is carried out according to the approach recommended by Eurocode 5 for the fire resistance of timber structures by applying the reduction factor Kθ to the strength of a softwood. The theoretical aspects and boundary conditions associated with the thermomechanical model are also discussed. The parameters of the model are identified with experimental data obtained from actual fire tests available in the literature. Several comparative applications are carried out. The finite element model accurately reproduces the distribution of the temperature profile in the thickness of timber planks, the formation of the charred layer, and the evolution of the mechanical resistance during exposure to fire

Em experimentos com um cilindro flexível com rigidez a flexão ortotrópica, proporcionando razão entre frequências naturais longitudinal e transversal muito próximas a quatro (fx1fy1/=4,08), Fujarra et al (2001) [17] revelaram um ramo de resposta em VIV em alta velocidade. Tal ramo de respostas estável, excitado por perturbações a montante, era caracterizado por amplitudes transversais ao escoamento com ordem de 1 diâmetro e componentes de alta frequência no espectro de energia, estendendo-se por faixa de velocidade reduzida 12 < U* < 20 e esvaindo-se a partir da emergência de oscilações no segundo modo de vibração. Almejando aprofundar as investigações acerca deste intrigante achado experimental, uma nova campanha investigativa foi planejada e executada. Quatro cilindros flexíveis com distintas razões de rigidez ortotrópica foram construídos em resina polimérica, com enrijecedores internos de seções retangulares feitos de alumínio, resultando um conjunto com frequências naturais, correspondentes a modos longitudinais e transversais, com razões relativas: 4:1, 3:1, 2:1 e 1:1. Os cilindros foram verticalmente fixados a uma célula de carga 3D. Uma série de ensaios foi conduzida, sob velocidade de escoamento crescente e decrescente. As vibrações dos cilindros flexíveis foram capturadas através de um sistema óptico subaquático, posicionado a jusante, que rastreava a posição de alvos constituídos por fitas refletivas afixadas ao longo do comprimento do cilindro. Clássicas técnicas de análise espectral, decomposição modal no domínio do tempo e a Transformada de Hilbert-Huang foram utilizadas de modo encadeado e recursivo com o fim de determinar as respostas de vibração, em amplitude e frequências dominantes, em função da velocidade reduzida. O ramo de resposta em altas velocidades reduzidas foi recuperado nos experimentos com os quatro cilindros. Análise comparativa sistemática permitiu concluir que o ramo de resposta em tela se deve ao lock-in de modos longitudinais, que são excitados em velocidades reduzidas tão mais altas quanto maior for a razão de frequências considerada. Empregando-se, então, os deslocamentos e velocidades modais medidos em formulação de Mineto (2013) [23], foi realizada estimativa de potência elétrica a ser extraída pelo emprego de finos filmes de material piezelétrico depositados sobre as lâminas enrijecedoras internas aos cilindros. / A previous work by Fujarra et al. (2001) revealed a \"high speed mode branch\" in cantilevered flexible cylinders subjected to VIV. That work studied a flexible cylinder with orthotropic bending stiffness in a recirculating water channel, by setting the ratio between the first natural frequencies, in the in-line and cross-wise directions to the flow, very close to four (fx1fy1/=4,08). Such a new stable response branch, triggered by upstream hydrodynamic perturbations, was characterized by amplitudes, perpendicular to the flow, of order of one diameter and by high frequencies components in the energy spectrum. The branch extends from reduced velocity circa 12 up to 20, being extinguished by the onset of the second vibration mode lock-in. Aiming at investigating further this intriguing experimental finding, a new campaign has been planned and performed. Four flexible cylinders with distinct orthotropic bending ratios were built, by molding thin aluminum stiffeners, of rectangular cross section, inside the cylinders made of a flexible resin. The respective natural frequencies ratio, between in-line and cross-wise bending modes, was set to 4:1, 3:1, 2:1 and 1:1. The flexible cylinders were vertically clamped to a 3D load cell. A series of experimental runs were carried out, under ascending and descending flow speeds. The flexible cylinder vibration was captured trough an underwater optical system, placed downstream, by tracking 3D Cartesian coordinates of reflective strips placed all along the span, at equi-spaced cross sections. Besides standard spectral analysis techniques, modal decomposition in time domain and the Hilbert-Huang Transform have been recursively used together to determine amplitude and dominant response frequencies. The \"high speed mode branch\" revealed for all four cylinders tested. Systematic comparative analysis allowed us to conclude that such a response branch is caused by the lock-in of longitudinal modes, excited at reduced velocities ranges that increase with the frequency ratio considered. Finally, using measured modal responses in Mineto (2013) [23] formulation, the electric power that would be extracted by the use of thin piezoelectric layers deposited over the internal stiffeners blades was estimated.

Le comportement géomécanique des ouvrages géotechniques à l’exemple des rideaux de palplanches est entaché d’incertitudes épistémiques liées aux hypothèses régissant le modèle géomécanique de calcul, mais aussi d’incertitudes aléatoires liées à la variabilité spatiale du sol. L’objectif principal de cette thèse est de mieux appréhender l’effet de ces incertitudes sur le comportement d’un rideau de palplanches. Pour cela le présent mémoire s’articule autour de quatre points principaux : Le premier point est relatif d’une part à l’analyse des hypothèses utilisées pour la modélisation géomécanique d’un rideau de palplanches et d’autre part à l’extension de la méthode des coefficients de réaction d’un système unidimensionnel basé sur une poutre et des appuis élastoplastiques à un système bidimensionnel de plaque orthotrope sur le même type d’appuis (MISS-CR-PLQ). Le deuxième point concerne la modélisation de la variabilité spatiale du sol. Après une comparaison entre deux méthodes de génération de champs aléatoires nous avons retenu la méthode Circulant Embedding pour son efficience. Plusieurs études paramétriques ont été menées pour analyser les effets des hypothèses prises lors de la génération des champs aléatoires. Le troisième point concerne la mise en place d’une démarche mécano-fiabiliste permettant d’intégrer la variabilité spatiale du sol pour le cas des rideaux de palplanches. Le quatrième point est consacré à l’application de la démarche développée pour un cas d’étude à travers des analyses probabilistes et fiabilistes. L’influence des paramètres statistiques (e.g. les longueurs de corrélations, la corrélation croisée, …), mécanique et géométrique a été étudiée. / The geomechanical behaviour of geotechnical structures such as sheet pile walls is subjected to epistemic uncertainties due to geomechanical models’ assumptions and also the aleatory uncertainties which could be related to the soil spatial variability. The main objective of this thesis is to gain more insight into the effect of these uncertainties on the sheet pile behaviour. To this end, this thesis focuses on four main issues: The first one is related on the one hand to the analysis of the used geomechanical hypotheses for modelling of retaining walls. On the other hand, to extend the one-dimensional subgrade reaction method which is based on a beam relying on elastoplastic supports to a two-dimensional system that call to an orthotropic plate relying on the same supports (MISS-CR-PLQ). The second issue concerns the soil spatial variability modelling. After a key comparison between two random field generation methods, we selected the Circulating Embedding method for its efficiency. Several parametric studies have been conducted to analyse the effects of different assumptions of random field generation. The third issue is related to the implementation of the proposed mechanical-reliability approach taking into account the soil spatial variability. The last issue is devoted to the application of the developed approach to a case study through probabilistic and reliability analyses. The influence of statistical parameters (e.g. correlation lengths, cross-correlation,...), mechanical and geometrical has been examined.

Em experimentos com um cilindro flexível com rigidez a flexão ortotrópica, proporcionando razão entre frequências naturais longitudinal e transversal muito próximas a quatro (fx1fy1/=4,08), Fujarra et al (2001) [17] revelaram um ramo de resposta em VIV em alta velocidade. Tal ramo de respostas estável, excitado por perturbações a montante, era caracterizado por amplitudes transversais ao escoamento com ordem de 1 diâmetro e componentes de alta frequência no espectro de energia, estendendo-se por faixa de velocidade reduzida 12 < U* < 20 e esvaindo-se a partir da emergência de oscilações no segundo modo de vibração. Almejando aprofundar as investigações acerca deste intrigante achado experimental, uma nova campanha investigativa foi planejada e executada. Quatro cilindros flexíveis com distintas razões de rigidez ortotrópica foram construídos em resina polimérica, com enrijecedores internos de seções retangulares feitos de alumínio, resultando um conjunto com frequências naturais, correspondentes a modos longitudinais e transversais, com razões relativas: 4:1, 3:1, 2:1 e 1:1. Os cilindros foram verticalmente fixados a uma célula de carga 3D. Uma série de ensaios foi conduzida, sob velocidade de escoamento crescente e decrescente. As vibrações dos cilindros flexíveis foram capturadas através de um sistema óptico subaquático, posicionado a jusante, que rastreava a posição de alvos constituídos por fitas refletivas afixadas ao longo do comprimento do cilindro. Clássicas técnicas de análise espectral, decomposição modal no domínio do tempo e a Transformada de Hilbert-Huang foram utilizadas de modo encadeado e recursivo com o fim de determinar as respostas de vibração, em amplitude e frequências dominantes, em função da velocidade reduzida. O ramo de resposta em altas velocidades reduzidas foi recuperado nos experimentos com os quatro cilindros. Análise comparativa sistemática permitiu concluir que o ramo de resposta em tela se deve ao lock-in de modos longitudinais, que são excitados em velocidades reduzidas tão mais altas quanto maior for a razão de frequências considerada. Empregando-se, então, os deslocamentos e velocidades modais medidos em formulação de Mineto (2013) [23], foi realizada estimativa de potência elétrica a ser extraída pelo emprego de finos filmes de material piezelétrico depositados sobre as lâminas enrijecedoras internas aos cilindros. / A previous work by Fujarra et al. (2001) revealed a \"high speed mode branch\" in cantilevered flexible cylinders subjected to VIV. That work studied a flexible cylinder with orthotropic bending stiffness in a recirculating water channel, by setting the ratio between the first natural frequencies, in the in-line and cross-wise directions to the flow, very close to four (fx1fy1/=4,08). Such a new stable response branch, triggered by upstream hydrodynamic perturbations, was characterized by amplitudes, perpendicular to the flow, of order of one diameter and by high frequencies components in the energy spectrum. The branch extends from reduced velocity circa 12 up to 20, being extinguished by the onset of the second vibration mode lock-in. Aiming at investigating further this intriguing experimental finding, a new campaign has been planned and performed. Four flexible cylinders with distinct orthotropic bending ratios were built, by molding thin aluminum stiffeners, of rectangular cross section, inside the cylinders made of a flexible resin. The respective natural frequencies ratio, between in-line and cross-wise bending modes, was set to 4:1, 3:1, 2:1 and 1:1. The flexible cylinders were vertically clamped to a 3D load cell. A series of experimental runs were carried out, under ascending and descending flow speeds. The flexible cylinder vibration was captured trough an underwater optical system, placed downstream, by tracking 3D Cartesian coordinates of reflective strips placed all along the span, at equi-spaced cross sections. Besides standard spectral analysis techniques, modal decomposition in time domain and the Hilbert-Huang Transform have been recursively used together to determine amplitude and dominant response frequencies. The \"high speed mode branch\" revealed for all four cylinders tested. Systematic comparative analysis allowed us to conclude that such a response branch is caused by the lock-in of longitudinal modes, excited at reduced velocities ranges that increase with the frequency ratio considered. Finally, using measured modal responses in Mineto (2013) [23] formulation, the electric power that would be extracted by the use of thin piezoelectric layers deposited over the internal stiffeners blades was estimated.

L’objectif principal de cette thèse est de modéliser en flambement des poutres pressurisées en tissu souple homogène orthotrope (THO) composite. La première partie détaille les études expérimentales qui ont été menées sur des poutres gonflables à certain niveaux de pression afin de caractériser les propriétés mécaniques du matériau et le comportement en flambement de la structure. Dans une deuxième partie, une approche analytique a été envisagée afin d’étudier le flambement ainsi que le comportement d’une poutre gonflable orthotrope. Un modèle 3D gonflables poutre orthotrope basé sur la cinématique de Timoshenko a été présenté brièvement. La charge critique a été étudiée pour différents cas de charge avec différentes conditions aux limites. Les résultats ont été confrontés aux résultats théoriques disponibles. Pour vérifier la limite de validité des résultats, la charge d’apparition des plis a également fait l’objet d’une étude pour chacun des cas. La dernière partie est consacrée à une étude linéaire et à une analyse non-linéaire du flambement de la poutre gonflable en THO composite. Le modèle éléments finis (MEF) établi ici implique un élément poutre de Timoshenko à trois-nœuds avec une continuité de type C0. Un test de convergence du maillage sur la force critique de la poutre a été réalisé par la résolution du problème aux valeurs propres. En outre, un MEF non-linéaire a été développé en utilisant la procédure itérative de quasi-Newton avec incréments de chargement adaptatif permettant le tracé pas à pas de la réponse charge-déflexion de la poutre. Les résultats ont été validés à partir d’un certain niveau de pression par des résultats expérimentaux et numériques / The main goals of this thesis are to modeling and to perform the buckling study of inflatable beams made from homogeneous orthotropic woven fabric (HOWF) composite. Three main scenarios were investigated in this thesis. The first is the experimental studies which were performed on HOWF inflatable beam in various inflation pressures for characterizing the orthotropic mechanical properties and buckling behaviors of the beam. In the second scenario, an analytical approach was considered to study the buckling and the behavior of an inflatable orthotropic beam. A 3D inflatable orthotropic beam model based on the Timoshenko's kinematics was briefly introduced: the nonlinearities (finite rotation, follower forces) were included in this model. The results were compared with theoretical results available in the literature. To check the limit of validity of the results, the wrinkling load was also presented in every case. The last scenario is devoted to the linear eigen and non-linear buckling analysis of inflatable beam made of HOWF. The finite element (FE) model established here involves a three-noded Timoshenko beam element with C0-type continuity for the transverse displacement and quadratic shape functions for the bending rotation and the axial displacement. In the linear buckling analysis, a mesh convergence test on the beam critical load was carried out by solving the linearized eigenvalue problem. In addition, a nonlinear FE model was developed by using the quasi-Newton iteration with adaptive load stepping for tracing load-deflection response of the beam. The results were validated from a certain pressure level by experimental and thin-shell FE results

The aim of this bachelor thesis is variant design and assessment of loadbearing structure of steel footbridge over I/11 route. Main superstructure will have two steel arched beams joined with lower orthotropic deck using suspenders in the „V“ shape. For assessment of superstructure a three-dimensional structural computational model was created in software Dlubal RFEM 5.20. The span of the footbridge is 48,71 m, free width is 4 m, height is 7,5 m. The structure was designed according to currently valid standarts to the ultimate limit state and serviceability limit state. Supporting elements are designed from steel of class S355.

The subject of this diploma thesis is static verification steel structure of exist railway bridge in accordance with the valid standards. The bridge have three simple spans with a span of 25; 98 and 25 meters, outer fields are simple beams, the middle field is the beam reinforced with an arch with vertical rods. Steel orthotropic deck with longitudinal stiffeners and crossbeams. Further were designed and analyse other possible options super structure of the middle field, and the resulting variant as a circle span with radial rods was detail solved and made documentation.

The objective of this diploma thesis is the stress-strain analysis of the crack terminating at the orthotropic bi-material interface suggested as the plane problem of the linear fracture mechanics. The first part is engaged in basic relations of the linear fracture mechanics. The second part is focused on the singularity exponent evaluation for the crack impinging and generally inclined with respect to the bi-material interface. It follows the determination of the generalized stress intensity factors applying the analytical-numerical approach represented by the finite element analysis. The last part of this work is focused on the testing of algorithms applied to the specific crack and bi-material interface configurations. A conclusion discusses the influence of the bi-material mechanical properties and the angel of the crack inclination to the obtained numerical results.