The bending and spring back behaviors of DP780 and DP980 were investigated using experiments, analytical models, and PEA. An PEA study using 3D shells was first performed of the work by Queener and DeAngelis (1968) and demonstrated that the 3D shell element behavior in bending and springback, is similar to that from simple bending theory. Experimental and FE studies were then performed using DP780 and DP980 steels under simple and general bending conditions. Simple bending conditions were studied in V -die bending. General bending was studied for DP780 using a commercial bending machine. The PEA examined the effect of element formulation and material hardening assumptions on springback, bending stresses, and the residual stress distributions after springback. Corresponding simple and general bending analytical models were also compared. The simple bending model was from Queener and DeAngelis ( 1968), and the general bending model was from Tan et al. ( 1995), modified for Ludwig hardening. Overall, the PEA predicted the springback magnitude in the order; 2D continuum >3D continuum> 3D shells, and kinematic hardening> mixed hardening> isotropic hardening. In the V -die bending study the 3D shell PEA, using a calibrated mixed hardening assumption, produced the most accurate results. The PEA using pure isotropic hardening demonstrated that bending and springback behaviors for both steels were consistent with that described by simple bending theory. The behaviors demonstrated by the FEA using mixed or pure kinematic hardening were not. In the general bending study, the 3D continuum element FEA using pure kinematic hardening was the most accurate. The 3D continuum element FEA captured the bending stress interaction with the hardening assumption as well as thinning deformation, in agreement with the analytical model and thinning measured experimentally. 3D Shell elements could not capture these behaviors and significantly under-predicted springback under the pure isotropic hardening assumption. / Thesis / Master of Applied Science (MASc)

This thesis presents two studies on elastic plates. In the first study, we discuss the choice of elastic energies for thin plates and shells, an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four bulk isotropic quadratic elastic theories have fundamentally different predictions with regard to bending behavior. At finite thickness, these qualitative effects persist near the limit of mid-surface isometry, and not all theories predict an isometric ground state. We discuss how certain kinematic measures that arose in early studies of rod mechanics lead to coherent definitions of stretching and bending, and promote the adoption of these quantities in the development of a covariant theory based on stretches rather than metrics. In the second work, the effects of in-plane swelling gradients on thin, anisotropic plates are investigated. We study systems with a separation of scales between bending energy terms. Warped equilibrium shapes are described by two parameters controlling the spatial "rolling up'' and twisting of the surface. Shapes within this two-parameter space are explored, and it is shown that shapes will either be axisymmetric or twisted depending on swelling function parameters and material anisotropy. In some axisymmetric shapes, pitchfork bifurcations to twisted solutions are observed by varying these parameters. We also show that a familiar soft mode of the catenoid to helicoid transformation of an isotropic material no longer exists with material anisotropy. / Master of Science / This thesis presents two studies on the subject of thin, elastic bodies, otherwise known as plates. Plate theory has important applications in many areas of life, ranging from the design and construction of civil structures to the mechanics of wrinkling sheets. In the first work, we discuss how different elastic plate theories have qualitatively different predictions on how a plate will behave when bent. We discuss the different physical implications of each model, and relate our findings to previous studies. Additionally, we promote the use of certain technical measures in the study of plates corresponding to the most coherent definitions of bending and stretching. In the second work, we study the effects of in-plane swelling gradients on elastic plates whose material stiffnesses vary with direction. Inspired by wood panels that warp when exposed to moisture, we model elastic plates exposed to various swelling patterns and determine the resulting warped shapes. We find that some shapes are axisymmetric, while others prefer to twist when exposed to moisture-induced swelling. By varying certain parameters of the swelling functions, or by increasing the material fiber stiffness, we also find a qualitative change in shape from an axisymmetric to a twisted surface.

Three tree species, Freeman maple (Acer x. freemanii), swamp white oak (Quercus bicolor (Willd.)) and shingle oak (Quercus imbricaria (Michx.)) were tested before and after pruning to determine the effectiveness of pruning on reducing drag and bending moment. Pruning methods were thin, reduce and raise and meet the requirements set by the American National Standard Institute A300 standards for Tree Care Operations Trees, Shrub, and Other Woody Plant Maintenance - Standard Practices (Pruning). Trees were tested up to speeds of 22.4m*s-1 over 1.6km by driving them in the bed of a truck. Drag, based on a centroid of the crown, and a bending moment was calculated. Drag and bending moment were also normalized by tree mass and crown area. Reduction pruning worked more effectively for Freeman maple and raise pruning for swamp white oak at reducing drag. Simple to measure tree characteristics were analyzed to determine the best predictors of drag and bending moment in the field. Tree mass frequently was the best predictor of drag and bending moment. Information should be used with caution due to the fact that the trees tested were small stature and a limited number of trees were tested. / Master of Science

Bending wood dates back to antiquity in the form of baskets from willow branches and when boats were no longer made of hollowed out logs. Fresh growth willow twigs are readily bent into practically any shape; however, when wood has been separated from the tree and dried it is more rigid, difficult to bend, and breakable. Steamed wood is less rigid since adding moisture and heat to wood results in plasticization. Steaming at atmospheric pressure is the common technique for wood bending where diffusion prevails as the predominant mechanism governing moisture movement. Applications using conventional atmospheric steaming are time consuming and can result in failed bends. While other wood plasticization methods exist, Vacuum Steam Technology offers a promising method that utilizes pressure differentials to accelerate the addition of steam to wood due to water vapor bulk flow and subsequently an accelerated temperature rise and moisture addition. The objectives of this work were: (1) determine whether cycles of vacuum and steaming could significantly improve the plastic-deformable state relative to the classic process of atmospheric steaming given equivalent treatment times when beginning with low moisture content (<10%) maple, and (2) compare the work required to bend to form between Vacuum Steam Technology treated maple and atmospheric-steamed maple when beginning with low moisture content (<10%) specimens. A procedure for Vacuum Steam Technology to enable rapid plasticization of maple specimens from a kiln-dried state was developed. Kiln dried maple specimens were either treated according to the Vacuum Steam Technology procedure or were atmospherically steamed for a time equivalent to the Vacuum Steam Technology treatment and then bent into a 180° semi-circular form. Vacuum Steam Technology treated specimens had 0 failed bends whereas the atmospheric steamed specimens resulted in 39% failed bends. Vacuum Steam Technology treated specimens resulted in 17% less work to bend. The results clearly indicate that Vacuum Steam Technology is a superior technique for attaining a plastic deformable state prior to bending when beginning with low moisture content maple. Additional results included time to temperature, rate of moisture content change, final moisture contents, specific gravity influence. / Master of Science

The author examines nonlinear aeroelastic responses of air vehicle systems. Herein, the governing equations for a cantilevered configuration are developed and the methods of analysis are explored. Based on the developed nonlinear bending-bending-torsion equations, internal resonance, which is possible in future air vehicles, and the possible cause of limit cycle oscillations of aircraft wings with stores are investigated. The nonlinear equations have three types of nonlinearities caused by wing flexibility, store geometry and aerodynamic stall, and retain up to third-order nonlinear terms. The internal resonance conditions are examined by the Method of Multiple Scales and demonstrated by time simulations. The effect of velocity change for various physical parameters and stiffness ratio is investigated through bifurcation diagrams derived from Poinar´e maps. The dominant factor causing limit cycle oscillations is the stiffness ratio between in-plane and out-of-plane motion.

The author examines nonlinear aeroelastic responses of air vehicle systems. Herein, the governing equations for a cantilevered configuration are developed and the methods of analysis are explored. Based on the developed nonlinear bending-bending-torsion equations, internal resonance, which is possible in future air vehicles, and the possible cause of limit cycle oscillations of aircraft wings with stores are investigated. The nonlinear equations have three types of nonlinearities caused by wing flexibility, store geometry and aerodynamic stall, and retain up to third-order nonlinear terms. The internal resonance conditions are examined by the Method of Multiple Scales and demonstrated by time simulations. The effect of velocity change for various physical parameters and stiffness ratio is investigated through bifurcation diagrams derived from Poinar´e maps. The dominant factor causing limit cycle oscillations is the stiffness ratio between in-plane and out-of-plane motion.

This thesis investigated the effect of the length of the superficial plate on the mechanical properties of a stacked-plate construct made with 2.0-2.7 Veterinary Cuttable platesTM (VCP). Stacking VCP increases construct stiffness compared to using a single VCP but increases stress protection and concentrates stress at the extremities of the implants. We hypothesized that shortening the superficial plate would not reduce the stiffness of the construct, and would reduce stress concentration at the plate ends. A fracture gap model was created with a bone surrogate (copolymer acetal rods), stacked 2.0-2.7 VCP and 2.7 screws. The constructs consisted of an 11-hole VCP bottom plate and a 5-, 7-, 9- or 11-hole VCP superficial plate. In phase one, 5 of each construct were randomly tested for failure in 4-point bending and axial loading. Stiffness, load at yield, and work until failure were measured. In phase two, strains were recorded during elastic deformation for each configuration. During both testing methods, stiffness, load at yield and work to failure progressively decreased when decreasing the length of the superficial plate. No statistically significant differences were obtained for load at yield in 4-point bending and work to failure in axial loading. The strain within the implant over the gap increased as the length of the superficial plate decreased. Shortening the superficial plate reduces the stiffness and strength of the construct, and decreases stress concentration at the implant ends. As the cross section of the implant covering the gap remained constant, friction between the plates may play a role in the mechanical properties of stacked VCP. / Synthes Canada - OVC Pet Trust Fund

O desenvolvimento de técnicas que deem sobrevida a navios com mais de 20 anos de navegação interior é crucialmente importante para um país com a demanda de mobilidade como a que tem o Brasil. Nesse sentido, uma técnica que pode ser citada é a determinação da vida útil potencial (VUP), que propõe uma forma de avaliar o aumento da vida útil de embarcações de navegação interior. Na busca por índices globais que identifiquem as condições do navio, considera-se o cálculo do momento fletor último da seção mestra do navio. O presente trabalho apresenta, de forma detalhada, a aplicação dos principais métodos de cálculo do momento fletor último em três casos de estudo: um perfil caixão, o perfil reduzido de embarcação de fundo duplo (estudada por Nishihara, 1983) e a seção mestra de uma embarcação típica utilizada para navegação na Bacia do Sudeste (NT Guarita). Os métodos empregados para o cálculo do momento fletor último são: métodos direto e iterativo propostos pela Associação Internacional de Sociedades Classificadoras (IACS 2008), Método da Resistência Direta, Método da Largura Efetiva e análises não lineares através do Método dos Elementos Finitos. Com o intuito de obter uma resposta mais coerente, é proposta uma modificação no Método Iterativo [IACS, 2008]. O método modificado é então utilizado no estudo de sensibilidade do momento fletor último frente à redução de espessura das chapas de convés (considerando a seção mestra da embarcação NT Guarita). Os resultados obtidos, bem como as conclusões a respeito, são apresentados ao final do trabalho. Adicionalmente, é proposto um índice para uso na avaliação do nível de não linearidade da resposta dos elementos locais, quando submetidos a reduções de espessura. / The increasing of ships life extension can only be provided by new methodologies development. A new method to determine the potential ship shelf life is being proposed, being part of the new method, in this document the ultimate bending momentum of the master ship section is study. The study presents the application of the most popular methods to calculate the ultimate bending for three different cases: box section, double hull ship studied by Nishihara, 1983 and master section of a typical boat used in Bacia do Sudeste, NT Guarita. The methods applied to calculate the ultimate bending momentum are: direct and iterative methods proposed by the International Association of Classification Societies, IACS 2008, Direct Strength Method, Method of Effective Width and also non-linear analysis using the Finite Element Method. In order to obtain a more coherent response, a change in the Iterative Method [IACS, 2008] has been proposed. The new method is used to study the sensitivity of the ultimate momentum to the reduction of deck thickness applied the NT Guarita. The results and conclusions will be presented in this study. Additionally, will be proposed an index to evaluate the level of non-linearity of the local elements response, when exposed to thickness reduction.

O desenvolvimento de técnicas que deem sobrevida a navios com mais de 20 anos de navegação interior é crucialmente importante para um país com a demanda de mobilidade como a que tem o Brasil. Nesse sentido, uma técnica que pode ser citada é a determinação da vida útil potencial (VUP), que propõe uma forma de avaliar o aumento da vida útil de embarcações de navegação interior. Na busca por índices globais que identifiquem as condições do navio, considera-se o cálculo do momento fletor último da seção mestra do navio. O presente trabalho apresenta, de forma detalhada, a aplicação dos principais métodos de cálculo do momento fletor último em três casos de estudo: um perfil caixão, o perfil reduzido de embarcação de fundo duplo (estudada por Nishihara, 1983) e a seção mestra de uma embarcação típica utilizada para navegação na Bacia do Sudeste (NT Guarita). Os métodos empregados para o cálculo do momento fletor último são: métodos direto e iterativo propostos pela Associação Internacional de Sociedades Classificadoras (IACS 2008), Método da Resistência Direta, Método da Largura Efetiva e análises não lineares através do Método dos Elementos Finitos. Com o intuito de obter uma resposta mais coerente, é proposta uma modificação no Método Iterativo [IACS, 2008]. O método modificado é então utilizado no estudo de sensibilidade do momento fletor último frente à redução de espessura das chapas de convés (considerando a seção mestra da embarcação NT Guarita). Os resultados obtidos, bem como as conclusões a respeito, são apresentados ao final do trabalho. Adicionalmente, é proposto um índice para uso na avaliação do nível de não linearidade da resposta dos elementos locais, quando submetidos a reduções de espessura. / The increasing of ships life extension can only be provided by new methodologies development. A new method to determine the potential ship shelf life is being proposed, being part of the new method, in this document the ultimate bending momentum of the master ship section is study. The study presents the application of the most popular methods to calculate the ultimate bending for three different cases: box section, double hull ship studied by Nishihara, 1983 and master section of a typical boat used in Bacia do Sudeste, NT Guarita. The methods applied to calculate the ultimate bending momentum are: direct and iterative methods proposed by the International Association of Classification Societies, IACS 2008, Direct Strength Method, Method of Effective Width and also non-linear analysis using the Finite Element Method. In order to obtain a more coherent response, a change in the Iterative Method [IACS, 2008] has been proposed. The new method is used to study the sensitivity of the ultimate momentum to the reduction of deck thickness applied the NT Guarita. The results and conclusions will be presented in this study. Additionally, will be proposed an index to evaluate the level of non-linearity of the local elements response, when exposed to thickness reduction.

O desenvolvimento de técnicas que deem sobrevida a navios com mais de 20 anos de navegação interior é crucialmente importante para um país com a demanda de mobilidade como a que tem o Brasil. Nesse sentido, uma técnica que pode ser citada é a determinação da vida útil potencial (VUP), que propõe uma forma de avaliar o aumento da vida útil de embarcações de navegação interior. Na busca por índices globais que identifiquem as condições do navio, considera-se o cálculo do momento fletor último da seção mestra do navio. O presente trabalho apresenta, de forma detalhada, a aplicação dos principais métodos de cálculo do momento fletor último em três casos de estudo: um perfil caixão, o perfil reduzido de embarcação de fundo duplo (estudada por Nishihara, 1983) e a seção mestra de uma embarcação típica utilizada para navegação na Bacia do Sudeste (NT Guarita). Os métodos empregados para o cálculo do momento fletor último são: métodos direto e iterativo propostos pela Associação Internacional de Sociedades Classificadoras (IACS 2008), Método da Resistência Direta, Método da Largura Efetiva e análises não lineares através do Método dos Elementos Finitos. Com o intuito de obter uma resposta mais coerente, é proposta uma modificação no Método Iterativo [IACS, 2008]. O método modificado é então utilizado no estudo de sensibilidade do momento fletor último frente à redução de espessura das chapas de convés (considerando a seção mestra da embarcação NT Guarita). Os resultados obtidos, bem como as conclusões a respeito, são apresentados ao final do trabalho. Adicionalmente, é proposto um índice para uso na avaliação do nível de não linearidade da resposta dos elementos locais, quando submetidos a reduções de espessura. / The increasing of ships life extension can only be provided by new methodologies development. A new method to determine the potential ship shelf life is being proposed, being part of the new method, in this document the ultimate bending momentum of the master ship section is study. The study presents the application of the most popular methods to calculate the ultimate bending for three different cases: box section, double hull ship studied by Nishihara, 1983 and master section of a typical boat used in Bacia do Sudeste, NT Guarita. The methods applied to calculate the ultimate bending momentum are: direct and iterative methods proposed by the International Association of Classification Societies, IACS 2008, Direct Strength Method, Method of Effective Width and also non-linear analysis using the Finite Element Method. In order to obtain a more coherent response, a change in the Iterative Method [IACS, 2008] has been proposed. The new method is used to study the sensitivity of the ultimate momentum to the reduction of deck thickness applied the NT Guarita. The results and conclusions will be presented in this study. Additionally, will be proposed an index to evaluate the level of non-linearity of the local elements response, when exposed to thickness reduction.