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.

Vlasov’s one-dimensional structural theory for thin-walled open section bars was originally developed and used for metallic elements. The theory was recently extended to laminated bars fabricated from advanced composite materials. The purpose of this research is to provide a study and assessment of the extended theory. The focus is on flexural and torsional-flexural buckling of thin-walled, open section, laminated composite columns. Buckling loads are computed from the theory using a linear bifurcation analysis, and are compared to available experimental data. Also, a geometrically nonlinear beam column analysis by the finite element method is developed from the theory. Results from the nonlinear compression response analysis are compared to limited available test data. The merits of the theory and its implementation are discussed. / Master of Science / incomplete_metadata

The work of this thesis sets out to give a clearer in-depth understanding of the failure mechanics of thin-walled compression members which are associated with complex interactions between the different buckling modes during the loading process. This thesis employs the finite element method in order to examine the effect of the modelling techniques imposed at the section junctions of short struts and to investigate the influence of the local and global end conditions with regard to support and loading on the compressive response of various sections, i.e. I-sections, plain channel sections, box-sections, and lipped channel sections. The thesis also details appropriate finite element modelling strategies and solution procedures taking due account of the influence of material nonlinearity and geometrical imperfections for the determination of the coupled mode interactive response of thin-walled compression members. A detailed account of the complete loading history of the compression members from the beginning of loading through to final collapse is given in the thesis. This involves elastic local buckling, nonlinear elastic and elasto-plastic post-buckling interaction behaviour and yield propagation leading to the development of an appropriate failure mechanism which causes final collapse and unloading. A new finite element modelling strategy has been developed in the thesis with particular reference to being able to deal with the classical assumption of the stress-free in-plane boundary conditions existing at the section junctions of short length strut members during post-local buckling. Also, for fixed-ended columns, with particular reference to singly-symmetric plain channel sections, it has been shown that column deflections are initiated from the onset of local buckling for the case of the constituent plate elements of the section being locally rotationally constrained at their ends. Such columns should not therefore be considered as an overall bifurcation problem of the locally buckled member. In the case of the pinned and fixed-ended boundary conditions of the columns, the finite element simulations are shown to be able to accurately describe the rather different complex failure mechanics with a high degree of imperfection sensitivity being shown to be in evidence for the pin-ended case. Considerably good agreement has been shown to occur with the independent simulations of other researchers using the finite strip method of analysis, with the analytical solution procedures of others and with the findings from independent test work and this has provided confidence in the viability and usefulness of the modelling strategies and solution procedures developed in this thesis.

The telescoping cantilever beam structure is applied in many different engineering sectors to achieve weight/space optimisation for structural integrity. There has been limited theory and analysis in the public domain of the stresses and deflections involved when applying a load to such a structure. This thesis proposes (a) The Tip Reaction Model, which adapts classical mechanics to predict deflection of a two and a three section steel telescoping cantilever beam; (b) An equation to determine the Critical buckling loads for a given configuration of the two section steel telescoping cantilever beam assembly derived from first principles, in particular the energy methods; and finally (c) the derivation of a design optimization methodology, to tackle localised buckling induced by shear, torsion and a combination of both, in the individual, constituent, hollow rectangular beam sections of the telescopic assembly. Bending stress and shear stress is numerically calculated for the same structure whilst subjected to inline and offset loading. An FEA model of the structure is solved to verify the previous deflection, stress and buckling predictions made numerically. Finally an experimental setup is conducted where deflections and stresses are measured whilst a two section assembly is subjected to various loading and boundary conditions. The results between the predicted theory, FEA and experimental setup are compared and discussed. The overall conclusion is that there is good correlation between the three sets of data.

Large wind turbine blades, manufactured from fibre reinforced laminated composite materials, are key structural components of wind turbine systems. The demands for efficient and accurate modelling techniques of these composite blades have significantly increased. Over past decades, although complex computational models have been widely developed, more analytically based models are still very much desired to drive the design and optimization of these composite blades forward to be lighter, stronger, efficient and durable. The research work in this thesis aims to develop such more analytically based aerodynamic, structural and aero-elasticity models for large wind turbine blades manufactured from fibre reinforced laminated composite materials. Firstly, an improved blade element momentum (BEM) model has been developed by collectively integrating the individual corrections with the classic BEM model. Compared to other existing models, present BEM model accounts for blade tip and root losses more accurately. For laminar flow, the 3-D cross-flow is negligibly small. In this case, present BEM model with statically measured 2-D aerodynamic coefficients agrees closely to experimental measurements. However, stall delay correction is required for a 3-D rotating blade in stall. A new stall delay model is developed based on Snel s stall delay model. Verifications are performed and discussed for the extensively studied NREL UAE phase-VI test. The predictions of distributive and collective factors, e.g. normalised force coefficients, shaft torque and etc. have been compared to experimental measurements. The present BEM model and stall delay model are original and more accurate than existing models. Secondly, significant deficiency is discovered in the analytical thin-walled closed-section composite beam (TWCSCB) model proposed by Librescu and Vo, which is widely used by others for structural modelling of wind turbine blades. To correct such deficiency, an improved TWCSCB model is developed in a novel manner that is applicable to both single-cell and multi-cell closed sections made of arbitrary composite laminates. The present TWCSCB model has been validated for a variety of geometries and arbitrary laminate layups. The numerical verifications are also performed on a realistic wind turbine blade (NPS-100) for structural analysis. Consistently accurate correlations are found between present TWCSCB model and the ABAQUS finite element (FE) shell model. Finally, the static aero-elasticity model is developed by combining the developed BEM model and TWCSCB model. The interactions are accounted through an iterative process. The numerical applications are carried out on NPS-100 wind turbine. The numerical results show some significant corrections by modelling wind turbine blades with elastic coupling.

Os perfis de aço formados a frio possuem até 3 modos de flambagem: local, distorcional e global. Essa diversificação torna muito complexa a verificação de esforços resistentes nesses perfis. Recorre-se, então a métodos simplificados e interativos, com o intuito de fornecer ao engenheiro civil ferramentas que sejam práticas e apresentem um bom resultado. Métodos numéricos, como o MFF (métodos das faixas finitas), apesar de serem mais precisos, não são ainda, de uso corrente em projetos. O enfoque principal deste trabalho são as normas brasileiras de perfis formados a frio NBR 14762:2001 “Dimensionamento de estruturas de aço constituídas por perfis formados a frio" e NBR 6355:2003 “Perfis estruturais de aço formados a frio - Padronização". Comparam-se as tabelas D1 e D2 na NBR14762:2001, referentes à flambagem distorcional, a resultados calculados por meio do processo recomendado pela norma. Verificaram-se quais perfis padronizados pela NBR 6355:2003 dispensam a verificação da resistência por distorção da seção transversal. Uma análise geral de perfis de aço formados a frio, a fim de identificar aqueles que possuem melhor eficiência (perfis que resistem esforços mais elevados com menor área da seção transversal) também é feita. Para a realização desta pesquisa foi desenvolvido um programa de computador. / The cold formed steel members have up to 3 buckling modes: local, distortional and global. This diversification makes very complex the verification of these members’ resistance. For this reason it is used simple and interactive methods to provide the Civil Engineers tools that are practical and present a good result. Although numerical methods such as FDM (Finite Strip Methods) are more precise, they are still not currently used in projects. The main focus of this dissertation is the Brazilian rules regarding the cold formed steel members NBR 14762:2001 “Dimensioning steel structures made of cold formed profiles" and NBR 6355:2003 “Cold formed steel members – Standardizing". It compares the D1 and D2 tables of NBR14762:2001, regarding the distortional buckling, with the calculated results recommended by these rules. In this way it is verified which NBR 6355:2003 standardized profiles do not require the verification of resistance by distortional buckling. It is also made a general analysis of these cold formed steel members. And to make this research it was developed a computer program.

This thesis is focused on the analysis and on the design of the milling technology of the components for the aerospace industry which are characterised by a high aspect ratio, reduced stiffness and all covered by a high demand on the fatigue performance. This work includes the experimental verification of the proposed technology using CNC machining center, evaluation of surface structure using optical high-resolution 3D surface measurement system ALICONA, analysis of the force loading using KISTLER device, fatigue testing and fatigue fracture analysis.

The purpose of this thesis is to develop corotational beam elements for the nonlinear dynamic analyse of flexible beam structures. Whereas corotational beam elements in statics are well documented, the derivation of a corotational dynamic formulation is still an issue. In the first journal paper, an efficient dynamic corotational beam formulation is proposed for 2D analysis. The idea is to adopt the same corotational kinematic description in static and dynamic parts. The main novelty is to use cubic interpolations to derive both inertia terms and internal terms in order to capture correctly all inertia effects. This new formulation is compared with two classic formulations using constant Timoshenko and constant lumped mass matrices. In the second journal paper, several choices of parametrization and several time stepping methods are compared. To do so, four dynamic formulations are investigated. The corotational method is used to develop expressions of the internal terms, while the dynamic terms are formulated into a total Lagrangian context. Theoretical derivations as well as practical implementations are given in detail. Their numerical accuracy and computational efficiency are then compared. Moreover, four predictors and various possibilities to simplify the tangent inertia matrix are tested. In the third journal paper, a new consistent beam formulation is developed for 3D analysis. The novelty of the formulation lies in the use of the corotational framework to derive not only the internal force vector and the tangent stiffness matrix but also the inertia force vector and the tangent dynamic matrix. Cubic interpolations are adopted to formulate both inertia and internal local terms. In the derivation of the dynamic terms, an approximation for the local rotations is introduced and a concise expression for the global inertia force vector is obtained. Four numerical examples are considered to assess the performance of the new formulation against two other ones based on linear interpolations. Finally, in the fourth journal paper, the previous 3D corotational beam element is extended for the nonlinear dynamics of structures with thin-walled cross-section by introducing the warping deformations and the eccentricity of the shear center. This leads to additional terms in the expressions of the inertia force vector and the tangent dynamic matrix. The element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transversal displacements and axial rotations. The performance of the formulation is assessed through five examples and comparisons with Abaqus 3D-solid analyses. / <p>QC 20131017</p>

A esbeltez dos perfis de aço formados a frio pode resultar na interação entre diferentes modos de flambagem, tornando a análise desses componentes uma tarefa complexa. Para o projeto de perfis formados a frio, é fundamental a compreensão da natureza do modo de flambagem ao qual estão submetidos. O cálculo de modos de flambagem puros e a quantificação da interação de modos contribuem para o estudo do comportamento desses perfis. Nesse trabalho, o cálculo da carga crítica elástica de modos de flambagem puros ou combinados é realizado através do uso de modelos de elementos finitos restringidos. Para o cálculo focado em uma classe de flambagem específica (de modos globais, distorcionais, locais ou outros), diferentes procedimentos de restrição são propostos. Utilizando um procedimento de restrição geral, o campo de deformações do modelo é restringido de acordo com uma combinação de modos de deformação da seção, definidos com base nos conceitos da teoria generalizada de vigas e do método das faixas finitas restringido. Na direção longitudinal do perfil, podem ser combinados diversos componentes harmônicos que respeitem as condições de contorno das extremidades. Também são mostrados casos em que todos os componentes harmônicos longitudinais possíveis podem ser automaticamente considerados. O cálculo de modos de flambagem combinados possibilita, automaticamente, a quantificação da interação dos modos considerados. Para validação dos procedimentos propostos, são apresentados resultados numéricos da análise de um perfil C com enrijecedores de borda, com duas diferentes condições de contorno das extremidades, e submetidos a dois tipos de carregamento. Os resultados são comparados com os fornecidos pela teoria generalizada de vigas e pelo método das faixas finitas restringido. Os procedimentos de restrição são aplicados na análise de um perfil inspirado em uma estrutura real com apoios intermediários (ao longo do comprimento), explorando a vantagem da implementação utilizando elementos finitos. O potencial dos procedimentos aqui propostos é discutido. Finalmente, foram sugeridos novos objetivos para a continuação desse trabalho. / The slenderness of cold-formed steel member can result in the interaction of different buckling modes, making the analysis of these members a complex task. In the design of thinwalled members, the understanding of the nature of the buckling mode is fundamental. The calculation of pure buckling modes and the evaluation of the interaction amongst the buckling modes help in the study of the behavior of thin-walled members. In this research, the elastic critical buckling load calculation of pure and combined buckling modes is carried out using constrained finite element models. Different constraining procedures are proposed for the calculation focused on each buckling class (of global, distortional, local or other modes). Using a general constraining procedure, the deformation fields of the model are constrained in accordance with a combination of section deformation modes, which are defined based on the concepts of the generalized beam theory and the constrained finite strip method. In the longitudinal direction on the member, several harmonic components may be combined, which must meet the boundary conditions of the member ends. Cases where all possible longitudinal harmonic components can be automatically considered are also presented. In order to validate the proposed procedures, numerical results are presented on the analysis of a lipped channel, with two different configurations of boundary conditions at member ends and submitted to two different types of loading. The results are compared to the ones provided by the generalized beam theory and the constrained finite strip method. The constraining procedures are applied to the analysis of a member inspired by a real structure with intermediate supports (between the member ends), exploring the advantages of the implementation using the finite element method. The potentiality of the procedures proposed herein is discussed. Finally, new aims are proposed in order to continue this research.

A esbeltez dos perfis de aço formados a frio pode resultar na interação entre diferentes modos de flambagem, tornando a análise desses componentes uma tarefa complexa. Para o projeto de perfis formados a frio, é fundamental a compreensão da natureza do modo de flambagem ao qual estão submetidos. O cálculo de modos de flambagem puros e a quantificação da interação de modos contribuem para o estudo do comportamento desses perfis. Nesse trabalho, o cálculo da carga crítica elástica de modos de flambagem puros ou combinados é realizado através do uso de modelos de elementos finitos restringidos. Para o cálculo focado em uma classe de flambagem específica (de modos globais, distorcionais, locais ou outros), diferentes procedimentos de restrição são propostos. Utilizando um procedimento de restrição geral, o campo de deformações do modelo é restringido de acordo com uma combinação de modos de deformação da seção, definidos com base nos conceitos da teoria generalizada de vigas e do método das faixas finitas restringido. Na direção longitudinal do perfil, podem ser combinados diversos componentes harmônicos que respeitem as condições de contorno das extremidades. Também são mostrados casos em que todos os componentes harmônicos longitudinais possíveis podem ser automaticamente considerados. O cálculo de modos de flambagem combinados possibilita, automaticamente, a quantificação da interação dos modos considerados. Para validação dos procedimentos propostos, são apresentados resultados numéricos da análise de um perfil C com enrijecedores de borda, com duas diferentes condições de contorno das extremidades, e submetidos a dois tipos de carregamento. Os resultados são comparados com os fornecidos pela teoria generalizada de vigas e pelo método das faixas finitas restringido. Os procedimentos de restrição são aplicados na análise de um perfil inspirado em uma estrutura real com apoios intermediários (ao longo do comprimento), explorando a vantagem da implementação utilizando elementos finitos. O potencial dos procedimentos aqui propostos é discutido. Finalmente, foram sugeridos novos objetivos para a continuação desse trabalho. / The slenderness of cold-formed steel member can result in the interaction of different buckling modes, making the analysis of these members a complex task. In the design of thinwalled members, the understanding of the nature of the buckling mode is fundamental. The calculation of pure buckling modes and the evaluation of the interaction amongst the buckling modes help in the study of the behavior of thin-walled members. In this research, the elastic critical buckling load calculation of pure and combined buckling modes is carried out using constrained finite element models. Different constraining procedures are proposed for the calculation focused on each buckling class (of global, distortional, local or other modes). Using a general constraining procedure, the deformation fields of the model are constrained in accordance with a combination of section deformation modes, which are defined based on the concepts of the generalized beam theory and the constrained finite strip method. In the longitudinal direction on the member, several harmonic components may be combined, which must meet the boundary conditions of the member ends. Cases where all possible longitudinal harmonic components can be automatically considered are also presented. In order to validate the proposed procedures, numerical results are presented on the analysis of a lipped channel, with two different configurations of boundary conditions at member ends and submitted to two different types of loading. The results are compared to the ones provided by the generalized beam theory and the constrained finite strip method. The constraining procedures are applied to the analysis of a member inspired by a real structure with intermediate supports (between the member ends), exploring the advantages of the implementation using the finite element method. The potentiality of the procedures proposed herein is discussed. Finally, new aims are proposed in order to continue this research.