The main aim of this thesis is to gain insight through experiments into how the deformation characteristics of a thin ring made of a metallic material such as aluminum depend on the strain-rate. More precisely, this study investigates the buckling behavior of thin metallic rings subjected to a dynamic radial compressive loading. To do so, a total of twelve experiments were performed: three experiments for each of four load levels. The specimens used were aluminum 6061-O circular rings, having a mean radius of 15.5 mm with a radius-to-thickness ratio of 31. The external pressure acting on the specimens was created via electromagnetic induction following a rapid discharge of high voltage through a solenoid that was specially manufactured to interact with the ring specimen. This created a magnetic field that interacted with the specimen and therefore set a pressure on it. Three experiments were performed for each of the following charge levels: 2 kV, 3 kV, 4 kV and 5 kV. These experiments created maximum external pressures in the specimens that varied between 7 MPa and 38 MPa. The dynamic response of the ring specimens was recorded using a digital high-speed camera; analyses of the images revealed the initial uniform radial acceleration of the rings followed by the onset and evolution of dynamic buckling. The buckling response of the aluminum rings revealed that several different wave lengths (or buckling modes) can be observed simultaneously. These wave lengths correspond to measured mode numbers between 3 and 44, depending on the rate of change of the applied loading with the higher modes selected at higher strain-rates. Superposition of several pictures taken at different times during the experiment shows that as the ring deforms, the buckling waves stay within the same angular sector, keeping the same mode numbers they initially selected all the way during deformation. Numerical simulations were performed with the finite element program ABAQUS and validated the observation that several different buckling modes appear simultaneously in the rings and that their localizations are governed by material and geometric imperfections in the specimens. / text

The acceptance and the use of cold-formed steel sections has significantly increased in recent years due to advantages such as consistency and accuracy of profile, ease of fabrication, high strength and stiffness to the lightness in the weight. For thin-walled columns, made by folding a plane plate into a section, it is possible that when they are subjected to compression loads they may buckle either locally, if the member is very short, or globally if the member is very long. In addition to local and global buckling, a thin-walled member of an open cross section may also show buckling involving a “distortion” of the cross section. Compared to local and global buckling, distortional buckling is not very familiar and has been discovered only in thin-walled members of open cross sections such as cold-formed steel section columns. The objective of this study is to investigate the behavior of polygonal semi-closed cross-section with pure compression. The study comprise to only elastic buckling and the methodology is consisted by using CUFSM analysis. In order to execute CUFSM of polygonal profiles, the scripts have created which match the Matlab script files (m-files) downloaded from CUFSM 4 open source. The distortional buckling mode is governing as a buckling failure, which occur and dominate in the cases where spring values are 100 kN or higher. However, the contrary result reveals by a decreasing of the spring values. The behavior of the cross-section is dependent on how the interaction of different buckling modes prevails at the corresponding critical half-wavelength. Considering the predomination of distortional buckling mode indicates that the most of polygonal cross-section do not behave as rigid, i.e. as whole cross-section. A reducing of distortional mode and increasing of local mode as well as global mode gives indication that the behavior of the cross-section has changed and turned significantly into more rigid and thus is expected to behave more as whole cross-section.  The more spring values decrease, the higher global mode arises and dominates for the lower slenderness range. The critical half-wavelength for each profile illustrates the needed density between bolts on the longitudinal part of the member. In the interest of eliminating distortional buckling failure, due the fact that distortional buckling is unpredictable, the bolt-density should be lower than the corresponding half-wavelength for the profile where the distortional mode is predominating.

Most thin-walled metallic structural members experience some extent of interactive buckling that corrodes the load carrying capacity. Current design methods predict the strength of thin-walled metallic structural members based on individual buckling limit-states and limited case of interactive buckling limit state. In order to develop design methods for most coupled buckling limit states, the interaction of buckling modes needs to be studied. This dissertation first introduces a generally applicable methodology for Generalized Beam Theory (GBT) elastic buckling analysis on members with holes, where the buckling modes of gross cross-section interact with those of net cross-section. The approach treats member with holes as a structural system consisting of prismatic sub-members. These sub-members are connected by enforcing nodal compatibility conditions for the GBT discretization points at the interfaces. To represent the shear lag effect and nonlinear normal stress distribution in the vicinity of a hole, GBT shear modes with nonlinear warping are included. Modifications are made to the GBT geometric stiffness because of the influence from shear lag effect caused by holes. In the following sections, the GBT formulation for a prismatic bar is reviewed and the GBT formulation for members with holes is introduced. Special aspects of analyzing members with holes are defined, namely the compatibility conditions to connect sub-members and the geometric stiffness for members with holes. Validation and three examples are provided. The second topic of this dissertation involves a buckling mode decomposition method of normalized displacement field, bending stresses and strain energy for thin-walled member displacement field (point clouds or finite element results) based on generalized beam theory (GBT). The method provides quantitative modal participation information regarding eigen-buckling displacement fields, stress components and elastic strain energy, that can be used to inform future design approaches. In the method, GBT modal amplitudes are retrieved at discrete cross-sections, and the modal amplitude field is reconstructed assuming it can be piece-wisely approximated by polynomials. The unit displacement field, stress components and strain energy are all retrieved by using reconstructed GBT modal amplitude field and GBT constitutive laws. Theory and examples are provided, and potential applications are discussed including cold-formed steel member design and post-disaster evaluation of thin-walled structural members. In the third part, post-buckling modal decomposition is made possible by development of a geometrically nonlinear GBT software. This tool can be used to assist understanding couple-buckling limit-states. Lastly, the load-deformation response considering any one GBT mode is derived analytically for fast computation and interpretation of structural post-buckling behavior. / Ph. D.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-10-11T18:37:37Z No. of bitstreams: 2 Dissertação - Danielly Luz Araújo de Morais - 2017.pdf: 12095443 bytes, checksum: a4733104fefc2df73c05b1bbb83c7895 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2017-10-11T21:27:00Z (GMT) No. of bitstreams: 2 Dissertação - Danielly Luz Araújo de Morais - 2017.pdf: 12095443 bytes, checksum: a4733104fefc2df73c05b1bbb83c7895 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-10-11T21:27:00Z (GMT). No. of bitstreams: 2 Dissertação - Danielly Luz Araújo de Morais - 2017.pdf: 12095443 bytes, checksum: a4733104fefc2df73c05b1bbb83c7895 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017-06-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In the analytical study of conoidal shallow shells, one has the difficulty in analytically representing their displacement fields. In this way a numerical analysis, such as the Finite Element Method (MEF), has been used in the study of this type of structure. In this work, a static analysis of conoidal shallow shells from curved parabolic or cylindrical edges of linear, homogeneous and isotropic elastic material is performed, subjected to a transversal uniformly load distributed along the surface. With the thin-plate formulation derived from Kirchhoff's hypotheses and the theory developed by Marguerre for thin shells, the non-linear equilibrium equations that govern the behavior of the conoidal shell were determined, considering that this is a plate with an initial displacement. A linear parametric analysis of the critical loads and of buckling modes through the MEF is performed using ABAQUS 6.11® program, varying the contour and height conditions of the curved edges. Analytically, a complexity of the components of the buckling mode displacement fields of a given geometry is evaluated by its decomposition into double Fourier series. With the non-linear analysis via MEF, the non-linear equilibrium trajectories of the displacements are obtained and the first non-linear loading limit points are obtained. Nonlinear parabolic or cylindrical geometric parabolic geometry trajectories with describable supports at their four edges are also compared, evaluating how the geometric non-linearities influence the modes of the displacement fields during loading. Finally, a non-linear parametric analysis of the influence of the variation of the curved edge heights on the equilibrium trajectories of the membrane stresses and resulting from internal moments of the conoidal shell is carried out. It is verified, with this work, that linear analyzes can underestimate, or overestimate, the nonlinear behavior of the conoid. As the parametric analysis influences the behavior of the conoid in front of the load, either in the linear analysis, resulting in different critical loads and modes of buckling, or in the nonlinear analysis, resulting in differentiated limits loads and nonlinear equilibrium trajectories of the displacements and membrane stresses and moments. / No estudo analítico de cascas conoidais abatidas, tem-se a dificuldade de representar analiticamente os seus campos de deslocamentos. Dessa forma a análise numérica, como por exemplo, via Método dos Elementos Finitos (MEF), vem sendo utilizada no estudo desse tipo de estrutura. Neste trabalho, elabora-se uma análise estática de cascas conoidais abatidas de bordas curvas parabólicas, ou cilíndricas, de material elástico linear, homogêneo e isotrópico, submetidas a um carregamento transversal uniformemente distribuído ao longo da superfície. Com a formulação para placas finas derivada das hipóteses de Kirchhoff e a teoria desenvolvida por Marguerre para cascas finas, determinam-se as equações não-lineares de equilíbrio que regem o comportamento da casca conoidal, considerando que esta seja uma placa com um deslocamento inicial. Faz-se uma análise paramétrica linear das cargas críticas e modos de flambagem através do MEF utilizando o programa ABAQUS 6.11®, variando-se as condições de contorno e altura das bordas curvas. Avalia-se, analiticamente, a complexidade das componentes dos campos de deslocamentos do modo de flambagem de uma dada geometria através de sua decomposição em séries duplas de Fourier. Com a análise não-linear via MEF, obtêm-se as trajetórias não-lineares de equilíbrio dos deslocamentos da casca e obtêm-se os primeiros pontos limites de carregamento não-lineares. Comparam-se também as trajetórias não-lineares de equilíbrio de conóides de geometrias parabólicas, ou cilíndricas, com apoios indeslocáveis em suas quatro bordas, avaliando como as não-linearidades geométricas influenciam nos modos dos campos de deslocamentos durante o carregamento. Por fim, efetua-se uma análise paramétrica não-linear da influência da variação das alturas das bordas curvas nas trajetórias de equilíbrio dos esforços de membrana e resultantes de momentos internos dos conóides. Verifica-se, com este trabalho, que análises lineares podem subestimar, ou superestimar, o comportamento não-linear do conóide. Sendo que a análise paramétrica influencia o comportamento do conóide frente ao carregamento, seja no âmbito da análise linear, resultando em diferentes cargas críticas e modos de flambagem, seja na análise não-linear, resultando em cargas limites e trajetórias não-lineares de equilíbrio dos deslocamentos e dos esforços de membrana e momentos, diferenciados.