published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

Steel silos are widely used as long-term or short-term containers for the storage of granular solids, of which a huge range are stored, from flour to iron ore pellets, coals, cement, crushed rocks, plastic pellets, chemical materials, sand, and concrete aggregates. The radius to thickness ratio for silos is in the range of 200 to 3000, so they fall into the category of thin shells, for which failure by buckling is the main concern and requires special attention in design. The primary aim of this thesis is to investigate the possible application of Fibre Reinforced Polymer (FRP) as a new repair and strengthening technique to increase the buckling capacity of thin metallic cylindrical shells. Extensive research has been conducted on the use of fibre reinforced polymer (FRP) composites to strengthen concrete, masonry and timber structures as well as metallic beams. However, all these studies were concerned with failure of the structure by material breakdown, rather than stability. As a result, this thesis marks a major departure in the potential exploitation of FRP in civil engineering structures. Many analyses of cylindrical shells are presented in the thesis. These are all focussed on strengthening the shell against different failure modes. Two loading conditions were explored: uniform internal pressure accompanied by axial load near a base boundary, and axial loads with geometric imperfections. For the latter, local imperfections are usually critical, and two categories of imperfection were studied in detail: an inward axisymmetric imperfection and a local dent imperfection. For the first loading condition, which leads to elephant’s foot buckling, an analytical method was used to derive general equations governing the linear elastic behaviour of a cylindrical shell that has been strengthened with FRP subject to internal pressure and axial compression. It was used to identify optimal application of the FRP. All the later studies were conducted using nonlinear finite element analysis (using the ABAQUS program) to obtain extensive predictions of many conditions causing shell buckling and the strengthening effect of well-placed FRP. In all the cases studied in this thesis, it was shown that a small quantity of FRP composite, applied within a small zone, can provide a significant enhancement of the resistance to buckling failure of a thin metal cylinder. These calculations demonstrate that this new technique is of considerable practical value. However, it is clear that not all the relevant questions have been fully answered, so the author poses appropriate questions and makes suggestions for future work.

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

Highly nonlinear structures exhibit complex responses to external loads, and often become unstable. In this thesis, I consider structures with either a nonlinear geometric response or material response. Geometrically nonlinear bistable shells have two stable configurations and can reversibly change between them via snap-through instabilities. This snap-through behavior can cause large geometric deformations in response to small changes in loading, and thus is ideal for designing various devices. For materially nonlinear structures, one recent focus is the potential to utilize granular jamming to construct structures. However, it is not yet fully understood how the stability of such nonlinear structures is governed by geometric and materials properties. This thesis aims to answer this question and propose design guidelines for engineering applications. This research will focus on the statics and dynamics of spherical shells, prestressed bistable shells and elastogranular columns. For spherical shells, we aim to find out under what geometric criteria can a shell be turned inside out, and as the shell goes through the snap-through instability, what dictates the shape and speed of it. Geometric criteria to predict whether a spherical shell is bistable or monostable is proposed based on precisely fabricated soft spherical shells. Point load indentation tests were performed to determine how stable a spherical shell is in its everted configuration. The results show a distinct difference between shallow shells and deep shells, which led to further studies on the snapping dynamics of spherical shells. High speed videos are recorded to track the motion of the apex of an everted spherical shell during its snap-through process, and we find that as the spherical shell goes from shallow to deep, the axisymmetric snapping will transform into asymmetric snapping. This change in snapping modes greatly affects the snapping dynamics of the everted spherical shells, and the shapes they adopt through the instability. Besides spherical shells, we also analyzed prestressed, bistable, cylindrical shells. Prestressed bistable shells fabricated by stretching and bonding multiple layers of elastomers can have various geometric shapes and can snap under external stimuli, but the governing parameters for the fabrication and snapping are not known yet. An analytical model was proposed based on non-Euclidean Plate Theory to predict the mean curvature of the prestressed shell, and the amount of stimulus that is needed to trigger the snapping. Numerical simulations are performed to compare with the analytical results. Based on the proposed theory, for given fabrication parameters and material properties, the final mean curvature of the bistable prestressed shell can be predicted accurately, as well as the amount of stretch that is needed to trigger snapping. This study can be used to design smart actuators or other soft, smart devices. To study material nonlinear structures, we use a mixture of grains and rods to enable the formation of stable structures via granular jamming. Understanding how these constituents govern the mechanical properties of the jammed structures is crucial for devising relevant engineering designs. We examine freestanding columns composed of rocks and string, and propose a simple physical model to explain the resulting structure’s mechanical behavior. The results indicate that exterior fiber mainly contributes to stiffness, while interior fiber increases the stored elastic energy and absorbed total energy of the structures under certain external load. By assembling the grains and strings in an engineer way, structures with robust mechanical properties can be formed. The results provide guidelines that allow the design of jammed elastogranular structures with desired mechanical properties. The research results of this thesis will open and guide a variety of possibilities in designing functional responsive devices or jamming structures.

O trabalho realizado consiste no desenvolvimento das equações pertinentes à teoria de cascas, implementação de programas de elementos finitos em Matlab e resolução de problemas de casca numéricos e analíticos. No desenvolvimento da teoria de cascas é evidenciada a aplicação da curvatura da estrutura no cálculo das forças e momentos resultantes para uma superfície de casca simplificada a uma estrutura localmente bidimensional. O problema de casca é resolvido analiticamente para um caso de curvatura simples e comparado com a resolução por elementos finitos em um programa desenvolvido pelo autor, em que a utilização da curvatura para o cálculo das forças e momentos resultantes é inserida na programação. A análise de elementos finitos é realizada para casos de casca com curvatura simples e dupla curvatura e de duas formas, sendo que a primeira utiliza elementos cujas normais médias são empregadas na montagem da matriz de rigidez, constituindo um elemento de casca e a segunda aplica normais a cada nó de cada elemento, tendo-se assim uma superfície facetada, com comportamento de placa em cada elemento. Os resultados obtidos mostram que o impacto da aplicação da curvatura em geral é pequeno nas regiões mais críticas para as forças e momentos resultantes, como na região de engaste. Porém, algumas regiões da casca apresentam grandes variações, e caso sejam de importância para o usuário, cabe uma análise mais detalhada em que o emprego da curvatura possa ser considerado. / This work presents the development of the shell theory equations, implementation of finite element programs in Matlab and the resolution of numerical and analytical shell problems. Along with the development of the shell theory, the application of the curvature of the structure in the calculation of stress and couple resultants for a shell structure simplified to a bidimensional problem become clear. The shell problem is solved analytically, by means of the application of the shell equations in a shell with simple curvature, and this solution is compared with the numerical solution using the finite element program implemented, considering the curvature of the structure for the stress and couple resultants. Finite element analysis is performed for the simple and double curvature cases of shells, and in two distinct ways, the first one considering averaged normals for neighbor elements, which produces shell elements, the second one using normals to each node of each element, which results in locally flat elements, behaving as plates. Results obtained show that the impact of the application of the curvature in the resultants is usually small in the most critical points, such as the crimp. However, some regions of the shell present huge variation, and further analysis is recommended, since the application of the curvature can be important.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / Microfiche copy available in Archives and Engineering. / Includes bibliographical references. / M.S.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Includes bibliographical references. / Ph.D.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Ocean Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Ph.D.

No presente trabalho caracterizou-se o padrão de utilização de conchas pelo ermitão Paguristes tortugae, habitante do infralitoral da Ilha Anchieta (Ubatuba), analisando-se comparativamente o padrão de seleção e de ocupação de conchas no ambiente natural e em laboratório. Para o estudo de ocupação de conchas no ambiente, os indivíduos foram coletados mensalmente (janeiro a dezembro/1998) na região infralitorânea de quatro áreas da Ilha, por mergulho autônomo. Os ermitões foram medidos quanto ao comprimento e largura do escudo cefalotorácico, altura e comprimento do própodo quelar, contados, determinado seu sexo e pesados. Para os experimentos de seleção de conchas, os animais foram mantidos vivos em aquário de vidro. Nestes experimentos laboratoriais, os animais foram retirados de suas conchas e colocados com um número suficiente de conchas com tamanhos apropriados. Após 72h os animais e as conchas escolhidas foram analisados quanto ao peso dos ermitões e das conchas e as respectivas medidas. A escolha quanto ao tipo de concha foi analisada de acordo com a porcentagem de ocupação de uma espécie em relação à outra. Para a escolha quanto ao tamanho da concha, avaliou-se as análises de regressão entre as dimensões dos ermitões e das conchas. Um total de 2429 exemplares de P. tortugae foram analisados (1092 machos, 495 fêmeas não-ovígeras e 842 fêmeas ovígeras), ocupando 21 espécies de conchas de gastrópodos. Este perfil, indicativo de ampla diversidade no padrão de ocupação, apresentou Pisania auritula (35.49%), Cerithium atratum (27.83%) e Morula nodulosa (12.70%) como as mais ocupadas. Os machos (38.46%) e as fêmeas ovígeras (38.00%) ocuparam, em maior porcentagem, as conchas de P. auritula, enquanto que as fêmeas não-ovígeras (39.40%) ocuparam C. atratum. Houve dimorfismo sexual quanto ao tamanho em favor dos machos e, a razão sexual foi de 1:1.2, em favor das fêmeas. Verificou-se que as conchas mais ocupadas foram as menos adequadas. Leucozonia nassa foi a mais adequada tanto no ambiente quanto no laboratório, corroborando a hipótese de que a ocupação das conchas está associada ao ambiente em que vivem e à sua disponibilidade. A maior correlação ocorreu entre as dimensões dos ermitões e o peso da concha, sendo esta a relação que melhor caracterizou a escolha e a ocupação das conchas por P. tortugae. Quanto ao sexo, as fêmeas ovígeras apresentaram as melhores correlações, estando melhor adequadas ao peso e ao volume interno da concha, favorecendo a fecundidade e o processo reprodutivo anual. Tal condição foi corroborada com os experimentos de laboratório, onde constatou-se que as fêmeas ovígeras apresentaram preferência por conchas com maior volume interno (L. nassa e C. atratum). Em laboratório, dentre as seis espécies de conchas com maior ocorrência de ocupação no ambiente, o padrão de preferência foi L. nassa > P. auritula > S. haemastoma > T. viridula para os indivíduos maiores e C. atratum > M. nodulosa para os indivíduos menores. Estes resultados, comparados aos da natureza, demonstraram que P. tortugae apresentou um padrão de preferência pelas conchas mais disponíveis na natureza, mesmo não sendo as mais adequadas quanto às dimensões. Neste sentido podemos inferir que o padrão de utilização de conchas de P. tortugae pode estar fortemente associado à disponibilidade de conchas, ao tamanho e à condição reprodutiva dos indivíduos. / This study characterized the pattern of shell utilization by the hermit crab Paguristes tortugae, inhabiting infralittoral areas of Anchieta Island (Ubatuba), analyzing comparatively the pattern of the shell occupation in the field and in the laboratory. For the shell occupation study in the field, the individuals were collected monthly (January to December/1998), by scuba methods in four infralittoral areas of the Island. The hermit crabs were measured on the basis of shield width and length, propodus height and length, sexed and weighed. In the shells selection experiments, the animals were maintained alive in the laboratory. All experiments were conducted in a glass aquarium where the hermit crabs were placed naked with a large number of shells of appropriate sizes. After 72h the hermit crabs and chosen shells were analyzed by preference and measured. The shell type preference was estimated by the percentage of occupation of the chosen species. The preferred shell type and size were determined by regression analysis. A total of 2429 individuals of P. tortugae were analyzed (1092 males, 495 non-ovigerous females and 842 ovigerous females), occupying 21 species of gastropod shells characterizing a considerable diversity in the shell occupation pattern. The most occupied shells were Pisania auritula (35.49%), Cerithium atratum (27.83%) and Morula nodulosa (12.70%). The males (38.46%) and the ovigerous females (38.00%) occupied in higher percentage P. auritula shells, while the non-ovigerous females (39.40%) occupied C. atratum. It was verified sexual size dimorphism, being the males larger than females. The sex ratio was 1:1.2 in favor of females. It was verified that the most occupied shells least adequate and that L. nassa was the most adequate in the field and in the laboratory, corroborating the hypothesis that the shell utilization is associated to the habitat and to the availability in the field. The highest correlation coefficients were obtained for the relations between the crab dimensions and shell dry weight. In relation to sex, the ovigerous females showed the best correlation coefficients being more adequate to the shell weight and internal volume, that may favor the fecundity and the annual reproductive process. This condition was corroborated by the laboratory experiments when the ovigerous females preferred shells with higher internal volume (L. nassa e C. atratum). In laboratory, among the six most occupied shell species in the field, the preference pattern was L. nassa > P. auritula > S. haemastoma > T. viridula to larger individuals and C. atratum > M. nodulosa to the small ones. These results, compared to the field study, showed that P. tortugae exhibited a pattern of preference for the most available shells in the field, even if they’re not the most adequate to the crab dimensions. In this sense we may infer that the shell utilization pattern of P. tortugae may be associated to the shell availability and to the size and reproductive conditions of the individuals.

The subject of free vibration analysis of thin cylindrical shells is one that extends well back into the last century. In general, the computational methods can be classified as analytical methods and numerical methods. Based on the Flugge thin shell theory, this thesis presents exact solutions for vibration of closed and open cylindrical shells. The state-space technique is adopted to derive the homogenous differential equations for a shell segment and the domain decomposition method is employed to impose the equilibrium and compatability requirements along the interfaces of the shell segments. Extensive analytical and numerical results have been obtained in this thesis for vibration of open/closed cylindrical shells with different boundary conditions, step-wise thickness variations, and multiple intermediate ring supports. The results can serve as useful benchmark values for researchers and engineers to validate their numerical method for shell analysis. / Doctor of Philosophy (PhD)