Thesis (M.S.)--University of Wisconsin--Madison, 1965. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 42.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

[pt] Neste trabalho a formulação do modelo de elementos finitos para cascas finas axissimétricas é estendida à análise numérica, incluindo os efeitos de não-linearidade do material, para a modelagem de fenômenos elasto-plásticos. O algoritmo utilizado emprega a solução incremental em um esquema explicito de integração com sub-incrementação da carga no processo iterativo de solução da equação de equilíbrio. Este esquema de integração da solução permite o controle do campo de estado de tensões mantendo a tensão equivalente no interior ou sobre a superfície de escoamento. Na implementação, o método de Newton Raphson, na forma modificada, é utilizado na solução do sistema de equações de equilíbrio resultante. A cinemática de deformação do modelo utilizado emprega apenas graus de liberdade de translação referidos à curva geratriz da superfície média da casca para representar as condições de compatibilidade geométrica da casca. Condições de contorno de continuidade e de fixação, referidas a rotação da normal à casca são impostas no modelo através do método de penalização. O desempenho do modelo proposto na análise não-linear elasto-plástica é avaliado através da comparação com outros resultados analíticos numéricos disponíveis na literatura e discutidas as características de convergência da solução no controle do erro numérico permitido entre duas iterações sucessivas. / [en] In this work the formulation of a finite element axisymetric thin wall shell is extended to the numerical analisys including material nonlinear effects such as elasto-plastic phenomena. The algorithm employs the incremental solution scheme in an explicit integration with a load sub-incrementation in the procedure for equilibrium equation solution. This solution integration scheme allows restraining of stress state field with the equivalent stress withn or on the yielding surface. The modified Newton- Raphson method is used in the solution of resulting system of equilibrium equation. The kinematics of deformation employed in the model uses only translation degrees-of-freedom refered to the generatrix of the element midsurface to represent geometric compatibility conditions of the shell. Boudary conditions such as normal rotation fixity and coontinuity are imposed to the model through the penalty method. Some numerical analyses are presented to evalute the model capabilities in nonlinear elastoplastic examples, which results are compared to other numerical analytic solutions available in the literature. Solution convergebce, within controlling of the error allowed in the numerical solution, in discussed and evaluated.

The introduction of creases into thin sheets has a dramatic effect on their global mechanical properties. This can be observed by manipulating a crumpled piece of paper which has been unfolded; it no longer deforms in the same way as the original sheet. Creases have typically been modelled as singular hinge lines, often accompanied by a torsional spring to provide some opening resistance; however, the appropriate stiffness of these springs is unclear. In reality, creases have a discrete geometry based on the method they were formed. This dissertation investigates the flexural behaviour of a creased thin metallic strip and the influence of the crease geometry. When a strip is bent perpendicular to the crease, putting the crease region in tension and the strip edges in compression, initially torsional deformations occur which ultimately coalesce into a central localised flattened region. An analytical model of this flexural behaviour is developed, which idealises the crease as an initially circular segment. Predictions show the bending resistance increases as the crease decreases in size. The model predictions are compared to finite element analysis and experimental results showing excellent agreement. When a strip is bent in the opposite direction, with the crease region in compression and the strip edges in tension, a bistable snap-through occurs. The deformed shape is characterised by a sharp vertex on the crease line. An analytical model is developed by generalising a Gauss mapping approach, and used to predict the deformed shape. These predictions match experimental results well. This dissertation provides an understanding of the mechanics of creased thin strips, where the crease is given a discrete geometry, and explores the nature of localisation. It also provides the foundation to explore the mechanics of thin sheets featuring a network of creases. This offers the opportunity to improve the efficiency of thin shell structures by using creasing to optimise the mechanics, leading to reduced material use, more sustainable construction, and fuel savings from lighter vehicles.

Resumo: Das primeiras atividades de exploração de petróleo offshore, em 1968 na Bacia de Sergipe, com lâmina d'água de cerca de aproximadamente 30m, até as explorações em águas profundas, entre 1000 e 2000 m, e ultra-profundas, acima de 2000 m, na Bacia de Campos (RJ), o Brasil tem-se destacado mundialmente neste tipo de exploração, a ponto de sermos hoje líderes mundiais neste setor. Muitos foram os desafios impostos para exploração de petróleo enquanto as profundidades das lâminas d'água aumentavam. As estruturas fixas (jaquetas), empregadas em águas mais rasas, começaram a ter seu uso inviabilizado, pois para águas profundas deveriam ser construídas estruturas excessivamente rígidas e caras. Nesse sentido, as plataformas de concreto demonstraram que seu comportamento em meio offshore é de boa qualidade, sobretudo devido à alta durabilidade do material concreto. Segundo Adebar e Collins (1994) os procedimentos para projetar estruturas de concreto offshore, embora as mesmas sejam estruturas mais complexas, são similares aos utilizados para construir grandes estruturas. No entanto, a verificação da capacidade de resistência em seções particulares para as forças transversais, o comportamento não-linear da estrutura de concreto deve ser levado em consideração, evitando problemas de dimensionamento como o ocorrido, por exemplo, com a plataforma Sleipner A. Desta maneira, utilizando o processo iterativo proposto por Lourenço e Figueiras (1993), foi feito o dimensionamento de elementos de cascas ensaiados experimentalmente sujeitos a forças de membrana e a momentos fletores obtidos da literatura. Depois de feito o dimensionamento dos elementos de cascas, o seu comportamento foi analisado e comparado com o resultado numérico obtido pelo DIANA, programa de elementos finitos utilizado para a análise não-linear de estruturas / Abstract: The first activities of offshore petroleum exploration in Brazil started in 1968 at Sergipe basin, approximately 30 meters depth until the explorations on deep water, between 1000 and 2000 meters, and ultra-deep water, greater than 2000 meters, at Campos basin, state of Rio de Janeiro, the Brazil has highlighted in the world in this kind of exploration, to become a world leaders in this sector. Many difficulties were imposed for the exploration of petroleum by the water depth increase. The fixed structures, known as jacket, used in shallow water, became impractical in deeper water, because, for this condition, these structures most be built too rigid and expensive. In this sense, reinforced concrete platforms have been demonstrating a better behavior in offshore environment, mainly due to the material high durability. In accordance with Collins e Adebar (1994), the procedures adopted in reinforced concrete offshore design are similar to those adopted in large structures design, though the offshore structure are much more complex. However, the material nonlinear behavior must be considered in the shear resistance capacity verification of particular cross-sections, so as to avoid problem with design as occurred, for example, with the platform Sleipner A. In this matter, using the iterative process proposed by Lourenço e Figueiras (1993), it will be made a design of shell elements tested experimentally subject to membrane force and bending moments found in the literature. After done the design of the shell elements, their behavior will be analyzed and compared to the numerical solution obtained with DIANA, a finite element program for non-linear structural analysis / Orientador: Mônica Pinto Barbosa / Coorientador: Tulio Nogueira Bittencourt / Banca: Gilberto Pechoto de Melo / Banca: Osvaldo Luís Manzoli / Mestre

Equations of motion with required boundary conditions for doubly curved deep and thick composite shells are shown using two formulations. The first is based upon the formulation that was presented initially by Rath and Das (1973, J. Sound and Vib.) and followed by Reddy (1984, J. Engng. Mech. ASCE). In this formulation, plate stiffness parameters are used for thick shells, which reduced the equations to those applicable for shallow shells. This formulation is widely used but its accuracy has not been completely tested. The second formulation is based upon that of Qatu (1995, Compos. Press. Vessl. Indust.; 1999, Int. J. Solids Struct.). In this formulation, the stiffness parameters are calculated by using exact integration of the stress resultant equations. In addition, Qatu considered the radius of twist in his formulation. In both formulations, first order polynomials for in-plane displacements in the z-direction are utilized allowing for the inclusion of shear deformation and rotary inertia effects (first order shear deformation theory or FSDT). Also, FSDTQ has been modified in this dissertation using the radii of each laminate instead of using the radii of mid-plane in the moment of inertias and stress resultants equations. Exact static and free vibration solutions for isotropic and symmetric and anti-symmetric cross-ply cylindrical shells for different length-to-thickness and length-to-radius ratios are obtained using the above theories. Finally, the equations of motion are put together with the equations of stress resultants to arrive at a system of seventeen first-order differential equations. These equations are solved numerically with the aid of General Differential Quadrature (GDQ) method for isotropic, cross-ply, angle-ply and general lay-up cylindrical shells with different boundary conditions using the above mentioned theories. Results obtained using all three theories (FSDT, FSDTQ and modified FSDTQ) are compared with the results available in literature and those obtained using a three-dimensional (3D) analysis. The latter (3D) is used here mainly to test the accuracy of the shell theories presented here.

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<p> This thesis consists of a rigorous development of the direct kinematic, small-displacement theory of thin elastic shells. The theory is developed, so as to facilitate a derivation of the equations of compatibility of middle-surface strains. These equations are developed by the kinematic approach and it is shown that this produces a more coherent relation of such equations to the general theory of shells, as no special techniques are required. The equations of compatibility are developed again by the formal Saint-Venant method; this development serves to substantiate the validity of the kinematic approach. At the same time, it provides many useful identities which are then employed as transformation relations, in order to compare the various forms of compatibility equations, as developed by other authors. A general comparison of kinematic shell theory with other nonkinematic methods is undertaken, and appended to the main discussion.</p> / Thesis / Master of Engineering (MEngr)

<p> The Rayleigh-Ritz method of Trial Function has been adopted to solve problems of translational shells under uniform external pressure. The basic energetical expressions have been written in terms of direct tensor notation. The stress-strain displacement relations are given in linear sense. Three different kinds of boundary conditions --- all four edges fixed, one pair of edges fixed and another pair of edges simply supported, and all four edges simply supported --- have been analysed. The stress and moment resultants at different points of the shell have been computed by means of IBM 7040, and are plotted into curves and figures to show their variations. The convergence of the displacement function uz is roughly verified. Certain comparison with other established results have been made. The results obtained by the present approach are satisfactory, at least from an engineering point of view.</p> / Thesis / Master of Engineering (MEngr)