Bolted cores made of coated silicon steel sheets constitute a vital part of heavy electrical equipment for transformers, motors and turbogenerators. Bolted laminates are eminently suitable for facilitating smooth magnetic flux paths, but, unfortunately, they are unable to suppress interlaminate shearing caused by flexural vibration generating noise levels often exceeding 100 dB during operation. The resulting din and cacophony in the surrounding has become a major environmental concern. This thesis makes an attempt to develop theoretical, experimental and numerical models for evolving an effective stiffness approach enhancing the design and analysis underlying nonlinear flexure of bolted laminates. While large machine cores contain thousands of thin sheets bolted together along with end plates, this thesis reports the results obtained on two different assemblies. Two 375 mm long 60 mm wide and 10 mm thick plates assembled with 3, 4 or 5 bolts constitute the first configuration. The second one which is much more realistic comprises 80 coated 270 micron silicon steel sheets with end plates of 2 or 4 mm thickness held together by 3 or 5 bolts. Static 3 point bend tests on these bolted assemblies are followed by instrumented impact tests. Static bending tests highlight the role of frictional nonlinearity inducing a drop in the stiffness due to sliding between the plates. An experimentally determined effective modulus in the initial linear range is utilized for static and dynamic finite element simulations. Nonlinear response of bolted plates is simulated using contact elements in between the sliding plates, plates and the bolts heads. Since the first fundamental mode of vibration dominates the tribomechanical vibration induced noise, the primary focus is on the fundamental frequency in bending. There is generally a good overall agreement in all the results obtained through theory, experiment and FE simulation. Experiments, however, unveil quite complex nonlinear effects induced by friction and plasticity outside the scope of this thesis. However, the low amplitude response of bolted laminates which is reasonably well captured in this thesis represents the starting point for initiating a more elaborate effort for addressing large amplitude nonlinear flexure in bolted laminates. These findings shed light on estimating and controlling noise and vibration levels in heavy electric machines.

The topic of this thesis is the numerical simulation of transversely isotropic 3D structures and laminates by means of the adaptive finite element method. To achieve this goal, the theoretical background of elastic deformation problems, transverse isotropy, plate theory, and the classical laminate theory is recapitulated. The classical laminate theory implies a combination of the membrane problem and the plate problem with additional coupling terms. The focus of this work is the adjustment of two integral parts of the adaptive FE algorithm according to the classical laminate theory. One of these parts is the solution of the FE system; a good preconditioner is needed in order to use the conjugate gradient method efficiently. It is shown via a spectral equivalence bound that the combination of existing preconditioners for the membrane and plate problems poses a capable preconditioner for the combined laminate problem. The other part is the error estimation process; the error estimator determines where the current mesh has to be refined for the next step. Existing results on residual error estimators for the elasticity problem, the biharmonic problem, and the plate problem are combined and extended to obtain a posteriori local residual error indicators for the classical laminate theory problem. The effectiveness of both results is demonstrated by numerical examples.

Made available in DSpace on 2016-12-23T13:51:45Z (GMT). No. of bitstreams: 1 Flavia Maria Silva Brito.pdf: 1958233 bytes, checksum: 19806ba42f2c6acb72b77967069c2d99 (MD5) Previous issue date: 2013-02-26 / Este trabalho teve como objetivos avaliar as características anatômicas e físicas do bambu in natura , analisar os efeitos da termorretificação nas propriedades tecnológicas do bambu laminado colado termorretificado (BLCTR) e na sua durabilidade natural. Foram coletados quatro colmos em idade adulta e cortados a cada 2,0 m, divididos em quatro secções no sentido longitudinal sendo imersas em água durante 10 dias e secas ao ar. As secções foram transformadas em taliscas com dimensões de 0,5 x 3,5 x 45 cm (espessura x largura x comprimento) e tratadas termicamente a 100, 140, 160, 180 e 200°C, durante uma hora para cada temperatura. Os adesivos utilizados foram o Cascophen RS-216-M , à base de resorcinol - formaldeído, Cascamite PL-2030 , à base de uréia - formaldeído, ambos termofixos e um termoplástico à base de acetato de polivinila, Cascorez 2500 . As taliscas termorretificadas foram dimensionadas conforme cada ensaio realizado. Observou-se que os colmos de bambu possuem uma frequência de vasos de 0 a 4 vasos.mm-2 com média de 2 vasos.mm-², fibras longas e estreitas com comprimento médio de 2,72 mm. A massa específica básica de 0,66 g.cm-3 e a retratibilidade volumétrica de 15,41%. Os teores de extrativos e lignina total aumentaram, conforme o incremento da temperatura, e o teor de holocelulose foi reduzido. A partir da temperatura de 160 °C ocorreu um ganho na durabilidade natural do bambu e na estabilidade dimensional do BLCTR aderido com RF, porém houve uma queda nos valores da massa específica básica e na resistência mecânica do material / This work aimed to evaluate the physical and anatomical characteristics of bamboo "in natura", analysing the effects of thermal treatment on the technological properties of glued laminated bamboo thermo-modified (GLBT) and in your natural durability. A total of four culms were collected in age adulthood and cut every to 2.0 m and divided into four lengthwise sections that were immersed in water for 10 days and air-dried. The sections were transformed into flights with dimensions of 0.5 x 3,5 x 45 cm (thickness x width x length) and thermal treated to 100, 140, 160, 180 and 200 °C for one hour for each temperature. T he adhesives used were Cascophen RS-216-M , based resorcinol formaldehyde, Cascamite PL-2030 , based on urea - formaldehyde, both thermoset and thermoplastic based on one polyvinylacetate, Cascorez 2500 . The flights thermal treated were scaled according to each proposed test. It was observed that the bamboo culms have a frequency of 0 to 4 vessels.mm-2, whith mean of vessels.mm-2, with long and narrow fibres with length average of 2.72 mm. The basic specific gravity was of 0.66 g.cm-3 and volumetric shrinkage of 15.41%. The total extractives and lignin contents increased as the temperature increase, and holocellulose content has been reduced. Since the temperature of 160 °C was a gain in durability natural bamboo and the dimensional stability of GLBT adhered to RF, but there was a decrease in the values of specific gravity and mechanicalproperties of the material

O trabalho de pesquisa realizado trata do comportamento dinâmico e aeroelástico em compósitos laminados de rigidez variável (LCRV). Em virtude dos avanços das técnicas de manufatura de laminados, este tema tem ganhado notoriedade internacional e sua importância se justifica pelo crescente número de trabalhos na área. Neste contexto, foram analisados dois tipos distintos de LCRV: o primeiro diz respeito a laminados fabricados com espaçamento variável entre as fibras paralelas; e o segundo trata de laminados fabricados com deposição das fibras por caminhos curvilíneos, termo em inglês tow steering. Com objetivo de explorar as características dos LCRV, foi desenvolvido um modelo aeroelástico baseado no método dos modos admitidos (Rayleigh-Ritz), utilizando as hipóteses da teoria clássica de laminação (TCL), e foi utilizado o modelo aerodinâmico baseado na teoria das faixas quase estacionária para as análises em escoamentos subsônicos, e na teoria dos pistões, para escoamentos supersônicos nas análises de flutter de painel. Assim, foi investigada a influência do efeito de diferentes funções de distribuição do volume de fibras no comportamento aeroelástico e nas três primeiras frequências naturais, constatando-se uma significativa influência nos resultados, justificando um tratamento adequado para modelagem microestrutural dos laminados com espaçamento variável. Por outro lado, com objetivo de analisar o efeito de incertezas no processo de fabricação nos LCRV fabricados com a tecnologia de tow steering, foi desenvolvida uma estratégia de identificação de incertezas e sua propagação no modelo numérico, além da otimização para obtenção de um projeto robusto. Constatou-se que a melhor configuração obtida pela otimização determinística apresentou grande dispersão quando perturbado o ângulo de definição da trajetória das fibras, diferentemente da configuração selecionada de maneira robusta, que apresentou resultados menos sensíveis a perturbações nos ângulos de deposição das fibras. Foi investigada também a viabilidade da utilização de LCRV do ponto de vista dinâmico, visando aumentar a frequência natural fundamental, e com aplicação em flutter de painel. Em ambas as aplicações foi otimizada a trajetória da deposição das fibras, com base nos polinômios interpoladores de Lagrange, sendo encontrados ganhos razoáveis quando comparados com os laminados de material composto tradicionais de rigidez constante (LCRC). Adicionalmente, foi verificado que os resultados obtidos para o LCRC e o LCRV analisados experimentalmente corroboraram os resultados obtidos numericamente no que diz respeito às frequências naturais e aos modos de vibrar. / The developed research work is related to the dynamic and aeroelastic behaviors of variable stiffness composite laminate plates (VSCL). Due to the advances in the manufacturing techniques, this research theme has been gaining international relevance and its importance is justified by the increasing number of research works in this area. In this context, two different types of VSCL are analyzed: the first regards variable fiber spacing laminates, and the second is manufactured using curvilinear paths (tow steering). In order to explore the VSCL characteristics, it was developed an aeroelastic model based on the assumed modes approach (Rayleigh-Ritz), using the hypotheses of “classical lamination theory” (CLT). Moreover, it was used the aerodynamic model based on the quasi-steady strip theory in the subsonic analyses, and the piston theory, for supersonic flows used in the evaluation of panel flutter. It was investigated the influence of different fiber volume distribution on the aeroelastic behavior and on the first three natural frequencies; it has been found that those influences are significant, which justifies the adequate treatment for the micro -structural model of VSCL. Also, to cope with uncertainties during manufacturing of steered composite laminates, it was developed a strategy for identification of those uncertainties and their propagation through the numerical model; also, an optimization procedure was proposed to achieve robust designs. It was noticed that the response of the optimal configuration obtained from deterministic optimization presented a large dispersion when the tow steering angles were perturbed, in contrast with the selected configuration obtained from robust optimization, in which the results were much less sensible to perturbations in the tow steering angles. Also, it was investigated the viability to use LCRV from the dynamic standpoint, aiming at increasing the fundamental frequency, and with application in flutter panel. For both applications, the fiber placement trajectory was optimized based on Lagrange polynomials. Reasonable gains were found with respect to constant stiffness composite laminates (CSCL). Additionally, it was verified that the obtained experimental results for VSCL and CSCL corroborate the counterparts obtained from numerical simulations regarding natural frequencies and mode shapes. / Tese (Doutorado)

Composite laminates are being more employed as fundamental structures due to its low weight and high stiffness. An example of this innovation is the primary structures of modern aircraft, which are lighter than the material formerly used. To predict the material response as load gradually increases can be quite demanding due to composite\'s complex failure mechanism. Hence superior computational models should be further investigated to precisely predict the mechanical behavior of composite media. This dissertation addresses an extended finite element procedure based on the layerwise displacement theory to simulate purely mode I delamination failure in composite laminates. The present model has the potential to perform structural analyzes in a pre-delaminated structure and also considering progressive failure. The type of element to be employed at the discretion of the model is the rectangular 4-node iso-parametric homogeneous element whose displacement field is approximated based in the layerwise theory. There are four types of degrees of freedom, one displacement in each direction, and one degree of freedom associated to the strong discontinuity. Numerical examples already solved in the bibliography are suggested in this dissertation, which demonstrate the potential of the model developed to accurately simulate pure mode I delamination in case of the investigation here is further elaborated. In addition, one possibility of future development of this dissertation is the modeling of fracture mode I without the need to discretize the cohesive planes as realized in traditional Cohesive Zone Methods. / Compósitos laminados estão sendo mais empregados como estruturas fundamentais devido ao seu baixo peso e alta rigidez. Um exemplo dessa inovação são as estruturas primárias das aeronaves modernas, que são mais leves do que as os materiais empregados antigamente. Prever a resposta do material à medida que a carga aumenta gradualmente pode ser difícil devido ao complexo mecanismo de falha dos compósitos. Portanto, modelos computacionais mais refinados devem ser investigados a fim de se prever um comportamento mecânico mais preciso. Esta dissertação aborda um procedimento de elementos finitos estendido baseado na teoria de deslocamento layerwise para simular falhas de delaminação modo I em laminados compósitos. O modelo abordado tem potencial para realizar análises em uma estrutura prédelaminada além de falha progressiva. O tipo de elemento a ser empregado na discrição do modelo é o isoparamétrico, homogêneo de 4 nós, retangular, e o campo de deslocamento é baseado na teoria layerwise. Existem quatro tipos de graus de liberdade, um deslocamento em cada direção, e um grau de liberdade associado à forte. Sugere-se nesse trabalho, exemplos, que são comparados com a bibliografia, e que apontam que o modelo desenvolvido nesta dissertação tem o potencial de simular o fenômeno de delaminação em modo I com acurácia, caso o estudo nessa dissertação seja estendido. Além disso, uma possibilidade de desenvolvimento futuro desse trabalho é a modelagem da fratura modo I sem a necessidade de discretizar os planos coesivos entre as lâminas, como realizado em métodos coesivos tradicionais.

Thesis deals with determination of layerwise mechanical properties of composite ceramics by indirect method, namely Youngs modulus. Based on literature review, it was found that a method to determine elastic properties of one or more components of multi layered composites based on experimental modal analysis and finite element modal analysis, or analytical approach exists. Method based on FE modal analysis was applied to ceramic laminate, where it was attempt to determine youngs modulus of one component. Beyond that, it was attempt to determine Youngs moduli of both components using first two bending resonant frequencies. Results were unsatisfying. Sensitivity analysis showed that layers with unknown Youngs modulus were overly sensitive to small changes in input parameters due to their small relative thickness with respect to thickness of laminate and due to location in laminate. Based on this conclusion, recommendations were made with respect to suitable geometry of test specimens.

The main objective of this work was to design a suitable composition of a protective coatings, made of several different layers of specific materials - with respect to residual stress, induced due to a mismatch in thermal expansion coefficients of each layer. Protective coating in this work means both the thermal and the environmental barrier. These coatings protect components against high temperatures and harsh environment. In this work, necessary theoretical background in the field of the thermal and environmental barrier coatings is introduced. There are mentioned some basic design approaches, commonly used materials and processing methods for the coating structure. The literature review gives an overview of modeling of such coated structures, in particular it is devoted to the thermal barrier coatings deposited by air plasma spray process. The next chapter closely describes classical laminate theory used for calculation of residual stresses in the coating. One of the assumptions of this theory is homogenous temperature field through the coating’s thickness. However, in this work was revealed a way to extend the classical lamination theory of such cases, in which the temperatures vary along the thickness of the coating. In the practical part, the analytical model was used for designing suitable properties of some coatings, which were consists of two, three and four layers. The calculations were performed both for constant temperature and for the temperature gradient. All results obtained from analytical approach were verified by numerical calculations.

The presence of the compressive or tensile thermal residual stresses in layers of a ceramic laminate induced due to different volume change of each layer´s material during the cooling from the sintering temperature can considerably affect resistivity of ceramics against contact damage. Within this work 2D parametric FEM models were created, in order to study the effect of the surface layer thickness, residual stress values and indenting body dimension on the initiation and propagation of the cone crack in the surface layer of the laminate. For the analysis of the critical conditions for the crack initiation, the coupled stress-energy criterion was used and for the determination of the direction of crack propagation we used the maximum tangential stress criterion. The results show that compressive thermal stresses in the surface layer increase the critical force for the crack initiation, shorten the crack distance from the contact area and shorten the occurred crack itself. Moreover, the compressive stresses enlarge the angle of the crack declination during the propagation process which cause an earlier crack arrest. The tensile thermal stresses have exactly the opposite effect. Results of simulations were compared to experimental results but due to lack of available measurements, the verification is partially limited.

Tato diplomová práce se zabývá numerickou simulací B3B zkoušky. Byla provedena rešerše v souvisejících oblastech. Poté byly provedeny numerické simulace této zkoušky pro mnoho různých konfigurací (rovný, zakřivený a zakřivený vrstvený vzorek) pro disk a desku. Byla zjištěna hyperbolická závislost mezi tloušťkou a f faktorem. Závislost f faktoru na křivosti byla lineární. Byla provedena demonstrace možnosti prasknutí na rozhraní vrstev. Poslední část ukázala, jak by zanedbání vlivu zbytkového napětí mohlo vést ke špatnému vyhodnocování experimentů

V současnosti jedna z metod spojování zejména tlustých a vysoce zatížených kompozitních komponent je šroubový spoj, který je možné rozebrat pro případ opravy na rozdíl od lepeného spoje. Kompozitní konstrukce se tradičně dimenzují tak, aby během provozu nedošlo k porušení první vrstvy laminátu, nicméně důležité je taky poznat chování laminátu po porušení první vrstvy. Pro strukturální analýzu nejenom spojů, ale také dalších komponent se používá metoda konečných prvků a protože moderní nelineání řešiče jsou schopné modelovat chování laminátu po porušení první vrstvy, tato schopnost jednoho z nich byla využita v této práci při zkoumaní chování sklolaminátu spojeného s hliníkovou částí šrouby. Konečno-prvkové modely dvou spojů kovové a kompozitní části konstrukce schopné popsat progresivní porušování laminátu byly postaveny s využitím tří různých poruchových kritérií – kritéria maximálního napětí, kritéria Hill a kritéria Tsai-Wu. Problém byl řešen s využitím řešiče Nastran. Křivky síla-posuv, tuhost-posuv a hodnoty zatížení při hraničním posuvu byly porov-nány s výsledky experimentů. Jelikož faktor zbytkové tuhosti ovlivňuje výsledky ana-lýzy progresivního porušování, byly provedeny citlivostní studie zkoumajíci vliv faktoru na přesnost a stabilitu výpočtu. Shoda výpočtu s experimentem v případe prvního šroubového spoje je méně uspokojivá, nicméně shoda v případě druhého spoje, který má zesilující tenkou ocelovou destičku na spodní straně, je podstatně lepší. Vý-borná shoda je zejména při použití interaktivních kritérií Hill a Tsai-Wu.