The aim of the project presented in this thesis is to demonstrate a modelling method for predicting the variability in the ultimate load of stiffened panel under axial compression due to manufacturing variability. Bulking is sensitive to imperfections. In the case of a post-buckled panel, manu-facturing variability produces a scatter in the ultimate load. Thus, reasonable leeway for imperfections and inherent variability must be allowed in their design. Firstly, a finite element model of a particular stiffened panel was developed, and all nonlinearities within the material, boundary condition and geometry were considered. Verification and validation were performed to examine the accuracy of the buckling behaviour prediction, especially ultimate load. Experiments on 5 identical panels in design were performed to determine the level of panel-panel variation in geometry and collapse load. A data reduction programme based on the practical geometry scanning was developed, in addi-tion to which, the procedure of importing measured imperfection into Finite Ele-ment model was introduced. To identify and apply representative imperfections to the panel model, a double Fourier series representation of the random geometric distributions is attempt-ed, and was used thereby to derive a series of shapes representing random ge-ometry scatters. With these newly generated geometric imperfections, the variation in collapse load was determined, using the validated FE analysis. And also, the probability of these predicted loads was generalized.

Asset protection in the form of fluid filtration makes up an ever-increasing part of the civilized and industrialized world. Fluid filtration applications in the conditioned environment and life sciences are affording the world’s population a chance to better realize their potential, while industrial applications help ensure that high demand processes can be carried out safely, reliably, and effectively. In the present work, a tool has been developed, using the computational fluid dynamics package FLUENT, to allow the designer to better predict the magnitude of geometric imperfections within a given pleat configuration. Pleated rectangular filters, intended to improve the quality of air for human occupants, with a U-shaped pleat form have been chosen as the focus of this study. A simulation study is developed to investigate the maximum local velocity normal to the filtration surface and to characterize the magnitude of the pleatwise velocity distribution across a range of pleated geometries and flow conditions. The geometry of the U-shaped pleat form can be characterized by, amongst other parameters, the width of the pleat channel, the overall height of the individual pleat, as well as the thickness of the filtration medium. The various geometries of the current study were developed by changing the width of the pleat channel, as well as the channel height, while keeping the medium thickness constant throughout. Changing the width of the pleat channel allows the designer to achieve varying pleat densities, expressed as a number of pleats along a one inch section of the overall pleated pack. Pleat densities of 6.5, 7, 7.5, 8, and 8.5 pleats per inch are considered in the current study. Pleat heights of 1.0, 0.75, and 0.50 inches are also investigated in the current study. Furthermore, the filter velocity can be characterized by the free stream velocity at the face of the filter pack, termed the face velocity, and by the velocity of the fluid at the interface with the filtration medium, referred to as media velocity. In the present work, the face velocity was adjusted in each case to achieve the desired media velocities across the study, which are 10.5, 9.0, 7.5, and 6.0 feet per minute. In an effort to more clearly communicate the results of the study, the results are presented in the form of a non-dimensionalized plots which present the designer with a way to quickly gauge the effect of pleat geometry on maximum velocity. Additionally, two tools are presented to aid the designer in more accurately predicting the maximum filtration velocity. These tools are then evaluated for effectiveness using the method of absolute relative percent error. The assumption of uniform flow through the filtration media leads to an average absolute relative percent error of 27%. The first tool the reader is presented with is a simple correction factor which predicts the maximum filtration velocity with an average absolute relative percent error of 10% over the study domain. The second tool, which takes a slightly more complicated y-intercept form, characterizes the maximum filtration velocity as a function of average velocity and aspect ratio. This approach further reduces the average absolute relative percent error to 4%. The results of the simulation herein are successfully employed to develop a set of simple yet effective tools that allow the filter designer to more accurately predict maximum velocities through a pleated air filter.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2017-08-16T11:51:58Z No. of bitstreams: 2 Dissertação - Jordana Lopes Morais - 2017.pdf: 10502975 bytes, checksum: eb09d5eefe42f47e2eed7a16b877ce9e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-08-16T12:53:54Z (GMT) No. of bitstreams: 2 Dissertação - Jordana Lopes Morais - 2017.pdf: 10502975 bytes, checksum: eb09d5eefe42f47e2eed7a16b877ce9e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-08-16T12:53:54Z (GMT). No. of bitstreams: 2 Dissertação - Jordana Lopes Morais - 2017.pdf: 10502975 bytes, checksum: eb09d5eefe42f47e2eed7a16b877ce9e (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-06-29 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / The objective of this work is the study of modal coupling in the field of transversal displacement and the search for the least amount of degrees of freedom possible to compose the modal expansion, in order to correctly represent the nonlinear behavior in cylindrical panels simply supported and submitted to a static axial loading. Nonlinear equations are deduced from their energy functionals, represented by the Airy stress function and the the strain field is based on the nonlinear Donnell shallow shell theory. The transverse displacement field is determined by the perturbation method, obtaining the non-linear modes that couple to the linear mode of vibration, then the non-linear equilibrium equations are discretized by the Galerkin method. Linear and non-linear analyzes were developed for many types of cylindrical panel geometries, varying values for radius, circumferential length and axial length. The linear analyzes aim to find the buckling modes with their respective buckling loads. In the nonlinear analysis the behavior of the cylindrical panels and the influences of the nonlinear couplings present in the transverse displacement field are studied in order to find a modal expansion that represents the correct behavior of the cylindrical panel with the least amount of possible coupled modes. The most appropriate modal solution is formed by a vibration mode described by sine-type harmonic functions, and a mode composed of harmonic functions of the cosine type. Then, from the modal expansion found, we study the static stability of the cylindrical panels by means of the equilibrium paths and the surfaces of total potential energy. In order to confirm the validity of the modal expansion that is presented as the most adequate, we investigate the static stability of cylindrical panels for two other models of modal solution. Also, the influence of initial geometric imperfections on the nonlinear behavior of cylindrical panels and the static stability of their equilibrium paths is verified. / O trabalho tem como objetivo o estudo do acoplamento modal no campo de deslocamento transversal e a busca pela menor quantidade de graus de liberdade possível para compor a expansão modal, de forma a representar corretamente o comportamento não linear em painéis cilíndricos simplesmente apoiados e submetidos à um carregamento axial estático. As equações não lineares de movimento são deduzidas a partir dos funcionais de energia, representadas pela função de tensão de Airy e pelos campos de deformações que seguem a teoria não linear de Donnell para cascas abatidas. O campo de deslocamento transversal é determinado através do método da perturbação, obtendo os modos não lineares que se acoplam ao modo linear de vibração, então as equações não lineares de equilíbrio são discretizadas pelo método de Galerkin. Desenvolveu-se neste trabalho análises lineares e não lineares para vários tipos de geometrias de painéis cilíndricos, variando valores para o raio, o comprimento circunferencial e o comprimento axial. As análises lineares têm como finalidade encontrar os modos de flambagem com suas respectivas cargas de flambagem. Nas análises não lineares estuda-se o comportamento dos painéis cilíndricos avaliando-se as interferências geradas pelos acoplamentos não lineares, presentes no campo de deslocamento transversal, a fim de encontrar uma expansão modal que represente o comportamento correto do painel cilíndrico com a menor quantidade de modos acoplados possível. A solução modal que se apresenta mais adequada é formada por um modo de vibração descrito por funções harmônicas do tipo seno, e um modo composto por funções harmônicas do tipo cosseno. Então, a partir da expansão modal encontrada, estuda-se a estabilidade estática dos painéis cilíndricos por meio dos caminhos de equilíbrio e das superfícies de energia potencial total. A fim de confirmar a validade da expansão modal que se apresenta como a mais adequada, investiga-se a estabilidade estática de painéis cilíndricos para outros dois modelos de solução modal. Ainda, verifica-se a influência de imperfeições geométricas iniciais no comportamento não linear dos painéis cilíndricos e na estabilidade estática dos seus caminhos de equilíbrio.

This diploma thesis deals with the subject of slenderness bars’ stability assessment, especially in the steel structures. Before the assessment of bars in the frame constructions, we search for the influence of the computational model’s settings on the final result. The initial geometrical imperfections are examined on the model of Euler’s bar. The influence of the rigidity of girders on the poles’ buckling length is examined on the basic frame construction. The buckling lengths are assessed in the comparison with the figures we got from the statistical tables and the computational software. The influence of construction’s initial tilt and its replacement by the system of outer forces is examined on the frame structure. Three-hinged frame structure with variable cross-section member is designed then and the influence of non-linear calculations on the inner forces is studied. In the complex frame assessment, the influence of the number of parts of variable cross-section member on the bars’ buckling length is examined.