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1

Reddy, Yeruva S. "Numerical simulation of damage and progressive failures in composite laminates using the layerwise plate theory." Diss., Virginia Tech, 1992. http://hdl.handle.net/10919/38534.

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2

Akileh, Aiman R. "Elastic-plastic analysis of axisymmetrically loaded isotropic circular and annular plates undergoing large deflections." PDXScholar, 1986. https://pdxscholar.library.pdx.edu/open_access_etds/3559.

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The concept of load analogy is used in the elastic and elastic-plastic analysis of isotropic circular and annular plates undergoing moderately large deflection. The effects of the nonlinear terms of lateral displacement and the plastic strains are considered as additional fictitious lateral loads, edge moments, and in-plane forces acting on the plate. The solution of an elastic or elastic-plastic Von Karman type plate is hence reduced to a set of two equivalent elastic plate problems with small displacements, namely, a plane problem in elasticity and a linear elastic plate bending problem. The
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3

Banan, Roshan Aerospace Civil &amp Mechanical Engineering Australian Defence Force Academy UNSW. "An engineering approach to modelling ballistic impact on hybrid polymer laminates." Publisher:University of New South Wales - Australian Defence Force Academy. Information Technology & Electrical Engineering, 2009. http://handle.unsw.edu.au/1959.4/44094.

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Hybrid polymer laminates of polycarbonate and PMMA have generated considerable interest among researchers as an alternative to traditional glass armours because of their potential for reduced cost and weight. Generally, the development of ballistic armour is carried out experimentally which is an expensive task in terms of time and cost. Numerical simulation provides a much greater facility to understand the phenomenon of ballistic impact and the effects of various parameters on the response to such impact. In addition it provides an easy means of comparing the impact performance of different
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4

Young, Andrew J. "Active control of vibration in stiffened structures." Title page, contents and abstract only, 1995. http://hdl.handle.net/2440/37722.

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Active control of vibration in structures has been investigated by an increasing number of researchers in recent years. There has been a great deal of theoretical work and some experiment examining the use of point forces for vibration control, and more recently, the use of thin piezoelectric crystals laminated to the surfaces of structures. However, control by point forces is impractical, requiring large reaction masses, and the forces generated by laminated piezoelectric crystals are not sufficient to control vibration in large and heavy structures. The control of flexural vibrations in sti
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5

Liu, Bing 1975. "FE analysis of plastic buckling of plates with initial imperfections and simulation of experiments." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100251.

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The general problem of plastic buckling of flat metal plates is a fundamental area of investigation in mechanics not only because of its intrinsic importance in the design of engineering structures, but also because it still has not been settled in a satisfying manner. Which theory of plasticity is the correct one to predict the buckling loads in the plastic range is a long-argued problem.<br>This thesis presents finite element analyses of plastic buckling and postbuckling behaviour of columns and plates, taking into account the presence of initial out-of-plane imperfections. The FE programs c
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6

Robbins, Donald H. "Hierarchical modeling of laminated composite plates using variable kinematic finite elements and mesh superposition." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/40117.

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7

CHAKRABARTI, SEKHAR KUMAR. "INELASTIC BUCKLING OF GUSSET PLATES." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/184188.

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The strength and behavior of gusset plates in buckling is evaluated herein based on data from the experimental investigations conducted by other researchers and the analytical work presented herein. A set of design guidelines has been recommended through the review of the current practice. Representative single and double brace gusset plates normally adopted for connections with compressive bracing/diagonal members in braced frames and trusses, were modeled and analyzed using linear and nonlinear finite element methods to determine the buckling loads. The buckling analysis data along with the
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8

Abel, Mary Sue M. "Four-bolt extended unstiffened moment end-plate connections." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-11242009-020221/.

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9

Montgomery, Darcy Thomas. "Milling of flexible structures." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29689.

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Current manufacturing research aims at increasing productivity by optimal selection of process parameters. This is accomplished by understanding the fundamental physics of individual manufacturing processes. In this thesis, peripheral milling of very flexible cantilevered plates is studied. The static and dynamic deflections of the plate under periodic milling forces are modelled. A new dynamic cutting force model is developed which considers five discrete zones of relative motion between the tool and the workpiece. The kinematics of both milling and vibratory motions are modelled, which is a
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10

張啓軍 and Qijun Zhang. "The Galerkin Element Method and power flow in acoustic-structural problems with damped sandwich plates." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31239742.

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11

Wong, Man-kie, and 黃文基. "A study of capacity predictions for driven piles by dynamic pile testing." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37106120.

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12

王偉洪 and Wai-hung Wong. "A study of constitutive models on engineering properties of Hong Kong marine clay." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31214745.

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13

Nugroho, Widijanto Satyo. "Waves generated by a load moving on an ice sheet over water." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ32720.pdf.

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14

Yu, Wenbin. "Variational asymptotic modeling of composite dimensionally reducible structures." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/12225.

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15

Skeen, Michael Berling Mechanical &amp Manufacturing Engineering Faculty of Engineering UNSW. "An investigation of energy flow through coupled plate structures." Publisher:University of New South Wales. Mechanical & Manufacturing Engineering, 2008. http://handle.unsw.edu.au/1959.4/43277.

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This PhD thesis presents research aims to improving the dynamic modelling of coupled plate structures across a wide frequency range by using analytical, statistical and experimental methods. The analytical waveguide method is used to model the flexural displacement of coupled plate structures which are simply supported along two parallel edges. A method of quickly predicting the average energy level in a plate from details of the waveguide model is described, and used for comparison with SEA models. The Poynting and Impedance methods of predicting the energy flow in coupled plate structures ar
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16

Chin, Victor B. L. "The dynamic response of pile-soil interfaces during pile driving and dynamic testing events." Monash University, Dept. of Civil Engineering, 2003. http://arrow.monash.edu.au/hdl/1959.1/9421.

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17

Sen, Sharma Pradeep Kumar. "Stress reduction in a plate with a hole by applied induced strains." Diss., Virginia Tech, 1993. http://hdl.handle.net/10919/27975.

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18

Jeyanayagam, Samuel S. "Engineering analysis of a Chinese-type anaerobic digester." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49800.

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19

Liu, Xing Lu. "Some problems and analysis for thermal bending plates." Thesis, University of Macau, 2010. http://umaclib3.umac.mo/record=b2148242.

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20

Chandrashekhara, K. "Geometric and material nonlinear analysis of laminated composite plates and shells." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/54739.

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An inelastic material model for laminated composite plates and shells is formulated and incorporated into a finite element model that accounts for both geometric nonlinearity and transverse shear stresses. The elasto-plastic material behavior is incorporated using the flow theory of plasticity. In particular, the modified version of Hill's initial yield criterion is used in which anisotropic parameters of plasticity are introduced with isotropic strain hardening. The shear deformation is accounted for using an extension of the Sanders shell theory and the geometric nonlinearity is considered i
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21

SUBRAMANIAN, BALAKRISHNAN. "GEOMETRICALLY NONLINEAR ANALYSIS OF THIN ARBITRARY SHELLS USING DISCRETE-KIRCHHOFF CURVED TRIANGULAR ELEMENTS (FINITE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188101.

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The research work presented here deals with the problems of geometrically nonlinear analysis of thin shell structures. The specific objective was to develop geometrically nonlinear formulations, using Discrete-Kirchhoff Curved Triangular (DKCT) thin shell elements. The DKCT elements, formulated in the natural curvilinear coordinates, based on arbitrary deep shell theory and representing explicit rigid body modes, were successfully applied to linear elastic analysis of composite shells in an earlier research work. A detailed discussion on the developments of classical linear and nonlinear shell
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22

Kumar, Neraj. "Detection of Variable Retention Time in DRAM." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/2103.

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This thesis investigates a test method to detect the presence of Variable Retention Time (VRT) bits in manufactured DRAM. The VRT bits retention time is modeled as a 2-state random telegraph process that includes miscorrelation between test and use. The VRT defect is particularly sensitive to test and use conditions. A new test method is proposed to screen the VRT bits by simulating the use conditions during manufacturing test. Evaluation of the proposed test method required a bit-level VRT model to be parameterized as a function of temperature and voltage conditions. The complete 2-state VRT
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23

Seward, Lori Welte. "A multiple stress, multiple component stress screening cost model." Thesis, Virginia Tech, 1985. http://hdl.handle.net/10919/41578.

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<p>Environmental stress screening is used to enhance reliability by decreasing the number of failures experienced during customer use. It is suggested that added benefit can be gained by applying multiple stresses rather than a single stress, as is done presently. A further modification is to apply the stress at the assembly level, accelerating different types of components at the same time. Different component E A e acceleration effects must then be considered.</p> <p> The problem these modifications present is how to choose the appropriate stress levels and the time duration of the stress sc
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24

Young, David T. "Optimal forms of rectangular-base, shallow shells with respect to buckling." Diss., Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/49967.

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Thin, elastic, shallow shells having uniform thickness and rectangular boundaries are investigated. The boundary conditions are either simply supported or claped, and the shell is subjected to a uniformly distributed load applied over either the full shell area or a central region. The thickness, material properties, edge lengths, and surface area of the shell are specified, and the objective is the determination of the shell shape which will maximize the buckling load. Marguerre's two, coupled, non-linear equations of equilibrium are used to describe prebuckling deformations and stresses. Co
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25

Kahle, Matthew Gilbert. "Partially restrained composite connections : design and analysis of a prototype structure." Thesis, Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/20830.

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26

Heller, Collin M. "A computational model of engineering decision making." Thesis, Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50272.

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The research objective of this thesis is to formulate and demonstrate a computational framework for modeling the design decisions of engineers. This framework is intended to be descriptive in nature as opposed to prescriptive or normative; the output of the model represents a plausible result of a designer's decision making process. The framework decomposes the decision into three elements: the problem statement, the designer's beliefs about the alternatives, and the designer's preferences. Multi-attribute utility theory is used to capture designer preferences for multiple objectives under unc
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27

Stephens, Max Taylor. "Numerical and Experimental Analysis of Composite Sandwich Links for the LCF System." PDXScholar, 2011. https://pdxscholar.library.pdx.edu/open_access_etds/579.

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Shear links are used as fuse elements in lateral load resisting systems to provide ductility and dissipate seismic energy. These links have traditionally been employed in eccentrically braced frames, but have more recently been suggested for use in the innovative linked column frame system (LCF). Current design specifications for shear links require intermediate web stiffeners to provide out-of-plane web stability so ductility requirements can be achieved. This research focused on moving from discrete transverse web stiffening to continuously stiffened webs in built up shear links. Built up li
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28

Lokuge, W. P. (Weena Priyanganie) 1967. "Stress-strain behaviour of confined high strength concrete under monotonically increasing and cyclic loadings." Monash University, Dept. of Civil Engineering, 2003. http://arrow.monash.edu.au/hdl/1959.1/9425.

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29

Perez, Ivan Rodolfo Duran Cruz. "Geração automatica de cenarios de teste a partir de modelos da especificação de sistemas." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/276180.

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Orientador: Eliane Martins<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação<br>Made available in DSpace on 2018-08-13T10:23:49Z (GMT). No. of bitstreams: 1 Perez_IvanRodolfoDuranCruz_M.pdf: 1633844 bytes, checksum: e823f99de0cc740109404e263028fac7 (MD5) Previous issue date: 2008<br>Resumo: As crescentes exigências em relação à melhoria de qualidade e a redução de custos e prazos têm tornado comum à busca por soluções mais eficientes para desenvolvimento e testes de sistemas. Com relação aos testes, uma recomendação é a de começá-los mais cedo, e, de pref
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30

Bienen, Britta. "Three-dimensional physical and numerical modelling of jack-up structures on sand." University of Western Australia. School of Civil and Resource Engineering, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0208.

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Mobile offshore jack-up drilling rigs are not custom-designed for a particular location but rated for typical operating characteristics, like water depths. They may be deployed at a number of different sites during their design life. Under the current guidelines, the jack-up is required to be assessed for its suitability for each new proposed location, assuming environmental loading conditions due to wind, waves and current corresponding to a 50-year return period storm applicable to the site. Traditionally, these assessments have been performed in two dimensions, simplifying the jack-up to a
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31

Widjaja, Budi R. "Analytical investigation of composite diaphragms strength and behavior." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-07112009-040307/.

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32

Mattos, Carlos Eduardo Lourenço. "Metodologia de ensaio de fluência em cabos de transmissão de energia elétrica." Universidade Tecnológica Federal do Paraná, 2015. http://repositorio.utfpr.edu.br/jspui/handle/1/1360.

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A construção de linhas de transmissão são obras de grande impacto ambiental e requerem grandes investimentos financeiros. Este projeto de pesquisa, visa por meio de ensaios de laboratório, conceber uma ferramenta sistêmica para o aperfeiçoamento do método de determinação da fluência em cabos condutores de energia e OPGW (Optical Ground Wire), que tem sido utilizada no Brasil durante os últimos 30 anos, e analisar os efeitos na construção das linhas aéreas de transmissão. Visa também, proporcionar ganhos de confiabilidade ao sistema de transmissão de energia elétrica, pois o projeto, a construç
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33

Edouard, Clément. "Vieillissement des batteries Li-ion de traction : des mécanismes vers le vieillissement accéléré." Thesis, Compiègne, 2015. http://www.theses.fr/2015COMP2221/document.

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En raison de leurs performances en termes de densités énergétiques et de puissance, les batteries Li-ion sont les systèmes de stockage électrique privilégiés pour les nouvelles générations de véhicules électriques. Leur modélisation est indispensable pour fournir une évaluation de leurs performances tout au long de leur durée de vie tout en limitant le nombre d'essais expérimentaux, et ceci dans le but de concevoir des configurations et des gestions optimales des packs batteries pour une application envisagée. Le but de ce travail consiste à proposer un modèle physique capable de prédire le co
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34

Thölken, Denise. "Efeito da rigidez de pilar parede no comportamento sísmico de edifício de concreto armado." Universidade Tecnológica Federal do Paraná, 2013. http://repositorio.utfpr.edu.br/jspui/handle/1/962.

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Este trabalho tem como objeto o estudo do efeito da rigidez de pilar parede no comportamento estrutural de edifícios de concreto armado submetidos a sismos. Foram consideradas as premissas da norma brasileira ABNT NBR15421:2006, que apresenta os critérios para projeto de estruturas resistentes a sismo. A análise linear com emprego dos métodos da norma - método das forças horizontais equivalentes, método espectral e histórico de aceleração no tempo - foi aplicada em edifícios com dois tipos de sistemas estruturais, sendo eles pórtico de concreto e sistema dual pórtico de concreto e pilar parede
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35

Pessôa, José Renato de Castro. "Análise numérico-experimental de estruturas de concreto com utilização da energia de fraturamento." Universidade do Estado do Rio de Janeiro, 2007. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=780.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>A evolução dos concretos utilizados nas últimas décadas deu origem ao Concreto de Alto Desempenho (CAD), que tem, entre suas características, alta resistência à compressão e baixa permeabilidade. Com o desenvolvimento dos produtos químicos utilizados na construção civil, em especial os superplastificantes e superfluidificantes, a utilização desse tipo de concreto tornou-se cada vez mais freqüente pela possibilidade de se obter uma mistura suficientemente trabalhável utilizando-se fatores água/cimento menores do que 0,35. Devido à s
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36

Nahan, Matthew F. "A nonlocal damage theory for laminated plate with application to aircraft damage tolerance." Thesis, 1997. http://hdl.handle.net/1957/34015.

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Design of commercial aircraft structure, composed of composite material, requires the prediction of failure loads given large scale damage. In particular, a fuselage of graphite/epoxy lamination was analyzed for damage tolerance given a standard large crack that severed both skin and internal structure. Upon loading, a zone of damage is known to develop in front of a crack-tip in composite laminates; and, its material behavior within the damage zone is characterized as strain softening. This investigation sought to develop a computational model that simulates progressive damage growth and pred
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37

Wu, Y. F. (Yu-Fei). "Seismic retrofitting of rectangular reinforced concrete columns with partial interaction plating." 2002. http://web4.library.adelaide.edu.au/theses/09PH/09phw9591.pdf.

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38

Wu, Y. F. (Yu-Fei). "Seismic retrofitting of rectangular reinforced concrete columns with partial interaction plating / by Yu-Fei Wu." Thesis, 2002. http://hdl.handle.net/2440/21836.

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"June 2002"<br>Includes bibliographical references (leaves 349-374)<br>xxxix, 416 leaves : ill., plates ; 30 cm.<br>Thesis (Ph.D.)--University of Adelaide, Dept. of Civil and Environmental Engineering, 2002
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39

Young, Andrew J. "Active control of vibration in stiffened structures." Thesis, 1995. http://hdl.handle.net/2440/37722.

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Active control of vibration in structures has been investigated by an increasing number of researchers in recent years. There has been a great deal of theoretical work and some experiment examining the use of point forces for vibration control, and more recently, the use of thin piezoelectric crystals laminated to the surfaces of structures. However, control by point forces is impractical, requiring large reaction masses, and the forces generated by laminated piezoelectric crystals are not sufficient to control vibration in large and heavy structures. The control of flexural vibration
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40

"Statistical learning and testing approaches for temporal dependence structures with application to financial engineering." Thesis, 2003. http://library.cuhk.edu.hk/record=b6073941.

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A technique called gaussian temporal factor analysis (gaussian TFA) proposed by Xu in 2000 may be used to test the APT model under the mild assumption that the efficient market hypothesis (EMH) is violated. We are motivated to investigate statistical behaviors of the gaussian TFA model.<br>According to a recent survey by Cochrane (1999), the multi-factor APT model is gaining popularity and recognition over CAPM by the investment community. While empirical evidence shows that mutual funds can earn average returns not explained by the CAPM by following a variety of investment styles, this anomal
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41

Schumann, Erwin Wilhelm. "Modelling and testing microwave magnetrons." Thesis, 1988. http://hdl.handle.net/10413/6903.

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Though declining in popularity over the last decade, the magnetron still has applications where portable high power is needed. This study examines the predicted performance of cylindrical microwave magnetrons using analytic lumped-spoke models based on the energy conservation principle. The analytic approach is still favoured when small computer systems are used and the overall performance of the tube is to be predicted. The magnetron elements are examined and the role they play in the overall device performance analysed. Simplified representations of these elements are used to construct a com
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42

Meyers, Anthony G. (Anthony Gerard). "The determination of rock mass strength for engineering design / Anthony G. Meyers." 1993. http://hdl.handle.net/2440/20601.

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Bibliography: leaves 385-395<br>xxv, 395 leaves : ill ; 30 cm.<br>Title page, contents and abstract only. The complete thesis in print form is available from the University Library.<br>Thesis (Ph.D.)--University of Adelaide, Dept. of Civil Engineering, 1993
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Meyers, Anthony G. (Anthony Gerard). "The determination of rock mass strength for engineering design / Anthony G. Meyers." Thesis, 1993. http://hdl.handle.net/2440/20601.

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44

Tso, Y. (Yan). "A study of the transmission of vibration in structures characteristic of naval ships / Yan Tso." 1996. http://hdl.handle.net/2440/18755.

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Bibliography: leaves 159-169.<br>xii, 170 leaves : ill. (some col.) ; 30 cm.<br>Title page, contents and abstract only. The complete thesis in print form is available from the University Library.<br>This thesis is concerned with the transmission and distribution of vibratory power in built-up structures, and in particular, structures characteristic of naval ships. The study consists of a detailed investigation of the wave transmission properties of structural junctions, followed by an analysis of the wave propagation through plates with periodic stiffeners. The results are used to develop Stat
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Tso, Y. (Yan). "A study of the transmission of vibration in structures characteristic of naval ships / Yan Tso." Thesis, 1996. http://hdl.handle.net/2440/18755.

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Bibliography: leaves 159-169.<br>xii, 170 leaves : ill. (some col.) ; 30 cm.<br>This thesis is concerned with the transmission and distribution of vibratory power in built-up structures, and in particular, structures characteristic of naval ships. The study consists of a detailed investigation of the wave transmission properties of structural junctions, followed by an analysis of the wave propagation through plates with periodic stiffeners. The results are used to develop Statistical Energy Analysis (SEA) models for the prediction of vibration levels in structures characteristic of naval ships
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46

Liang, Bin. "Estimation of Time-dependent Reliability of Suspension Bridge Cables." Thesis, 2016. https://doi.org/10.7916/D8V69JTN.

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The reliability of the main cable of a suspension bridge is crucial to the reliability of the entire bridge. Throughout the life of a suspension bridge, its main cables are subject to corrosion due to various factors, and the deterioration of strength is a slowly evolving and dynamic process. The goal of this research is to find the pattern of how the strength of steel wires inside a suspension bridge cable changes with time. Two methodologies are proposed based on the analysis of five data sets which were collected by testing pristine wires, artificially corroded wires, and wires taken from
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47

Karanci, Efe. "Modeling Corrosion in Suspension Bridge Main Cables." Thesis, 2017. https://doi.org/10.7916/D8RB7H05.

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Accurately determining the current state of a suspension bridge’s main cables is a critical component to reliably assessing the safety of the bridge. The primary cause for the deterioration of cable strength with time is universally recognized to be the corrosion of high strength steel wires, which together comprise the main cable. Hidden from view by the cable wrapping, this corrosion often goes undetected for years and is typically only discovered during costly and intrusive inspections. Furthermore, current inspection methods provide an incomplete picture of the variation in wire condition
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Law, J. R. "Time varying probability of failure of steel floor beams subjected to real fire." Thesis, 1997. https://vuir.vu.edu.au/18185/.

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A model for estimating the time-dependent reliability of steel beams under real fire conditions has been developed. It gives a more rational basis than time of failure modelling does for design. From risk modelling, some small resistance time from the probabilistic distribution times of failure can be deduced, which gives an acceptably small risk of failure. Time of failure modelling by itself can only give the mean time failure which could lead to excessive risk if the variability of time of failure is large. The model comprises submodels for fire severity, heat transfer, mechanical prope
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Knoesen, Darryn Marc. "The development and assessment of techniques for daily rainfall disaggregation in South Africa." Thesis, 2005. http://hdl.handle.net/10413/3439.

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The temporal distribution of rainfall , viz. the distribution of rainfall intensity during a storm, is an important factor affecting the timing and magnitude of peak flow from a catchment and hence the flood-generating potential of rainfall events. It is also one of the primary inputs into hydrological models used for hydraulic design purposes. The use of short duration rainfall data inherently accounts for the temporal distribution of rainfall, however, there is a relative paucity of short duration data when compared to the more abundantly available daily data. One method of overcoming this i
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Beale, Michael P. "New Approaches to Analyze Sound Barrier Effectiveness." 2012. http://hdl.handle.net/1805/3240.

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Indiana University-Purdue University Indianapolis (IUPUI)<br>Highway noise can cause annoyance, affect sleep patterns, and reduce the property value for people in the proximity. Current methods for analyzing the effectiveness of sound barriers only take loudness into consideration. This paper introduces new methods that can be used to analyze the effectiveness of the sound barriers. Our approach uses psychoacoustic measures including sharpness, roughness, fluctuation, strength, and annoyance. Highway noise is non-stationary, therefore each of these metrics are calculated over a short time. Fin
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