No description available.

Métodos convencionais, tais como o método da chapa ortotrópica, têm sido aplicados por muitos anos no estudo de painéis reforçados pela sua simplicidade e facilidade de aplicação na determinação de tensões agentes nas fases iniciais da espiral projeto. Não estão disponíveis na literatura, porém, análises comparativas do método da chapa ortotrópica com procedimentos numéricos utilizando elementos finitos (MEF) que permitam a determinação da acurácia ou da ordem de grandeza dos desvios inerentes à aplicação desta metodologia. O presente trabalho apresenta análises comparativas entre estas duas metodologias na solução de painéis reforçados submetidos a carga lateral uniforme, tipicamente aplicados a estruturas navais (chapa em apenas um dos lados com reforçadores em T). Com este objetivo foram construídos modelos de painéis simplesmente apoiados e engastados (modelagem com elementos de viga e casca) com diferentes espaçamentos e diferentes inércias de reforçadores, configurando uma ampla matriz de análise paramétrica. Os resultados de deflexões e tensões nas vigas e chapas obtidos dos modelos MEF foram parametrizados em função das variáveis da chapa ortotrópica (razão de aspecto virtual), (coeficiente de torção) e K (parâmetro adimensional de tensões e de deflexão). Esta parametrização permite gerar curvas numéricas de tensão e deflexão dos modelos em estudo. As curvas numéricas assim geradas são comparadas com as curvas propostas pelo método da chapa ortotrópica para painéis reforçados simplesmente apoiados, de tal maneira que sua comparação permita, além de determinar a sensibilidade dos resultados numéricos em função das mudanças de inércia e espaçamento entre reforçadores, aferir o nível de desvio oriundo do uso da metodologia da chapa ortotrópica em relação ao método dos elementos finitos. Resultados mostram que as curvas derivadas da metodologia da chapa ortotrópica fornecem bons resultados para as deflexões e tensões transversais nas vigas no centro do painel reforçado. Para as tensões longitudinais nas vigas, uma curva corrigida de tensões longitudinais máximas é fornecida. No caso das curvas de tensões longitudinais e transversais na chapa, as curvas da chapa ortotrópica fornecem valores conservadores de tensão no centro do painel em relação aos valores obtidos dos modelos MEF. Adicionalmente, uma vez que o método da chapa ortotrópica só fornece curvas para chapa sem reforçadores no caso de condição de engaste, curvas numéricas das diferentes variáveis são fornecidas para esta condição. Analogias são feitas com a solução fornecida pelo método da chapa ortotrópica para painéis reforçados com razão de aspecto =, borda longitudinal engastada e borda transversal apoiada. Adicionalmente, resultados analíticos baseados na teoria de grelhas são comparados com os valores fornecidos pelas curvas numéricas para painel engastado obtendo-se resultados consistentes. Com esta análise foi possível determinar a aplicabilidade e limitações do método da chapa ortotrópica no estudo de painéis reforçados simplesmente apoiados. O estudo também fornece novas curvas numéricas para painéis reforçados engastados. / Conventional methods, such as the orthotropic plate, have been applied for many years in the study of stiffened plates to obtain the stresses acting on the structure in the early stages of the structural design, because of its simplicity and easy application. However, comparative analyses of the orthotropic plate method with numerical methods using finite element analyses (FEM) to determine its accuracy or inherent errors are not available in the literature. This study presents comparative analyses between the solutions of the two methodologies for reinforced panels subjected to lateral uniform load, typically applied to marine structures (plate only on one side with T beams). Models of reinforced panels were implemented for a simply supported and clamped boundary conditions with different spacing between stiffeners and different stiffeners`s inertia, setting up a broad array of parametric analysis. The deflections and stresses in beams and plate derived from the MEF analyses were parameterized as function of the orthotropic plate parameters: (virtual aspect ratio), (torsion coefficient) and K (dimensionless parameter of stress and deflection). This enables the generation of parametric numerical curves of stresses and deflections for the models under study. The numerical curves generated in this way were compared with the analytic curves proposed by the orthotropic plate theory for reinforced panels with simply supported boundary conditions. The comparisons allow, in addition to a sensitivity analysis of the numerical curves as a function of inertia and spacing between stiffeners, the assessment of inherent deviation for the orthotropic plate theory when compared with the finite element analyses. From the comparative analyses, it is possible to conclude that the curves proposed for the orthotropic theory for deflection and stresses of the transverse beam at the center of the reinforced panels have a good correlation with the numeric curves and provide accurate results. For the stresses on longitudinal beam, a revised curved for maximum stresses is provided. For the curves of plate stresses in the longitudinal and transverse directions at the center of the panels, the orthotropic plate theory provides conservative values when compared with the values of FEM models. The orthotropic plate method only provides curves for unstiffened plate under clamped boundary condition. Numerical curves for reinforced panels with clamped boundary condition are provided. Analogies are made between the solution provided by the orthotropic theory for a reinforced panel with an infinite virtual aspect ratio = , longitudinal edges clamped and transverse edges simply supported. Additionally, analytical results based on grillage theory were compared with the values provided by the numerical curves for clamped reinforced panels, obtaining a consistent results and a good correlation. This analysis provides a critic overview of the applicability and limitations of the orthotropic plate method for the analyses of reinforced panels with simply supported boundary condition. The study also provides new numerical solutions for reinforced panels with clamped boundary condition.

Este trabalho verifica, por meio de análises numérico-paramétricas de lajes nervuradas, o quanto a desconsideração (ou a consideração de maneira simplificada) da excentricidade existente entre os eixos das nervuras e o plano médio da capa influencia nos resultados de deslocamentos e esforços atuantes nas peças que compõem estes sistemas. Foram apresentados os conceitos teóricos relativos à cada modelo de cálculo permitido pelas normas técnicas, e foram realizadas análises considerando variações nos seguintes parâmetros: relação entre a altura da capa e a altura total da laje nervurada; relação entre a distância entre os eixos das nervuras e a distância entre os pontos de apoio, e espaçamento entre os eixos das nervuras. Os diferentes modelos mecânicos foram analisados utilizando o método dos elementos finitos, por meio do programa computacional ANSYS 5.5, considerando-se um comportamento elástico-linear para o material concreto armado. Foram relacionados aspectos importantes a serem observados na escolha do modelo adequado, de acordo com os parâmetros analisados, para serem aplicados nos escritórios de cálculo. Verificou-se a necessidade da consideração da excentricidade, seja por modelo realista, ou por modelos simplificados, para a obtenção de resultados numéricos mais próximos do comportamento da estrutura real. / This work verifies, through parametric-numerical analysis of slabs stiffened with ribs, how much the disregard (or regard in a simplified way) of the existent eccentricity between the axis of the ribs and the medium plan of the plate influences on the results of displacements and acting efforts over the parts wich make the system. The theorical concepts related to each model of calculation allowed through technical codes have been presented, and, analysis have been made considering variations in the following parameters: relation between plate height and total height of the waffle slab; relation of distance between the axis of the ribs and the distance between the supporting points, and the gap between the axis of the ribs. Different mechanical models have been analysed using the finite element analysis, through the computer program ANSYS 5.5, considering an elastic-linear behaviour for the reinforced concrete material. Important aspects have been disclosed and should be carefully looked into for an adequate model choice, according to the analysed parameters to be applied in the design\'s offices. The need for eccentricity consideration has been verified, be it by using a realistic model or by simplified models, for close numerical results gathering of the real structural behaviour.

Este trabalho verifica, por meio de análises numérico-paramétricas de lajes nervuradas, o quanto a desconsideração (ou a consideração de maneira simplificada) da excentricidade existente entre os eixos das nervuras e o plano médio da capa influencia nos resultados de deslocamentos e esforços atuantes nas peças que compõem estes sistemas. Foram apresentados os conceitos teóricos relativos à cada modelo de cálculo permitido pelas normas técnicas, e foram realizadas análises considerando variações nos seguintes parâmetros: relação entre a altura da capa e a altura total da laje nervurada; relação entre a distância entre os eixos das nervuras e a distância entre os pontos de apoio, e espaçamento entre os eixos das nervuras. Os diferentes modelos mecânicos foram analisados utilizando o método dos elementos finitos, por meio do programa computacional ANSYS 5.5, considerando-se um comportamento elástico-linear para o material concreto armado. Foram relacionados aspectos importantes a serem observados na escolha do modelo adequado, de acordo com os parâmetros analisados, para serem aplicados nos escritórios de cálculo. Verificou-se a necessidade da consideração da excentricidade, seja por modelo realista, ou por modelos simplificados, para a obtenção de resultados numéricos mais próximos do comportamento da estrutura real. / This work verifies, through parametric-numerical analysis of slabs stiffened with ribs, how much the disregard (or regard in a simplified way) of the existent eccentricity between the axis of the ribs and the medium plan of the plate influences on the results of displacements and acting efforts over the parts wich make the system. The theorical concepts related to each model of calculation allowed through technical codes have been presented, and, analysis have been made considering variations in the following parameters: relation between plate height and total height of the waffle slab; relation of distance between the axis of the ribs and the distance between the supporting points, and the gap between the axis of the ribs. Different mechanical models have been analysed using the finite element analysis, through the computer program ANSYS 5.5, considering an elastic-linear behaviour for the reinforced concrete material. Important aspects have been disclosed and should be carefully looked into for an adequate model choice, according to the analysed parameters to be applied in the design\'s offices. The need for eccentricity consideration has been verified, be it by using a realistic model or by simplified models, for close numerical results gathering of the real structural behaviour.

Presented diploma thesis deals with parametric optimization of wing caisson of L 410 NG aircraft to reduce its‘structure weight. The paper is mainly focused on description and application of optimization methods with the use of finite element methods in MSC Nastran. Moreover the thesis contains loading state check of optimized design, done in STAUNO software.

No description available.

Noise and vibration suppression is an important aspect in the design process of structures and machines. Undesirable vibrations can cause fatigue in a structure and are, therefore, a risk to the safety of a structure. One of the most effective and widely used methods of mitigating these unwanted vibrations from a system is passive damping, by using a viscoelastic material. This dissertation will primarily focus on constrained layer passive damping treatments in structures and the investigation of associated complex modes. The key idea behind constrained damping treatment is to increase damping as affected by the presence of a highly damped core layer vibrating mainly in shear. Our main goal was to incorporate viscoelastic material in a thick stiffened panel with plate-strip stiffeners, to enhance the damping characteristics of the structure. First, we investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the principle of virtual work, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the viscoelastic material was modeled using the complex modulus approach. We used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, by including complex modulus in the base and constraining layers. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically damped and non-proportionally damped structures. Secondly, we studied the free vibration response of an integrally stiffened and/or stepped plate. The stiffeners used here were plate-strip stiffeners, unlike the rib stiffeners often investigated by researchers. Both plate and stiffeners were analyzed using the first-order shear deformation theory. The deflections and rotations were assumed as a product of Timoshenko beam functions, chosen appropriately according to the given boundary conditions. Unlike Navier and Levy solution techniques, the approach used here can also be applied to fully clamped, free and cantilever supported stiffened plates. The governing differential equations were solved using the Rayleigh-Ritz method. The development of the stiffness and the mass matrices in the Ritz analysis was found to consume a huge amount of CPU time due to the recursive integration of Timoshenko beam functions. An approach is suggested to greatly decrease this amount of CPU time, by replacing the recursive integration in a loop structure in the computer program, with the analytical integration of the integrand in the loop. The numerical results were compared with the exact solutions available in the literature and the commercially available finite-element software ABAQUS. Some parametric studies were carried out to show the influence of certain important parameters on the overall natural frequencies of the stiffened plate. Finally, we investigated the damped response of an adhesively bonded plate employing plate-strip stiffeners, using FSDT for both the plate and stiffeners. The problem was analyzed using the principle of virtual work. At first, we did not consider damping in the adhesive in order to validate our code, by comparing our results with those available in the literature as well as with the results obtained using ABAQUS 3D model. The results were found to be highly satisfactory. We also considered the effect of changing the stiffness of the adhesive layer on the vibration of the bonded system. As a second step, we included damping in the stiffened structure using complex modulus approach, a widely used technique to represent the rheology of the viscoelastic material. We observed an overall increase in the natural frequencies of the system, due to the damping provided by the viscoelastic material. Moreover, it was noticed that when the thickness of the adhesive layer is increased, the natural frequencies and loss factor of the stiffened structure decrease. A viscoelastic material with high loss factor and small thickness will be a perfect design variable to obtain overall high damping in the structure. / Ph. D.

The structural optimization of a cantilever aircraft wing with curvilinear spars and ribs and stiffeners is described. The design concept of reinforcing the wing structure using curvilinear stiffening members has been explored due to the development of novel manufacturing technologies like electron-beam-free-form-fabrication (EBF3). For the optimization of a complex wing, a common strategy is to divide the optimization procedure into two subsystems: the global wing optimization which optimizes the geometry of spars, ribs and wing skins; and the local panel optimization which optimizes the design variables of local panels bordered by spars and ribs. The stiffeners are placed on the local panels to increase the stiffness and buckling resistance. The panel thickness, size and shape of stiffeners are optimized to minimize the structural weight. The geometry of spars and ribs greatly influences the design of stiffened panels. During the local panel optimization, the stress information is taken from the global model as a displacement boundary condition on the panel edges using the so-called "Global-Local Approach". The aircraft design is characterized by multiple disciplines: structures, aeroelasticity and buckling. Particle swarm optimization is used in the integration of global/local optimization to optimize the SpaRibs. The interaction between the global wing optimization and the local panel optimization is usually computationally expensive. A parallel computing technology has been developed in Python programming to reduce the CPU time. The license cycle-check method and memory self-adjustment method are two approaches that have been applied in the parallel framework in order to optimize the use of the resources by reducing the license and memory limitations and making the code robust. The integrated global-local optimization approach has been applied to subsonic NASA common research model (CRM) wing, which proves the methodology's application scaling with medium fidelity FEM analysis. Both the global wing design variables and local panel design variables are optimized to minimize the wing weight at an acceptable computational cost. The structural weight of the wing has been, therefore, reduced by 40% and the parallel implementation allowed a reduction in the CPU time by 89%. The aforementioned Global-Local Approach is investigated and applied to a composite panel with crack at its center. Because of composite laminates' heterogeneity, an accurate analysis of these requires very high time and storage space. In the presence of structural discontinuities like cracks, delaminations, cutouts etc., the computational complexity increases significantly. A possible alternative to reduce the computational complexity is the global-local analysis which involves an approximate analysis of the whole structure followed by a detailed analysis of a significantly smaller region of interest. We investigate here the performance of the global-local scheme based on the finite element method by comparing it to the traditional finite element method. To do so, we conduct a 2D structural analysis of a composite square plate, with a thin rectangular notch at its center, subjected to a uniform transverse pressure, using the commercial software ABAQUS. We show that the presence of the thin notch affects only the local response of the structure and that the size of the affected area depends on the notch length. We investigate also the effect of the notch shape on the response of the structure. Stiffeners attached to composite panels may significantly increase the overall buckling load of the resultant stiffened structure. Buckling analysis of a composite panel with attached longitudinal stiffeners under compressive loads is performed using Ritz method with trigonometric functions. Results are then compared to those from ABAQUS FEA for different shell elements. The case of composite panel with one, two, and three stiffeners is investigated. The effect of the distance between the stiffeners on the buckling load is also studied. The variation of the buckling load and buckling modes with the stiffeners' height is investigated. It is shown that there is an optimum value of stiffeners' height beyond which the structural response of the stiffened panel is not improved and the buckling load does not increase. Furthermore, there exist different critical values of stiffener's height at which the buckling mode of the structure changes. Next, buckling analysis of a composite panel with two straight stiffeners and a crack at the center is performed. Finally, buckling analysis of a composite panel with curvilinear stiffeners and a crack at the center is also conducted. ABAQUS is used for these two examples and results show that panels with a larger crack have a reduced buckling load. It is shown also that the buckling load decreases slightly when using higher order 2D shell FEM elements. A damage tolerance framework, EBF3PanelOpt, has been developed to design and analyze curvilinearly stiffened panels. The framework is written with the scripting language PYTHON and it interacts with the commercial software MSC. Patran (for geometry and mesh creation), MSC. Nastran (for finite element analysis), and MSC. Marc (for damage tolerance analysis). The crack location is set to the location of the maximum value of the major principal stress while its orientation is set normal to the major principal axis direction. The effective stress intensity factor is calculated using the Virtual Crack Closure Technique and compared to the fracture toughness of the material in order to decide whether the crack will expand or not. The ratio of these two quantities is used as a constraint, along with the buckling factor, Kreisselmeier and Steinhauser criteria, and crippling factor. The EBF3PanelOpt framework is integrated within a two-step Particle Swarm Optimization in order to minimize the weight of the panel while satisfying the aforementioned constraints and using all the shape and thickness parameters as design variables. The result of the PSO is used then as an initial guess for the Gradient Based Optimization using only the thickness parameters as design variables. The GBO is applied using the commercial software VisualDOC. / Ph. D.

Ce travail de recherche répond aux besoins actuels et futurs dans le domaine de l’Aérospatial de faire évoluer les règles de dimensionnement au flambage des réservoirs structuraux de l’Etage Principal Cryogénique (EPC) des lanceurs. Ces réservoirs, composés de coques cylindriques, peuvent être associés à un faible raidissage en termes de masse ajoutée. L’objectif d’alléger le lanceur pour optimiser la charge utile, conduit au choix de coques constitutives de plus en plus minces, le risque de flambage sous diverses sollicitations est donc d’autant plus accru. Le dimensionnement au flambage de l’EPC est basé principalement sur la norme NASA SP8007 qui date de 1968, et qui semble trop conservative, notamment aux basses pressions. Précisons aussi, que l’EPC est équipé d’une couche de protection thermique (PT) qui n’est pas prise en compte dans le design au vue de sa très faible rigidité de membrane. La contribution de cette couche à la capacité de flambage de la coque est cependant un sujet ouvert. / This research work responds to the current and future requirements in Aerospatiale are to improve the design for buckling of the tanks of the Cryogenic Main Stage (EPC) of the launcher. These tanks are composed of cylindrical shells and can be associated with weak stiffening, which are becoming thinner and therefore more susceptible to a risk of buckling. The buckling design of the EPC based mainly on the NASA SP8007 standard, which is ac-cording to many specialists too preservative, especially under low pressure. Moreover, the EPC is equipped with a thermal protection layer (PT), which is extremely light and has an excellent thermal insulation property but very low mechanical properties. The contribution of this layer to the buckling capacity of a lightly pressurized thin cylindrical shell under var-ious solicitations, therefore, appears to be a major subject.

A utilização de aços de alta resistência em terças formadas a frio faz com que as espessuras sejam cada vez mais reduzidas e, como consequência, os fenômenos de instabilidade mais pronunciados. Para melhorar a eficiência estrutural, enrijecedores longitudinais podem ser inseridos na alma, aumentando a resistência em relação ao modo de instabilidade local. Ainda que a utilização de seções com alma enrijecida seja uma prática comum, os procedimentos adequados para seu dimensionamento são pouco abordados na literatura. O objetivo deste trabalho foi estudar o comportamento estrutural de terças formadas a frio de seção transversal ZAE, com enrijecedores de borda a 90º e dois enrijecedores longitudinais na alma. Para tanto, foram realizadas análises teórica e experimental de um conjunto formado por terças com alma enrijecida ZAE e suas equivalentes de alma plana, as seções Z com enrijecedores de borda a 90°. Apesar de ter sido dada ênfase às solicitações por força cortante e por combinação de momento fletor e força cortante, foram realizados ensaios complementares para avaliar a predominância de momento fletor. As alterações nos esforços críticos elásticos devido à presença dos enrijecedores foram analisadas teoricamente, e os dados experimentais e numéricos foram utilizados para prever a interação. Os resultados teóricos indicaram que os enrijecedores longitudinais têm pequena influência nos modos de instabilidade distorcional e global, porém grande influência no modo local, promovendo um aumento significativo das tensões críticas em relação às seções correspondentes de alma plana. Já os resultados experimentais mostraram que a capacidade resistente das seções Z foi superior a das seções ZAE, devido principalmente à mobilização do campo de tração e à maior restrição rotacional da mesa conferida pela ligação. Os protótipos sem restrição à distorção apresentaram falha prematura, ocasionada pela rotação da mesa na região dos apoios. Considerando os protótipos com restrição à distorção, os resultados atenderam às curvas de interação circular e trilinear. Concluiu-se que o projeto de terças com alma enrijecida pode ser realizado utilizando a expressão de interação trilinear e o momento fletor resistente do modo distorcional. / The use of high strength steel in cold-formed purlins leads to a reduction in thickness and, as a consequence, the instability becomes more significant. In order to improve the structural efficiency of the sections, longitudinal stiffeners can be inserted into the web, increasing the strength in relation to local buckling. Although the use of sections with stiffened web is a common practice, the appropriate procedures for design are rarely discussed in scientific literature. The purpose of this work was to study the structural behavior of cold-formed steel purlins ZAE-sections, with 90º lips and two longitudinal stiffeners in the web. Therefore, theoretical and experimental analyses were performed, involving a set of purlins with stiffened web ZAE-sections and their equivalent plain web, the Z-sections with 90º lips. Although emphasis was given in shear and combined bending and shear, additional experimental tests were performed to evaluate the predominance of bending. Changes in critical elastic buckling stresses due to longitudinal stiffeners were evaluated and experimental and numerical data were used to predict the interation. Theoretical results indicated that longitudinal stiffeners of the ZAE-sections have little influence on distortional and global buckling. However, it has a great influence on local buckling, promoting a significant increase of the critical stresses in relation to the Z-sections. Experimental results showed that the ultimate strength of the Z-sections was higher than ZAE-sections, mainly due to the development of tension field action and the rotational restraint of the web conferred by the connection. The prototypes without distortion restraint presented premature failure, caused by rotation of the web in the region of the supports. Considering the distortion-constrained prototypes, the results satisfied the \"circular\" and \"trilinear\" interaction curves. It was concluded that design of purlins with stiffened web can be performed using the \"trilinear\" interaction expression and the distortional buckling moment capacity.