Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / Spherical shells are widely used in aerospace, mechanical, marine, and other industrial applications. Accordingly, the accurate determination of their behavior becomes more and more important. One of the most important problems in spherical shell behavior is the determination of buckling loads either experimentally or theoretically. Therefore, in this study some elastic and plastic buckling problems associated with spherical shells are investigated. The first part of this research study presents the analytical, numerical, and experimental results of moderately thick and thin hemispherical metal shells into the plastic buckling range illustrating the importance of geometry changes on the buckling load. The hemispherical shell is rigidly supported around the base circumference against horizontal translation and the load is vertically applied by a rigid cylindrical boss (Loading actuator) at the apex. Kinematics stages of initial buckling and subsequent propagation of plastic deformation for a rigid-perfectly plastic shell models are formulated on the basis of Drucker- Shield's limited interaction yield condition. The effect of the radius of the boss used to apply the loading, on the initial and subsequent collapse load is studied. In the numerical model, the material is assumed to be isotropic and linear elastic perfectly plastic without strain hardening obeying the Tresca or Von Mises yield criterion. Finally, the results of the analytical solution are compared and verified with the numerical results using ABAQUS software and experimental findings. Good agreement is observed between the load-deflection curves obtained using three different fundamental approaches. In the second part, the Southwell’s nondestructive method for columns is analytically extended to spherical shells subjected to uniform external pressure acting radially. Subsequently finite element simulation and experimental work shown that the theory is applicable to spherical shells with an arbitrary axi-symmetrical loading too. The results showed that the technique provides a useful estimate of the elastic buckling load provided care is taken in interpreting the results. The usefulness of the method lies in its generality, simplicity and in the fact that, it is non-destructive. Moreover, it does not make any assumption regarding the number of buckling waves or the exact localization of buckling

The purpose of the work presented in this thesis is to implement co-rotational beam elements and branch-switching procedures in order to analyse elastic and elastoplasticinstability problems. For the 2D beam elements, the co-rotational framework is taken from Crisfield [23]. The main objective is to compare three different local elasto-plastic elements. The 3D co-rotational formulation is based on the work of Pacoste and Eriksson [73],with new items concerning the parameterisation of the finite rotations, the definitionof the local frame, the inclusion of warping effects through the introduction of aseventh nodal degree of freedom and the consideration of rigid links. Differenttypes of local formulations are considered, including or not warping effects. It isshown that at least some degree of non-linearity must be introduced in the localstrain definition in order to obtain correct results for certain classes of problems. Within the present approach any cross-section can be modelled, and particularly, the centroid and shear center are not necessarily coincident.Plasticity is introduced via a von Mises material with isotropic hardening. Numericalintegration over the cross-section is performed. At each integration point, theconstitutive equations are solved by including interaction between the normal andshear stresses. Concerning instabilities, a new numerical method for the direct computation of elasticcritical points is proposed. This is based on a minimal augmentation procedure asdeveloped by Eriksson [32–34]. In elasto-plasticity, a literature survey, mainly concernedwith theoretical aspects is first presented. The objective is to get a completecomprehension of the phenomena and to give a basis for the two branch-switchingprocedures presented in this thesis.A large number of examples are used in order to assess the performances of the elements and the path-following procedures. / QC 20100512

Dentre os principais problemas que ocorrem na estampagem de chapas metálicas estão a fratura, e estricção (necking) e o enrugamento (wrinkling). Este último pode fazer com que a peça fabricada seja rejeitada por problemas que vão desde motivos estéticos até dificuldades de montagem destas peças e desgaste excessivo da ferramenta. Diversos pesquisadores tem estudado o problema de instabilidade à compressão que origina o fenômeno de enrugamento. Pretende-se estudar os principais métodos para predição do enrugamento, a saber, a teoria da bifurcação, a introdução de uma falha induzida e a aplicação do indicador proposto por Nordlund e Häggblad (coeficiente NH). O método escolhido será implementado junto a um programa de análise por elementos finitos de modo a obter diagramas limite de estabilidade, para então ser aplicado a peças mais genéricas. O procedimento é aplicado a peças de geometria relevante para serem ensaiadas experimentalmente de modo a validar as simulações numéricas propostas. / Among the main problems in sheet metal forming processes are the fracture, the necking and the wrinkling behavior of the material. The last one can produce rejected parts due difficulties in the assembly of these parts or excessive wear of the tooling. Many researchers have been studied the problem of the compression instability phenomenon that origins the wrinkling behavior. The objective of this work is the study of the main available methods to the wrinkling prediction, as the bifurcation theory, the induced defect and an indicator proposed by Nordlund and Häggblad (NH coefficient). The more suitable method is implemented into a finite element analysis software in order to obtain the stability limit diagrams that can be used in the design of generic shape parts. Experimental studies will be done in parts subjected to compressive forming loads in order to validate the numerical simulations.

Elementos estruturais como as placas finas fazem parte de um grande número de aplicações nas mais diversas áreas da engenharia e são de grande importância para a engenharia naval e aeronáutica, na construção de cascos de embarcações e estruturas offshore, e na construção de fuselagens de aviões. Por constituírem-se em um elemento estrutural esbelto, estão sujeitas a um comportamento mecânico diferenciado denominado de flambagem, proveniente de um carregamento de compressão uniaxial. O fenômeno da flambagem pode ser dividido em flambagem elástica e elasto-plástica, sendo dependente de aspectos dimensionais, construtivos e/ou operacionais. A inclusão de perfurações em placas provoca uma redistribuição de suas tensões internas, afetando não apenas a sua resistência, mas também as suas características de flambagem. Neste trabalho, desenvolveu-se a análise do comportamento mecânico de placas finas perfuradas de aço, simplesmente apoiadas em suas bordas, e submetidas à compressão. Serão analisados dois graus de liberdade: H/L e H0/L0. Para H/L, serão analisadas placas com H/L = 1,00 e H/L = 0,50, sendo que H e L representam, respectivamente, a largura e o comprimento da placa. Para H0/L0, serão analisadas infinitas possibilidades, sendo que H0 e L0 representam, respectivamente, a largura e o comprimento da perfuração. As placas utilizadas possuem espessura (h) de 10,00 mm e perfuração centralizada. Quanto às perfurações, estas serão dos tipos: oblonga longitudinal, oblonga transversal, elíptica, retangular, losangular, hexagonal longitudinal e hexagonal transversal. Ainda em relação às perfurações, serão consideradas as seguintes frações ϕ = 0,08; 0,10; 0,15; 0,20 e 0,25, sendo que (ϕ) corresponde ao volume da perfuração. Para a determinação das cargas crítica e última de flambagem, foi utilizada a simulação numérica com o auxílio do software Ansys®, que é baseado no método dos elementos finitos. A aplicação do método Design Construtal, possibilitou a determinação das geometrias ótimas para todos os tipos de perfurações, todos os valores de (ϕ) e para todas as relações de H/L. Os resultados obtidos mostram que há influência do tipo, da forma e do tamanho da perfuração na definição das curvas limites à flambagem e das curvas à flambagem elasto-plástica. Foi possível definir, para cada tipo de perfuração e para todos os valores de (ϕ), os pontos de transição entre a flambagem elástica e à elasto-plástica, assim como os pontos que definem os valores máximos para o fator TLNMáx (tensão limite normalizadora). / Structural elements such as thin plates are part of a large number of applications in various areas of engineering and are of great importance for marine and aerospace engineering, construction and offshore structures hulls, and the construction of airplane fuselages. Being a slender structural element, they are subject to a different mechanical behavior known as buckling, caused by a compressive loading. The phenomenon of buckling can be divided in elastic and elasto-plastic buckling, being dependent dimensional, construction and / or operational aspects. The inclusion of perforations in plates causes a redistribution of its internal stress, affecting not only their resistance but also their buckling characteristics. In this work it was performed the analysis of the mechanical behavior of thin perforated steel plates, simply supported on its edges, and subjected to compression. In the analysis it was considered two degrees of freedom: H/L and H0/L0. For H/L will be analyzed plates with H/L = 1.00 and H/L = 0.50, wherein H and L represent respectively the width and length of the plate. There are endless possibilities for the relation H0/L0. The studied plates have a thickness (h) of 10.00 mm and centralized perforation. The following types of perforation will be used: longitudinal oblong, transverse oblong, elliptical, rectangular, diamond, longitudinal hexagonal and transverse hexagonal. Also in relation to perforations, it will be considered the following fractions (ϕ = 0.08; 0.10; 0.15; 0.20 and 0.25), wherein (ϕ) corresponds to the volume ratio of the perforation. For determining the critical and ultimate buckling loads it was utilized numerical simulation with the assistance of Ansys® software, which is based on the finite element method. The application of the Constructal Design method of this study made it possible to determine the optimal geometries for all types of perforations, for all values of (ϕ) and all the relations H/L. The results show that there is an influence of the perforation type, shape and size, in defining the limit curves of the buckling and the curves of the elasto-plastic buckling. It was also possible to define, for each type of perforation and for all (ϕ) values, the transition points between elastic and elasto-plastic buckling; as well as the points that define the maximum values for the TLNMáx factor (normalized limit stress).

The recent substantial increase in world demand for energy and raw material resources has accelerated oil and gas exploration and production. At the same time, the depletion of onshore and shallow water oil resources presents a challenge to engineers to develop new means of harvesting and transporting oil and gas from harsh and remote areas. Sandwich Pipe (SP) is a relatively new design concept developed to address the transportation of oil in deep and ultra-deep waters as well as in cold environments. The main focus of this thesis is on the characterization of the structural performance of these novel systems. Deep and ultra-deep water offshore pipelines are subjected to excessive hydrostatic external pressure during installation and operation. In this research, an innovative analytical solution was developed to evaluate the external pressure capacity of SPs by calculating the linear eigenvalues of the characteristic equations of the system. In the proposed solution, the interface condition between the layers of the system is accounted for in the governing equations. As well, a set of comprehensive parametric studies using the Finite Element (FE) method was developed to investigate both the elastic and plastic buckling response of SPs. The influence of various structural parameters such as the material, geometrical and intra-layer interaction properties on the characteristic behavior and the buckling pressure of SPs was examined. In addition to the proposed analytical solution, two sets of semi-empirical equations based on the FE analysis results were recommended in calculating the elastic and plastic buckling pressure of SPs. As bending represents an important loading state in the installation and service life of SPs, it should be considered a governing loading scenario. In this thesis, the behavior of SPs under bending was investigated using a comprehensive set of parametric studies. SP systems with a wide practical range of physical parameters were analyzed using the FE method, and the influence of various structural parameters on the characteristic response and bending capacity of the system was explored, including pipe geometry, core layer properties, material yield anisotropy of high-grade steel pipes, and various intra-layer adhesion configurations.

Elementos estruturais como as placas finas fazem parte de um grande número de aplicações nas mais diversas áreas da engenharia e são de grande importância para a engenharia naval e aeronáutica, na construção de cascos de embarcações e estruturas offshore, e na construção de fuselagens de aviões. Por constituírem-se em um elemento estrutural esbelto, estão sujeitas a um comportamento mecânico diferenciado denominado de flambagem, proveniente de um carregamento de compressão uniaxial. O fenômeno da flambagem pode ser dividido em flambagem elástica e elasto-plástica, sendo dependente de aspectos dimensionais, construtivos e/ou operacionais. A inclusão de perfurações em placas provoca uma redistribuição de suas tensões internas, afetando não apenas a sua resistência, mas também as suas características de flambagem. Neste trabalho, desenvolveu-se a análise do comportamento mecânico de placas finas perfuradas de aço, simplesmente apoiadas em suas bordas, e submetidas à compressão. Serão analisados dois graus de liberdade: H/L e H0/L0. Para H/L, serão analisadas placas com H/L = 1,00 e H/L = 0,50, sendo que H e L representam, respectivamente, a largura e o comprimento da placa. Para H0/L0, serão analisadas infinitas possibilidades, sendo que H0 e L0 representam, respectivamente, a largura e o comprimento da perfuração. As placas utilizadas possuem espessura (h) de 10,00 mm e perfuração centralizada. Quanto às perfurações, estas serão dos tipos: oblonga longitudinal, oblonga transversal, elíptica, retangular, losangular, hexagonal longitudinal e hexagonal transversal. Ainda em relação às perfurações, serão consideradas as seguintes frações ϕ = 0,08; 0,10; 0,15; 0,20 e 0,25, sendo que (ϕ) corresponde ao volume da perfuração. Para a determinação das cargas crítica e última de flambagem, foi utilizada a simulação numérica com o auxílio do software Ansys®, que é baseado no método dos elementos finitos. A aplicação do método Design Construtal, possibilitou a determinação das geometrias ótimas para todos os tipos de perfurações, todos os valores de (ϕ) e para todas as relações de H/L. Os resultados obtidos mostram que há influência do tipo, da forma e do tamanho da perfuração na definição das curvas limites à flambagem e das curvas à flambagem elasto-plástica. Foi possível definir, para cada tipo de perfuração e para todos os valores de (ϕ), os pontos de transição entre a flambagem elástica e à elasto-plástica, assim como os pontos que definem os valores máximos para o fator TLNMáx (tensão limite normalizadora). / Structural elements such as thin plates are part of a large number of applications in various areas of engineering and are of great importance for marine and aerospace engineering, construction and offshore structures hulls, and the construction of airplane fuselages. Being a slender structural element, they are subject to a different mechanical behavior known as buckling, caused by a compressive loading. The phenomenon of buckling can be divided in elastic and elasto-plastic buckling, being dependent dimensional, construction and / or operational aspects. The inclusion of perforations in plates causes a redistribution of its internal stress, affecting not only their resistance but also their buckling characteristics. In this work it was performed the analysis of the mechanical behavior of thin perforated steel plates, simply supported on its edges, and subjected to compression. In the analysis it was considered two degrees of freedom: H/L and H0/L0. For H/L will be analyzed plates with H/L = 1.00 and H/L = 0.50, wherein H and L represent respectively the width and length of the plate. There are endless possibilities for the relation H0/L0. The studied plates have a thickness (h) of 10.00 mm and centralized perforation. The following types of perforation will be used: longitudinal oblong, transverse oblong, elliptical, rectangular, diamond, longitudinal hexagonal and transverse hexagonal. Also in relation to perforations, it will be considered the following fractions (ϕ = 0.08; 0.10; 0.15; 0.20 and 0.25), wherein (ϕ) corresponds to the volume ratio of the perforation. For determining the critical and ultimate buckling loads it was utilized numerical simulation with the assistance of Ansys® software, which is based on the finite element method. The application of the Constructal Design method of this study made it possible to determine the optimal geometries for all types of perforations, for all values of (ϕ) and all the relations H/L. The results show that there is an influence of the perforation type, shape and size, in defining the limit curves of the buckling and the curves of the elasto-plastic buckling. It was also possible to define, for each type of perforation and for all (ϕ) values, the transition points between elastic and elasto-plastic buckling; as well as the points that define the maximum values for the TLNMáx factor (normalized limit stress).

Elementos estruturais como as placas finas fazem parte de um grande número de aplicações nas mais diversas áreas da engenharia e são de grande importância para a engenharia naval e aeronáutica, na construção de cascos de embarcações e estruturas offshore, e na construção de fuselagens de aviões. Por constituírem-se em um elemento estrutural esbelto, estão sujeitas a um comportamento mecânico diferenciado denominado de flambagem, proveniente de um carregamento de compressão uniaxial. O fenômeno da flambagem pode ser dividido em flambagem elástica e elasto-plástica, sendo dependente de aspectos dimensionais, construtivos e/ou operacionais. A inclusão de perfurações em placas provoca uma redistribuição de suas tensões internas, afetando não apenas a sua resistência, mas também as suas características de flambagem. Neste trabalho, desenvolveu-se a análise do comportamento mecânico de placas finas perfuradas de aço, simplesmente apoiadas em suas bordas, e submetidas à compressão. Serão analisados dois graus de liberdade: H/L e H0/L0. Para H/L, serão analisadas placas com H/L = 1,00 e H/L = 0,50, sendo que H e L representam, respectivamente, a largura e o comprimento da placa. Para H0/L0, serão analisadas infinitas possibilidades, sendo que H0 e L0 representam, respectivamente, a largura e o comprimento da perfuração. As placas utilizadas possuem espessura (h) de 10,00 mm e perfuração centralizada. Quanto às perfurações, estas serão dos tipos: oblonga longitudinal, oblonga transversal, elíptica, retangular, losangular, hexagonal longitudinal e hexagonal transversal. Ainda em relação às perfurações, serão consideradas as seguintes frações ϕ = 0,08; 0,10; 0,15; 0,20 e 0,25, sendo que (ϕ) corresponde ao volume da perfuração. Para a determinação das cargas crítica e última de flambagem, foi utilizada a simulação numérica com o auxílio do software Ansys®, que é baseado no método dos elementos finitos. A aplicação do método Design Construtal, possibilitou a determinação das geometrias ótimas para todos os tipos de perfurações, todos os valores de (ϕ) e para todas as relações de H/L. Os resultados obtidos mostram que há influência do tipo, da forma e do tamanho da perfuração na definição das curvas limites à flambagem e das curvas à flambagem elasto-plástica. Foi possível definir, para cada tipo de perfuração e para todos os valores de (ϕ), os pontos de transição entre a flambagem elástica e à elasto-plástica, assim como os pontos que definem os valores máximos para o fator TLNMáx (tensão limite normalizadora). / Structural elements such as thin plates are part of a large number of applications in various areas of engineering and are of great importance for marine and aerospace engineering, construction and offshore structures hulls, and the construction of airplane fuselages. Being a slender structural element, they are subject to a different mechanical behavior known as buckling, caused by a compressive loading. The phenomenon of buckling can be divided in elastic and elasto-plastic buckling, being dependent dimensional, construction and / or operational aspects. The inclusion of perforations in plates causes a redistribution of its internal stress, affecting not only their resistance but also their buckling characteristics. In this work it was performed the analysis of the mechanical behavior of thin perforated steel plates, simply supported on its edges, and subjected to compression. In the analysis it was considered two degrees of freedom: H/L and H0/L0. For H/L will be analyzed plates with H/L = 1.00 and H/L = 0.50, wherein H and L represent respectively the width and length of the plate. There are endless possibilities for the relation H0/L0. The studied plates have a thickness (h) of 10.00 mm and centralized perforation. The following types of perforation will be used: longitudinal oblong, transverse oblong, elliptical, rectangular, diamond, longitudinal hexagonal and transverse hexagonal. Also in relation to perforations, it will be considered the following fractions (ϕ = 0.08; 0.10; 0.15; 0.20 and 0.25), wherein (ϕ) corresponds to the volume ratio of the perforation. For determining the critical and ultimate buckling loads it was utilized numerical simulation with the assistance of Ansys® software, which is based on the finite element method. The application of the Constructal Design method of this study made it possible to determine the optimal geometries for all types of perforations, for all values of (ϕ) and all the relations H/L. The results show that there is an influence of the perforation type, shape and size, in defining the limit curves of the buckling and the curves of the elasto-plastic buckling. It was also possible to define, for each type of perforation and for all (ϕ) values, the transition points between elastic and elasto-plastic buckling; as well as the points that define the maximum values for the TLNMáx factor (normalized limit stress).

Dentre os principais problemas que ocorrem na estampagem de chapas metálicas estão a fratura, e estricção (necking) e o enrugamento (wrinkling). Este último pode fazer com que a peça fabricada seja rejeitada por problemas que vão desde motivos estéticos até dificuldades de montagem destas peças e desgaste excessivo da ferramenta. Diversos pesquisadores tem estudado o problema de instabilidade à compressão que origina o fenômeno de enrugamento. Pretende-se estudar os principais métodos para predição do enrugamento, a saber, a teoria da bifurcação, a introdução de uma falha induzida e a aplicação do indicador proposto por Nordlund e Häggblad (coeficiente NH). O método escolhido será implementado junto a um programa de análise por elementos finitos de modo a obter diagramas limite de estabilidade, para então ser aplicado a peças mais genéricas. O procedimento é aplicado a peças de geometria relevante para serem ensaiadas experimentalmente de modo a validar as simulações numéricas propostas. / Among the main problems in sheet metal forming processes are the fracture, the necking and the wrinkling behavior of the material. The last one can produce rejected parts due difficulties in the assembly of these parts or excessive wear of the tooling. Many researchers have been studied the problem of the compression instability phenomenon that origins the wrinkling behavior. The objective of this work is the study of the main available methods to the wrinkling prediction, as the bifurcation theory, the induced defect and an indicator proposed by Nordlund and Häggblad (NH coefficient). The more suitable method is implemented into a finite element analysis software in order to obtain the stability limit diagrams that can be used in the design of generic shape parts. Experimental studies will be done in parts subjected to compressive forming loads in order to validate the numerical simulations.

Cette étude vise à analyser la coque qui est en contact avec un matériau qui la confine, et qu’elle subite une pression latérale externe. Les conditions de contact entre les deux corps, frottant ou pas, la rigidité du confinement ainsi que les conditions de chargement, la pression qui peut être directement appliquée à la coque comme elle peut être induite par le matériau de confinement qui par retrait ou retreint ou convergence radiale induit des contraintes, ceux sont là les paramètres qui nous paraissent essentiels à jauger pour la problématique du flambage avec contact d’une coque sous pression externe. Une campagne expérimentale où plusieurs configurations de confinement sont considérées. La nature du milieu extérieur associé au confinement et donc sa rigidité, le type de confinement, discret ou locale au bien total (surface entière de la coque), sont évalués. Une instrumentation adéquate, couplant des mesures ponctuelles et de champ nous a permis de correctement mettre en exergue la phénoménologie. Les simulations numériques par éléments finis à l’aide du code de calcul Abaqus/Standard 6.12-3 intègrent les différentes non linéarité mise en musique dans ce problème, les grands déplacements et rotations du fait du flambage, la non linéarité matériau. Ces travaux montrent que même pour un confinement externe avec une très faible rigidité de membrane, comme pour le sable ou le polystyrène expansé, un gain important de capacité portante est observé, le flambage est retardé. L’augmentation est substantielle dans le cas d’un confinement total, non négligeable et consistante dans le cas d’un confinement local. Nous avons aussi constaté que la charge de flambage et le mode associé dépendent de la configuration de contact, notamment de la rigidité à la flexion du confinement. / Motivated by practical engineering applications, thin-walled cylindrical shells are widely used as structural elements. Because of their low flexural strength, these structures are very sensitive to buckling when exposed to external pressur. Conventional stiffening which makes it possible to improve the bearing capacity is to add stiffening rings connected by axial stiffeners or axial stiffeners. In these configurations the stiffening elements are an integral part of the structure with a continuity of material. One can ask the question of the effect of contiguous but non-continuous adjacent external structures ensuring total or local surface external contact. These are real configurations, such as those of buried pipelines, pipelines, or the case of insulated structures. This study aims to analyze these cases where the shell is in contact with a material which confines it, and that it undergoes an external lateral pressure. The contact conditions between the two bodies, whether rubbing or not, the stiffness of the confinement as well as the loading conditions, the pressure which can be directly applied to the shell as it may be induced by the confinement material which by withdrawal or shrinkage or Radial convergence induces stresses, these are the parameters that we consider essential for gauging the problem of buckling with contact of an external pressure shell. To answer these questions, we conducted an experimental campaign where several configurations of confinement are considered. The nature of the external environment associated with the confinement and therefore its rigidity, the type of confinement, discrete local or the total property (entire surface of the shell), are evaluated. Appropriate instrumentation, coupling point and field measurements, has allowed us to correctly highlight the phenomenology. Numerical modeling is also carried out using finite element method by Abaqus/Standard 6.12-3 code. Numerical simulations integrate the different nonlinearities in this problem, large displacements and rotations due to buckling, nonlinearity material, in some cases the buckling is plastic, but also the nonlinearity induced by an evolutionary contact. The modeling is carried out in 2D and 3D mesh, and in the latter case either by means of shell elements or by massive elements, the first aim being to corroborate the experimental observations more or less precisely. This work shows that even for external confinement with very low membrane rigidity, as for sand or expanded polystyrene, a significant gain in bearing capacity is observed, the buckling is delayed. The increase is substantial in the case of a total confinement which is not negligible and consistent in the case of local confinement. We have also found that the buckling load and the associated mode depend on the contact configuration, in particular the flexural rigidity of the confinement.