No description available.

<p align="justify">In a context of restoration of historical masonry structures, it is crucial to properly estimate the residual strength and the potential structural failure modes in order to assess the safety of buildings. Due to its mesostructure and the quasi-brittle nature of its constituents, masonry presents preferential damage orientations, strongly localised failure modes and damage-induced anisotropy, which are complex to incorporate in structural computations. Furthermore, masonry structures are generally subjected to complex loading processes including both in-plane and out-of-plane loads which considerably influence the potential failure mechanisms. As a consequence, both the membrane and the flexural behaviours of masonry walls have to be taken into account for a proper estimation of the structural stability.</p> <p align="justify">Macrosopic models used in structural computations are based on phenomenological laws including a set of parameters which characterises the average behaviour of the material. These parameters need to be identified through experimental tests, which can become costly due to the complexity of the behaviour particularly when cracks appear. The existing macroscopic models are consequently restricted to particular assumptions. Other models based on a detailed mesoscopic description are used to estimate the strength of masonry and its behaviour with failure. This is motivated by the fact that the behaviour of each constituent is a priori easier to identify than the global structural response. These mesoscopic models can however rapidly become unaffordable in terms of computational cost for the case of large-scale three-dimensional structures.</p> <p align="justify">In order to keep the accuracy of the mesoscopic modelling with a more affordable computational effort for large-scale structures, a multi-scale framework using computational homogenisation is developed to extract the macroscopic constitutive material response from computations performed on a sample of the mesostructure, thereby allowing to bridge the gap between macroscopic and mesoscopic representations. Coarse graining methodologies for the failure of quasi-brittle heterogeneous materials have started to emerge for in-plane problems but remain largely unexplored for shell descriptions. The purpose of this study is to propose a new periodic homogenisation-based multi-scale approach for quasi-brittle thin shell failure.</p> <p align="justify">For the numerical treatment of damage localisation at the structural scale, an embedded strong discontinuity approach is used to represent the collective behaviour of fine-scale cracks using average cohesive zones including mixed cracking modes and presenting evolving orientation related to fine-scale damage evolutions.</p> <p align="justify">A first originality of this research work is the definition and analysis of a criterion based on the homogenisation of a fine-scale modelling to detect localisation in a shell description and determine its evolving orientation. Secondly, an enhanced continuous-discontinuous scale transition incorporating strong embedded discontinuities driven by the damaging mesostructure is proposed for the case of in-plane loaded structures. Finally, this continuous-discontinuous homogenisation scheme is extended to a shell description in order to model the localised behaviour of out-of-plane loaded structures. These multi-scale approaches for failure are applied on typical masonry wall tests and verified against three-dimensional full fine-scale computations in which all the bricks and the joints are discretised.</p>

The Analytical Strip Method (ASM) for the analysis of thin cylindrical shells is presented in this dissertation. The system of three governing differential equations for the cylindrical shell are reduced to a single eighth order partial differential equation (PDE) in terms of a potential function. The PDE is solved as a single series form of the potential function, from which the displacement and force quantities are determined. The solution is applicable to isotropic, generally orthotropic, and laminated shells. Cylinders may have simply supported edges, clamped edges, free edges, or edges supported by isotropic beams. The cylindrical shell can be stiffened with isotropic beams in the circumferential direction placed anywhere along the length of the cylinder. The solution method can handle any combination of point loads, uniform loads, hydrostatic loads, sinusoidal loads, patch loads, and line loads applied in the radial direction. The results of the ASM are compared to results from existing analytical solutions and numerical solutions for several examples; the results for each of the methods were in good agreement. The ASM overcomes limitations of existing analytical solutions and provides an alternative to approximate numerical and semi-numerical methods.

Au cours des processus de conception,l’optimisation de formes apporte aux industriels dessolutions pour l’amélioration des performances desproduits. En particulier, les structures minces quiconstituent environ 70% d’un véhicule, sont une préoccupationdans l’industrie automobile. La plupartdes méthodes d’optimisation pour ces structures surfaciquesprésentent certaines limites et nécessitent desexpertises à chaque niveau de la procédure d’optimisation.L’objectif de cette thèse est de proposer une nouvellestratégie d’optimisation de formes pour les coquesminces. L’approche présentée consiste à exploiter leséquations de coques du modèle de Koiter en se basantsur une analyse isogéométrique. Cette méthode permetde réaliser des simulations sur la géométrie exacteen définissant la forme à l’aide de patchs CAO. Lesvariables d’optimisation choisies sont alors les pointsde contrôle permettant de piloter leur forme. La définitiondes patchs permet également de dégager ungradient de forme pour l’optimisation à l’aide d’uneméthode adjointe.Cette méthode a été appliquée pour des critères mécaniquesissus des bureaux d’études Renault. Des résultatsd’optimisation pour un critère de compliance sontprésentés. La définition et l’implémentation de critèresvibro-acoustiques sont discutés à la fin de cette thèse.Les résultats obtenus témoignent de l’intérêt de la méthode.Toutefois, de nombreux développements serontnécessaires avant d’être en mesure de l’appliquer dansl’industrie. / During the design process, optimizationof shapes offers manufacturers solutions for improvingproducts performances. In particular, thin shellstructures that represent about 70 % of a vehicle, area concern in the automotive industry. Most optimizationmethods for surface structures have limitationsand require expertise at every level of the optimizationprocedure.The aim of this thesis is to propose a new strategyfor the shape optimization of thin shell structures.The approach presented rely on using the Koiter’sshell model based on an isogeometric analysis. Thismethod allows for simulations on the exact geometryby defining the shape using CAD patches. Selectedoptimization variables are the control points used tocontrol the shape of the CAD patches. Variations ofthese points allows to scan a wide design space withfew parameters. The definition of patchs also enablesto find a gradient with respect to the shape for theoptimization by using the adjoint state method.This method was applied to mechanical criteria fromthe Renault design offices. Optimization results for acompliance criterion are presented. The definition andimplementation of vibro-acoustic criteria are discussedat the end of this thesis. The results demonstratethe interest of the method. However, many developmentswill be needed before being able to apply it inthe industry.

Uma metodologia para simular o crescimento de trincas por fadiga em estruturas pressurizadas de cascas delgadas e enrijecidas é implementada por meio de uma estrutura de software, que consiste em um programa de simulação de fraturamento associado a um programa de análise por elementos finitos. Permite-se que as trajetórias das trincas sejam arbitrárias, sendo calculadas incrementalmente como parte da simulação. As trajetórias são representadas em uma região localizada do modelo, que pode ser remodelada automaticamente a cada incremento de trinca por meio de um algoritmo de geração de malha de elementos de casca quadrilaterais. Duas alternativas de modelagem da região em torno da ponta da trinca são apresentadas: por elementos finitos de casca e por elementos sólidos. A metodologia assume que o crescimento da trinca seja caracterizado por quatro fatores de intensidade de tensão que modelam o comportamento de membrana pela teoria da elasticidade bidimensional, em estado plano de tensões, e o comportamento de placa pela na teoria de Kirchhoff. A resposta da estrutura de casca delgada pressurizada é determinada por meio do programa ADINA (Automatic Dynamic Incremental Nonlinear Analysis), que utiliza um procedimento de análise geometricamente não linear para elementos finitos de casca, formulados pela teoria de Reissner-Mindlin. Um estudo mostra que os fatores de Kirchhoff podem ser correlacionados aos fatores de Reissner-Mindlin por meio de expressões semi-empíricas. Fatores tridimensionais médios de intensidade de tensão são definidos e relacionados aos fatores das teorias da elasticidade bidimensional e de Reissner-Mindlin. Um exemplo de aplicação é apresentado, comparando-se os resultados das três teorias. A validação da metodologia é discutida por meio da simulação do crescimento de trincas por fadiga em um painel de teste em escala real da fuselagem de um Boeing 737. / A methodology for modeling fatigue crack growth in pressurized, stiffened, thin shell structures is implemented within a software framework that consists of a fracture simulation code associated with a finite element analysis code. Crack trajetories are allowed to be arbitrary and are computed incrementally as a part of the simulation. Trajectories are represented in a localized model region that can be remeshed automatically at each crack increment using a quadrilateral element surface meshing algorithm. Two alternatives for meshing the near crack tip region are presented: by shell finite elements and by solid finite elements. The methodology assumes that the crack growth is caracterized by four stress intensity factors that model the membrane behavior using two-dimensional plane stress elasticity and the plate behavior using Kirchhoff plate theory. The structural response of the pressurized thin shell is computed by ADINA (Automatic Dynamic Incremental Nonlinear Analysis) code, using a geometrically non-linear shell fiinite element analysis procedure, formulated by Reissner-Mindlin theory. A study shows that for thin shells the Kirchhoff factors can be related to the Reissner-Mindlin factors by mean of semi-empirical expressions. Three-dimensional average stress intensity factors are defined and related to the factors of the two-dimensional elasticity and the Reissner-Mindlin theories. An application example is presented and the results of the three theories are compared. The metodology validation is discussed by mean of a fatigue crack growth simulation in a full-scale pressurized panel test of a Boeing 737.

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.

Uma metodologia para simular o crescimento de trincas por fadiga em estruturas pressurizadas de cascas delgadas e enrijecidas é implementada por meio de uma estrutura de software, que consiste em um programa de simulação de fraturamento associado a um programa de análise por elementos finitos. Permite-se que as trajetórias das trincas sejam arbitrárias, sendo calculadas incrementalmente como parte da simulação. As trajetórias são representadas em uma região localizada do modelo, que pode ser remodelada automaticamente a cada incremento de trinca por meio de um algoritmo de geração de malha de elementos de casca quadrilaterais. Duas alternativas de modelagem da região em torno da ponta da trinca são apresentadas: por elementos finitos de casca e por elementos sólidos. A metodologia assume que o crescimento da trinca seja caracterizado por quatro fatores de intensidade de tensão que modelam o comportamento de membrana pela teoria da elasticidade bidimensional, em estado plano de tensões, e o comportamento de placa pela na teoria de Kirchhoff. A resposta da estrutura de casca delgada pressurizada é determinada por meio do programa ADINA (Automatic Dynamic Incremental Nonlinear Analysis), que utiliza um procedimento de análise geometricamente não linear para elementos finitos de casca, formulados pela teoria de Reissner-Mindlin. Um estudo mostra que os fatores de Kirchhoff podem ser correlacionados aos fatores de Reissner-Mindlin por meio de expressões semi-empíricas. Fatores tridimensionais médios de intensidade de tensão são definidos e relacionados aos fatores das teorias da elasticidade bidimensional e de Reissner-Mindlin. Um exemplo de aplicação é apresentado, comparando-se os resultados das três teorias. A validação da metodologia é discutida por meio da simulação do crescimento de trincas por fadiga em um painel de teste em escala real da fuselagem de um Boeing 737. / A methodology for modeling fatigue crack growth in pressurized, stiffened, thin shell structures is implemented within a software framework that consists of a fracture simulation code associated with a finite element analysis code. Crack trajetories are allowed to be arbitrary and are computed incrementally as a part of the simulation. Trajectories are represented in a localized model region that can be remeshed automatically at each crack increment using a quadrilateral element surface meshing algorithm. Two alternatives for meshing the near crack tip region are presented: by shell finite elements and by solid finite elements. The methodology assumes that the crack growth is caracterized by four stress intensity factors that model the membrane behavior using two-dimensional plane stress elasticity and the plate behavior using Kirchhoff plate theory. The structural response of the pressurized thin shell is computed by ADINA (Automatic Dynamic Incremental Nonlinear Analysis) code, using a geometrically non-linear shell fiinite element analysis procedure, formulated by Reissner-Mindlin theory. A study shows that for thin shells the Kirchhoff factors can be related to the Reissner-Mindlin factors by mean of semi-empirical expressions. Three-dimensional average stress intensity factors are defined and related to the factors of the two-dimensional elasticity and the Reissner-Mindlin theories. An application example is presented and the results of the three theories are compared. The metodology validation is discussed by mean of a fatigue crack growth simulation in a full-scale pressurized panel test of a Boeing 737.

Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.