Este trabalho trata da formulação do Método dos Elementos de Contorno para o problema de flexão de placas através da teoria clássica de Kirchhoff. Ênfase especial é dada a placas com variação de espessura uma vez que este tema é muito pouco abordado. O estudo de flexão de placas com variação de espessura é exercida em vários campos, tais como engenharia civil, engenharia aeroespacial e projeto de máquinas. Adotou-se uma variação linear da rigidez, resultando nas equações integrais de deslocamentos com termos de domínios, que serão tratados por discretização do domínio em células. / This work deals with the formulation of the Boundary Element Method applied to plate bending problem using the Kirchhoff\'s theories. Special emphasis is given to plates with varying thickness since this subject is not much tackled. The study of the bending of plates of variable thickness is pursued in various fields, such as civil engineering, aerospace engineering, and the design of machines. It was adopted linearly varying rigidity, giving integral equations of displacements with domain terms, that will be treated by domain discretization into cells.

O objetivo deste trabalho é apresentar uma nova formulação direta do Método dos Elementos de Contorno (M.E.C.) para análise de placas, utilizando a teoria de Kirchhoff, admitindo três parâmetros nodais de deslocamentos para sua representação integral: deslocamento transversal e suas derivadas nas direções normal e tangencial ao contorno. Dois valores nodais são usados para os esforços, momento fletor normal mn e força cortante equivalente Vn. Desta forma são escritas três equações integrais de contorno por nó, obtidas a partir da discretização da placa, segundo a forma usual do método. A vantagem mais perceptível desta formulação é a possibilidade de se fazer a ligação da placa analisada pelo M.E.C. com elementos lineares, representados por três valores nodais de deslocamentos que passam a ser compatibilizados diretamente, para a análise de edifícios. São apresentados exemplos numéricos da formulação e das ligações para comprovação da formulação. / The aim of this work is to present an alternative formulation for plate bending analysis, using Kirchhoff\'s theory, in wich the boundary equation for displacements and its derivative in tangential and normal directions to the boundary for each boundary node are used. The efforts, according to Kirchhoff\'s theory, are the normal bending mn and the equivalent shear force Vn. This formulation is adequate for the analysis of plates coupled with flexible colunms and beams because these structural elements have three nodal displacement values at its nodes. Many examples of single plates and buildings slab are presented using the formulation proposed in this work.

O presente trabalho teve como objetivo: projetar, construir e testar os imas principais do acelerador race-track microtron booster do ifusp, que tem como funcao defletir e focalizar o feixe de eletrons, permitindo a sua recirculacao. Esses imas desempenham papel fundamental quanto a qualidade do feixe obtido que, por sua vez, constitui um fator primordial para experiencias em fisica nuclear. O trabalho desenvolve a teoria do funcionamento do acelerador e os calculos analiticos que fundamentam a geometria dos imas. A ausencia da uniformidade do campo magnetico e a presenca de campos de borda inadequados comprometem o sincronismo. Utilizou-se bobinas corretoras confeccionadas na forma de circuitos impressos, que limitaram a falta de uniformidade a valores relativos de campo magnetico da ordem de \'10 POT.-5\'. Os imas possuem pecas polares auxiliares (clamps) que criam campos de borda reversos ao campo principal. Os clamps foram projetados por meio de simulacoes realizadas com os programas poisson e ptrace, de forma a se obter uma distribuicao para o campo magnetico que propicie aceleracao para uma distancia conveniente entre os imas / The present work had the purpose of designing, building and testing the bending magnets of the IFUSP race-track microtron booster that deflect and focus the electron beam and allow its recirculation. These magnets play a fundamental role in terms of the beam quality, which is important in Nuclear Physics research. This work develops the theory conceming the functioning of the accelerator and the analytical calculations that establish the geometry ofthe magnets. The lack of magnetic field uniformity and the presence of inadequate fringing fields damage the synchronism. The magnetic fields were corrected using coils made of etched printed circuit boards. This method provides uniformity of a few parts in 10 \'10 POT.-5\' . The magnets have auxiliary poles (clamps) that produce reverse fringing fields. The clamps were designed using Poisson and Ptrace programs in order to get a magnetic field distribution that allows acceleration for a convenient distance between the magnets. The beam trajectories determined by Ptrace program were confirmed with agreement of 0,1% using the floating wire technique.

This paper concerns the solution of plate bending problems in domains composed of rectangles. Domain decomposition (DD) is the basic tool used for both the parallelization of the conjugate gradient method and the construction of efficient parallel preconditioners. A so-called Dirich- let DD preconditioner for systems of linear equations arising from the fi- nite element approximation by non-conforming Adini elements is derived. It is based on the non-overlapping DD, a multilevel preconditioner for the Schur-complement and a fast, almost direct solution method for the Dirichlet problem in rectangular domains based on fast Fourier transform. Making use of Xu's theory of the auxiliary space method we construct an optimal preconditioner for plate problems discretized by conforming Bogner-Fox-Schmidt rectangles. Results of numerical experiments carried out on a multiprocessor sys- tem are given. For the test problems considered the number of iterations is bounded independent of the mesh sizes and independent of the number of subdomains. The resulting parallel preconditioned conjugate gradient method requiresO(h^-2 ln h^-1 ln epsilon^-11) arithmetical operations per processor in order to solve the finite element equations with the relative accuracy epsilon.

Additive manufacturing offers a manufacturing technique to produce complex geometry prototypes at a rapid pace and low cost. These advantages advocate additive manufacturing for the design and production of cellular structures. Cellular structures are interesting because they contain a large amount of porosity (void space of air) to manifest a lightweight structure. Designs of cellular structures generate a periodic pattern; often of complex geometry, called a lattice. There has been a significant amount of research to maximize specific stiffness of lattice structures but little to evaluate low-stiffness lattices. Low-stiffness structures benefit energy absorbance through bending of the lattice. This research seeks to assess diamond lattices as low stiffness, bending structures. The research involves PA2200 (Nylon 12) laser sintered diamond lattices with experimental compression testing and direct FEA model comparison. A correction factor is applied for a design offset of laser sintered lattices. Once applied, the experimental and FEA data agree in validating the diamond lattice as a bending-dominated structure. Diamond lattices show a 4th order relationship between stiffness and parameters of thickness and unit cell length. For density, stiffness maintains a 2nd order relationship, as predicted by bending dominated structures. The resulting stiffness can be tuned over a stiffness range of four orders of magnitude. Further research shows the results for modifying the diamond lattice and scaling stiffness and density using other materials (like metals) to expand the range of stiffness and compare diamond lattices on material property charts. Lastly, the effective Poisson’s ratio varies from 0.5 to 0.4 depending on the (t/L) ratio.

This thesis studies the static and fatigue failure of carbon fibre-epoxy composite for marine use. The primary objective is to investigate the effects of sea water ingress on the static and cyclic performance of laminated composites, by using the combination of experimental, numerical and analytical approaches. Experiments were carried out to collect evidence, including data and images, for further analysis. Samples were made from autoclave-cured carbon fibre-epoxy pre-preg for the static, moisture diffusion and fatigue tests. Three chambers were used in the diffusion test, containing fresh water (tap water), sea water and sea water at 70 bar hydrostatic pressure respectively. And the chambers were placed in an oven at a constant temperature 50 °C in order to accelerate the water absorption. Optical and scanning electron microscopies (SEM) were employed to inspect for manufacturing defects and to identify the failure modes. Some formulae were derived to predict the material properties of laminated composites, to validate the mechanical tests, and to explain the failure criteria of composites. Finite element analysis (FEA) was employed to study the phenomena that were observed in the experiments. FEA has the aim to simulate the static, diffusion and fatigue behaviour involving multiphysics and multiscale effects. The FEA modelling has revealed details of the stress and moisture distributions, which have helped to understand the failure mechanisms of laminated composites. Classical laminate theory (CLT) was employed to develop an analytical model. The basic principles of CLT were extended to three-dimensions, and the analytical solution was critically compared with the FEA results. Some MATLAB tools based on CLT were developed to predict the properties of laminated composites and to analyse the experimental data. These MATLAB codes are shown in the appendix. This thesis has contributed to an improved knowledge of the failure mechanisms of composite materials in both normal and marine environments, and to optimize structural design of FRP composites.

Exploring how drought influences growth, performance, and survival in different species is crucial to understanding the impacts of climate change on forest ecosystems. Here, we investigate the responses of two co-occurring pines (Pinus nigra and Pinus sylvestris) to interannual drought in east-central Spain by dendrochronological and wood anatomical features integrated with isotopic ratios of carbon (delta C-13) and oxygen (delta O-18) in tree rings. Our results showed that drought induces both species to allocate less carbon to build tracheid cell-walls but increases tracheid lumen diameters, particularly in the transition wood between early and latewood, potentially maximizing hydraulic conductivity but reducing resistance to embolism at a critical phase during the growing season. The thicker cell-wall-to-lumen ratio in P. nigra could imply that its xylem may be more resistant to bending stress and drought-induced cavitation than P. sylvestris. In contrast, the higher intrinsic water-use efficiency (iWUE) in P. sylvestris suggests that it relies more on a water-saving strategy. Our results suggest that narrower cell-walls and reduced growth under drought are not necessarily linked to increased iWUE. At our site P. nigra showed a higher growth plasticity, grew faster and was more competitive than P. sylvestris. In the long term, these sustained differences in iWUE and anatomical characters could affect forest species performance and composition, particularly under increased drought stress.

Dans le cadre de l’utilisation de plus en plus courante des BFUP dans des structures techniquement ou architecturalement complexes et de la recherche d’optimisation de la quantité de matériau mis en œuvre, cette thèse s’intéresse au fonctionnement des jonctions en BFUP. Son objectif principal est de mettre en évidence les phénomènes physiques qui interviennent dans la jonction et de mieux les retranscrire dans les méthodes de calcul afin de mieux en maîtriser la sécurité et d’optimiser la matière mise en oeuvre.Le travail de thèse s’articule en quatre étapes :- Une étude bibliographique a permis d’établir les bases de connaissances permettant de dimensionner les campagnes expérimentales et de proposer une structure de modélisation des jonctions âme-membrure.- Le développement d’un modèle analytique avancé permettant de prédire le comportement d’une poutre en Té soumise à une sollicitation combinée de flexion longitudinale (et donc de cisaillement longitudinal dans la table) et de flexion transversale.- L’étude expérimentale, à l’échelle du matériau, du comportement des BFUP sous sollicitation de cisaillement pur. Cette étude permet d’enrichir les connaissances sur le comportement des BFUP (données encore indisponibles dans la carte d’identité des différents matériaux) et constitue également une donnée d’entrée pour la compréhension quantitative des phénomènes qui interviennent dans la jonction, à l’échelle de la structure, lorsqu’elle est sollicitée en cisaillement longitudinal.- Enfin, l’essai à rupture de 6 poutres en Té à l’échelle 1 a permis d’étudier le comportement expérimental des jonctions soumises à des sollicitations de cisaillement longitudinal. Les résultats expérimentaux de cette étude ont été comparés aux différentes prédictions analytiques possibles, y compris le modèle proposé.Ces travaux de thèse ont permis d’apporter de nouveaux outils de dimensionnement (notamment dans le cadre de l’étude de la résistance des jonctions en BFUP sous sollicitation de cisaillement pur). Ils mériteraient d’être complétés par des essais de poutres soumis à une sollicitation concomitante de flexion longitudinale et de flexion transversale, pour mieux conforter les méhodes d’analyse proposées / Ultra-high performance fiber-reinforced concrete (UHPFRC) are increasingly used for technically or architecturally complex structures and research is going on to optimize design and save implemented material quantities. In this context, this thesis focuses on the mechanical behavior of junctions in UHPFRC structures. The main goal is to highlight physical phenomena occurring in the junctions in order to optimally transpose them into calculation methods. In this way, both safety and cost-efficience should be better controlled.This thesis is divided in four steps :- A literature review enabled to establish the background knowledge allowing to design the experimental campaigns and to suggest a modeling for web-flange junctions.- An advanced analytical model was developed in order to predict the behavior of a T-beam subjected to combined longitudinal bending (and therefore longitudinal shear in the table) and transverse bending.- The expérimental study, at the material scale, of UHPFRC behavior under pure shear stress, allowed enriching the knowledge in this field (data still unavailable in the identity card of current UHPFRC mixes). It also constituted an input for the quantitative understanding of the phenomena occuring in the junction, at the structure scale, when it is loaded in longitudinal shear.- Finally, the test of 6 full scale T-beams up to failure made it possible to study the experimental behavior of the junctions subjected to longitudinal shear stresses. The experimental results were compared with the various analytical predictions, including the proposed model.A new approch has thus been proposed to design junctions under longitudinal shear. It should be completed with experiments on T-beams under combined longitudinal and transverse bending to further validate the proposed analysis methods

Diploma thesis discusses and summarizes the problematic how ovality effects durability of bended tubes. The work presents an approach to the solution, the experiments concerning change of ovality, changes in the thickness of the distorted cross-section. Final results represent connection between ovality and durability.

Abstract This thesis investigates the reliability of printed conductors on flexible substrates under cyclic bending. The topic is approached by studying the effects of several key design parameters on the bending lifetime of printed conductors under dynamic loading. In this thesis, the test specimens with various cross-sectional geometries were printed on different plastic and paper substrates. The test samples were fabricated with two printing methods, silk screen and roll-to-roll printing, by utilizing three different silver pastes as the conductive material. To evaluate the long-term performance of the printed traces, the test specimens were exposed to cyclic bending and their electrical behaviour during the test was monitored with resistance measurements. The bending test results were analysed by utilizing the Weibull analysis, with a 20% increase in resistance as the failure criterion. This method yielded a characteristic lifetime for a test population, including 10 individual test specimens. When comparing the characteristic lifetimes of all of the fabricated test populations, it was observed that all of the varied design parameters had an effect on the bending reliability of the printed traces. However, within the studied geometries and materials, the substrate was found to have the highest impact on the long-term electrical performance of printed conductors under cyclic bending. The study proves that the bending reliability of printed conductors can be enhanced by proper design choices. This is done by minimizing the strain when the printed trace is subjected to bending. / Tiivistelmä Tässä työssä tutkitaan joustaville substraateille painettujen johdinten luotettavuutta syklisessä taivutuksessa. Aihetta lähestytään tutkimalla useiden tärkeiden suunnitteluparametrien vaikutusta painettujen johdinten elinikään dynaamisessa rasituksessa. Työssä painettiin poikkileikkausgeometrialtaan vaihtelevia testirakenteita erilaisille muovi- ja paperisubstraateille. Testinäytteet valmistettiin käyttäen kahta painotekniikkaa, silkkipainoa ja rullalta rullalle painoa, hyödyntäen kolmea erilaista hopeapastaa johtavana materiaalina. Painettujen johdinten pitkäaikaisen suorituskyvyn arvioimiseksi testinäytteet altistettiin sykliselle taivutukselle ja niiden sähköistä käyttäytymistä monitoroitiin testin aikana resistanssimittauksilla. Taivutustestin tulokset analysoitiin Weibull analyysin avulla käyttäen 20%:n kasvua resistanssissa vikakriteerinä. Tämän menetelmän lopputuloksena saatiin karakteristinen elinikä testipopulaatiolle koostuen kymmenestä yksittäisestä testinäytteestä. Vertailtaessa kaikkien valmistettujen testipopulaatioiden karakteristisiä elinikiä, havaittiin kaikilla vaihdelluilla parametreilla olevan vaikutusta painettujen johdinten luotettavuuteen. Tästä huolimatta, tutkittujen geometrioiden ja materiaalien rajoissa, substraatilla todettiin olevan suurin vaikutus painettujen johdinten pitkä-aikaiseen sähköiseen suorituskykyyn syklisessä taivutuksessa. Tämä tutkimus osoittaa, että painettujen johdinten taivutusluotettavuutta voidaan parantaa oikeilla suunnitteluvalinnoilla. Tämä voidaan toteuttaa minimoimalla venymä painetun johtimen ollessa taivutuksessa.