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.

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.

Orientador: Raquel Gonçalves / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Agricola / Made available in DSpace on 2018-08-13T08:01:34Z (GMT). No. of bitstreams: 1 GiaconJunior_Milton_M.pdf: 1896488 bytes, checksum: 79f0b46b132ced75cc6c5b25d89a7c45 (MD5) Previous issue date: 2009 / Resumo: Os postes de concreto apresentam, para os diferentes fabricantes, grande variabilidade em termos de qualidade e resistência inicial. Essas diferenças, provenientes de problemas durante a fabricação, têm se refletido na vida útil dos postes instalados na rede de distribuição de energia. Para ser aceito como fornecedor de poste de uma determinada concessionária, o fabricante deve submeter um poste de cada modelo que deseja comercializar a ensaios destrutivos de flexão. Os fabricantes tomam inúmeros cuidados durante a produção deste poste padrão, mas nem sempre estes cuidados são usuais durante o processo rotineiro de industrialização. Como conseqüência, muitos postes apresentam problemas de qualidade e de durabilidade quando em serviço. Assim, o ensaio por amostragem tem se mostrado pouco eficaz. A adoção de sistema de classificação que permita avaliar a qualidade dos postes de forma individualizada poderia minimizar os problemas relativos à qualidade inicial e consequentemente, aumentar a vida útil dos mesmos. No entanto, para viabilizar este procedimento é necessário o uso de ensaio não destrutivo cuja realização seja fácil e rápida. O ultra-som é um ensaio que já tem sido utilizado, principalmente em outros países, em avaliações de peças de concreto em estruturas convencionais (vigas, lajes, pilares). No entanto, o poste tubular é uma estrutura diferenciada, pois apresenta uma pequena camada de concreto na qual é inserida uma grande quantidade de aço, além de ter grande porcentagem de sua seção transversal oca. Dessa forma, para a aplicação do método na classificação de postes tubulares novos, torna-se necessário conhecer a influência das armaduras e do vazio interno na propagação das ondas de ultra-som. Assim, os objetivos deste trabalho foram avaliar a influência desses dois aspectos peculiares do poste de concreto tubular na propagação de ondas de ultra-som e propor faixas de classificação utilizando a velocidade de propagação. Paralelamente foi realizada avaliação da possibilidade de se utilizar o ultra-som como ferramenta de caracterização do concreto em corpos-de-prova cilíndricos ou cúbicos. Para o desenvolvimento da pesquisa foram efetuadas medições de velocidade de propagação das ondas de ultra-som em protótipos de postes tubulares de três diferentes formas: direta (VL), indireta ou superficial (VS) e radial (VR), utilizando transdutores de onda longitudinal de 45 kHz de freqüência. Nos corpos de prova as medições foram realizadas somente de forma direta (VL) e utilizando-se transdutores de 100 kHz longitudinal e de cisalhamento. No caso dos corpos-de-prova, além da velocidade, foi obtida também a matriz de rigidez [C] e, por meio da sua inversa, a matriz de flexibilidade [S], que permitiu a obtenção dos módulos de elasticidade longitudinal (Eus), transversal (Gus) e coeficiente de Poisson (u). Os corpos-de-prova foram também ensaiados a compressão para a determinação da resistência (fc) e dos módulos de deformação inicial (Ei) e módulo de deformação tangente inicial (Eci). Com os resultados foi possível propor faixas de classificação de postes tubulares utilizando as velocidades VL e VS. A armadura não teve influência em VL, VS ou VR e o vazio interno só teve influência na VR, de forma que este tipo de medição deve ser evitado na classificação. Também foi possível concluir que a aplicação do ensaio de ultra-som em corpos-de-prova cúbicos permite a caracterização do concreto, uma vez que os resultados de Eus, Ei e Eci foram estatisticamente equivalentes. / Abstract: The concrete poles present, in the different manufacturers, great variability in quality and initial strength. Those differences, coming from problems during the production, have consequences in the useful life of the poles in the network. To be accepted as poles supplier of a certain one concessionary, the manufacturer should submit a pole, of each model that wants to market, to a destructive testing in bending. The manufacturers are countless careful during the production of this standard post, but not always these cares are usual during the routine process of industrialization. Consequently, many poles present quality problems and have its useful live reduced when in service. For these reasons, the tests using sampling are not effective. The adoption of classification system that allows evaluating the quality of the poles in an individualized way could minimize the problems related to the initial quality and, consequently, could increase the useful life of the concrete poles. However, to make possible this procedure it is necessary the use of non destructive tests whose execution was easy and fast. The ultrasound has been already used, mainly in other countries, to evaluate conventional reinforced concrete structures (beams, slabs and columns). However, the tubular pole is a differentiated structure; hence it presents a small concrete layer in which a great amount of steel is inserted, besides having a hollow in its traverse section. So, for the application of the method in the classification of new tubular poles, it is necessary to know the influence of the steel and of the internal hole in the ultrasonic wave propagation. The objectives of this work was to evaluate the influence of those two peculiar aspects of the tubular concrete poles in the ultrasonic waves propagation and to propose a tubular concrete poles classification using ranges of velocity of waves propagation. Additionally it was evaluate the use of ultrasound to determine properties of strength and rigidity of the concrete in cylindrical and cubic specimens. For the development of the research, measurements of velocity of wave propagations were made in prototypes of tubular poles in three different ways: direct (VL), indirect or superficial (VS) and radial (VR), using transducers of longitudinal wave with 45 kHz frequency. In the specimens the measurements were only accomplished in a direct way (VL) and using 100 kHz longitudinal and transverse transducers. For the specimens, besides the velocity, it was also obtained the stiffness matrix [C] and, through your inverse, the compliance matrix [S], that allowed the obtaining the longitudinal modulus of elasticity (Eus), traversal modulus of elasticity (Gus) and coefficient of Poisson (u). The specimens were also tested in compression for the determination of the strength (fc) and of the initial modulus of deformation (Ei) and tangent modulus of deformation (Eci). With the results it was possible to propose ranges of tubular poles classification using ranges of VL or VS. The reinforced steel didn't have any influence in VL, VS or VR and the internal hole only had influence in VR, so this type of measurement should be avoided in the pole classification. It was also possible to conclude that the use of ultrasonic wave propagation in cylindrical concrete specimens allows determining the strength and rigidity characteristics of the concrete, once the results of Eus, Ei and Eci were statistically equivalent. / Mestrado / Construções Rurais e Ambiencia / Mestre em Engenharia Agrícola

Various models are currently in existence for determining the deflection of lithospheric plates under an applied transverse load. The most popular models treat lithospheric plates as thin elastic or thin viscoelastic plates. The equations governing the deflection of such plates have been solved successfully in two dimensions using integral transform techniques. Three dimensional models have been solved using Fourier Series expansions assuming a sinusoidal variation for the load and deflection. In the engineering context, the finite element technique has also been employed. The current aim, however, is to develop an efficient solver for the three dimensional elastic and viscoelastic problems using finite difference techniques. A variety of loading functions may therefore be considered with minimum work involved in obtaining a solution for different forcing functions once the main program has been developed. The proposed method would therefore provide a valuable technique for assessing new models for the loading of lithospheric plates as well as a useful educational tool for use in geophysics laboratories. The multigrid method, which has proved to be a fast, efficient solver for elliptic partial differential equations, is examined as the basis for a solver of both the elastic and viscoelastic problems. The viscoelastic problem, being explicitly time-dependent, is the more challenging of the two and will receive particular attention. Multigrid proves to be a very effective method applicable to the solution of both the elastic and viscoelastic problems. / Science, Faculty of / Mathematics, Department of / Graduate

Slender structures like plates and shells -- for which at least one dimension is much smaller than the others -- are lightweight, flexible, and offer considerable strength with little material. As such, these structures are abundant in nature (e.g. flower petals, eggshells, and blood vessels) and design (e.g. bridge decks, fuel tanks, and soda cans). However, with slenderness comes suceptibility to large and often sudden deformations, which can be wildly nonlinear, as bending is energetically preferable to stretching. Though once considered categorically undesirable, these instabilities are often coveted nowadays in the engineering community. They provide mechanical explanations for observations in nature like the wrinkled structure of the brain or the snapping mechanism of the Venus fly trap, and when precisely controlled, enable the design of functional devices like artificial muscles or self-propelling microswimmers. As a prerequisite, these achievements require a thorough understanding of how thin structures "shape-shift" in response to stimuli and confinement. Advancing this fundamental knowledge is the goal of this thesis. In the first two chapters, we consider the shape-selection of shells and plates that are confined by their environment. The shells are made by residual swelling of silicone elastomers, a process that mimics differential growth, and causes initially flat structures to irreversibly morph into curved shapes. Flattening the central region forces further reconfiguration, and the confined shells display multi-lobed buckling patterns. These experiments, finite element (FE) simulations, and a scaling argument reveal that a single geometric confinement parameter predicts the general features of this shape-selection. Next, in experiments and molecular dynamics (MD) simulations, we constrain intrinsically flat sheets in the same manner, so that their center remains flat when we quasi-statically force them through a ring. In the absence of planar confinement, these sheets form a well-studied conical shape (the developable cone or d-cone). Our annular d-cone buckles circumferentially into patterns that are qualitatively similar to the confined shells, despite the distinct curvatures and loading methods. This is explained by the dominant role of confinement geometry in directing deformation, which we uncover via a scaling argument based on the elastic energy. There are also marked differences between the way plates and shells change shape, which we highlight when we investigate the rich dynamics of reconfiguration. In the final two chapters, we demonstrate how mechanics, geometry, and materials can inform the design of structures that use instabilities to function. We observe in experiments that dynamic loading causes a spherical elastomer shell to buckle at ostensibly subcritical pressures, following a substantial time delay. To explain this, we show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This work offers a pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers. The final chapter aims at reducing the energy input required for bistable actuators, wherein snap-through instability is typically induced by a stimulus applied to the entire shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimuli--responsive material. We demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, while preserving snap-through behavior. These results are stimulus-agnostic, which we demonstrate with two sets of experiments, using residual swelling of bilayer silicone elastomers as well as a magneto-active elastomer. Our findings elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through. / 2022-05-06T00:00:00Z

No description available.

No description available.

An optimization system based on the finite element code CSM Testbed and the optimization program ADS is described. The optimization system can be used to obtain minimum-weight designs of composite stiffened structures. Ply thicknesses, ply orientations, and stiffener heights can be used as design variables. Buckling, displacement, and material failure constraints can be imposed on the design. The system is used to conduct a design study of geodesically stiffened shells. For comparison purposes, optimal designs of unstiffened shells and shells stiffened by rings and stringers are also obtained. Trends in the design of geodesically stiffened shells are identified. An approach to include local stress concentrations during the design optimization process is then presented. The method is based on a global/local analysis technique. It employs spline interpolation functions to determine displacements and rotations from a global model which are used as "boundary conditions" for the local model. The organization of the strategy in the context of an optimization process is described. The method is validated with an example. / Ph. D.

The objective of this work is to study the local and global nonlinear vibrations of isotropic single-layered and multi-layered cross-ply doubly curved shallow shells with simply supported boundary conditions. The study is based-on the full nonlinear partial-differential equations of motion for shells. These equations of motion are based-on the von K\'rm\'{a}n-type geometric nonlinear theory and the first-order shear-deformation theory, they are developed by using a variational approach. Many approximate shell theories are presented. We used two approaches to study the responses of shells to a primary resonance: a $direct$ approach and a $discretization$ approach. In the discretization approach, the nonlinear partial-differential equations are discretized using the Galerkin procedure to reduce them to an infinite system of nonlinearly coupled second-order ordinary-differential equations. An approximate solution of this set is then obtained by using the method of multiple scales for the case of primary resonance. The resulting equations describing the modulations of the amplitude and phase of the excited mode are used to generate frequency- and force-response curves. The effect of the number of modes retained in the approximation on the predicted responses is discussed and the shortcomings of using low-order discretization models are demonstrated. In the direct approach, the method of multiple scales is applied directly to the nonlinear partial-differential equations of motion and associated boundary conditions for the same cases treated using the discretization approach. The results obtained from these two approaches are compared. For the global analysis, a finite number of equations are integrated numerically to calculate the limit cycles and their stability, and hence their bifurcations, using Floquet theory. The use of this theory requires integrating $2n+(2n)^2$ nonlinear first-order ordinary-differential equations simultaneously, where $n$ is the number of modes retained in the discretization. A convergence study is conducted to determine the number of modes needed to obtain robust results. The discretized system of equation are used to study the nonlinear vibrations of shells to subharmonic resonances of order one-half. The effect of the number of modes retained in the approximation is presented. Also, the effect of the number of layers on the shell parameters is shown. Modal interaction between the first and second modes in the case of a two-to-one internal resonance is investigated. We use the method of multiple scales to determine the modulation equations that govern the slow dynamics of the response. A pseudo-arclength scheme is used to determine the fixed points of the modulation equations and the stability of these fixed points is investigated. In some cases, the fixed points undergo Hopf bifurcations, which result in dynamic solutions. A combination of a long-time integration and Floquet theory is used to determine the detailed solution branches and chaotic solutions and their stability. The limit cycles may undergo symmetry-breaking, saddle node, and period-doubling bifurcations. / Ph. D.

No / This paper considers both the linear elastic and creep buckling of polymeric pipe linings used for the rehabilitation of gravity pipes, for which external groundwater pressure has been identified as the prime source of loading. Theoretically perfect and imperfect conditions are considered, with the imperfections taken to be in the form of a concentric or eccentric annulus between the rigid host pipe (cylindrical constraint) and polymeric lining. Under these conditions two recently obtained mathematical procedures for the prediction of linearly and non-linearly elastic buckling are compared with the results of complementary laboratory testing. Linear elastic conditions are shown to be well approximated by undertaking short-term (¿30 min) testing under increasing pressure to failure. Controlled imperfections are introduced into the laboratory tests and excellent correlation with the theoretical predictions is obtained. In particular, the dominant geometrical imperfections are shown to be major influences on the obtained buckling pressure. The mathematical models are then adapted to simulate the creep buckling process under long-term constant pressure. The results obtained are again compared with those provided by complementary physical testing, and appropriate conclusions are made.