<p> This thesis deals with the analytical and experimental study of buckling strength, of thin walled channel struts, of different geometrical dimensions. The influence of the dimensions of the columns on the buckling strength has been studied.</p> <p> The experimental work consisted of testing different channels of thin sheeting to failure. Comparison has been made with the previous work done and a comparison is made between the theoretical predicted values and the experimental results. The Appendix includes detailed mathematical procedure and matrices formulations.</p> / Thesis / Master of Engineering (MEngr)

Macro lambda is a parameter for predicting the weight savings for using different material. Macro lambda approximates the response of a thin-walled structure to a change in material thickness. The relationship between macro lambda and weight savings for material substitution is given. The results of nine major joints for a car cab model are given. Two kinds of structural element for weight advantage of aluminum, magnesium and other light materials are given: curved beam in-plane bending, curved beam out-of-plane bending. Bulkhead reinforcement is given for a T-Joint model. The application shows a dramatic reduction of macro lambda for T-Joint x moment and y moment load, which means the weight advantage of light materials is reduced after the reinforcement applied. For the z moment load T-Joint model, adding center layer reinforcement gives the largest reduction of macro lambda and maximum von Mises stress. The bulkhead reinforcement is then used for two car cab joints: B-pillar to rocker joint and hinge pillar to rocker joint. The results indicate that the bulkhead reinforcement near the center area gives the biggest reduction for macro lambda. Micro lambda, which is a value for element level, is introduced. The relationship between micro lambda and force distribution is given. Then it is used for the analysis of the force distribution along curved beam model when the thickness of the model is doubled. The results indicate that the force is redistributed from the corner to center of the flange for the curved beam model. So for curved beam model, light material such as aluminum, magnesium, which is thicker, is more efficiently used than steel. Micro lambda is used for the analysis of B-pillar to rocker joint of a car cab. The result indicates that the maximum micro lambda area is just the area where we apply the optimum bulkhead reinforcement. Micro lambda is also used for the analysis of AISI PNGV bending model. The result shows that the C-pillar area is the major problem area. Several reinforcements for the C-pillar area are given. The result shows that layer 31172 is most important for increasing the stiffness.

This thesis examines the effects of cold forming on the material properties of steel and stainless steel structural members. Extensive research has been carried out over many years on both of these materials as they are used to manufacture structural sections to various design specifications which exist in many different countries. However, to date, no design code exists in the UK for cold formed stainless steel structural members. A significant amount of research has focused on the localised effect of cold forming on material properties such as the yield and ultimate tensile strengths, particularly of steel, and this is discussed at length in Chapter 1- Literature Review. Less attention has been placed on stainless steel, but over the last 20 years with the advent of design specifications particularly in the USA, stainless steel has gained popularity for cold forming. Chapter 1 describes the research that has been carried out on stainless steel, with particular emphasis on localised forming effects. Chapter 2 gives a general introduction to Thin-Walled Structures since cold-formed structural sections are commonly used as thin-walled members. The deformation and properties of metallic materials are described in Chapter 3 showing the particular relevance to the cold forming process. This chapter is extended into Chapter 4 where the strengthening, forming and properties of metallic materials are discussed in detail, with particular attention given to the cold forming processes. Chapter 5 describes existing analytical and design code approaches to determine the increase in strength of cold formed steel structural sections, along with an empirically derived relationship to calculate the increased yield strength of stainless steel sections. Chapter 6 describes the recommendations provided by various design specifications on evaluation of the axial compression capacity of short struts subject to varying degrees of cold forming. This chapter also describes the recommendations provided by various design specifications on evaluation of both the axial compression and the combined bending and axial compression load capacities of cold formed lipped channel section stainless steel columns of short-to-medium length. The results obtained from Chapters 5 and 6 are compared to the results obtained from an extensive experimental approach as described in Chapter 7. A finite element non-linear analysis using the ANSYS finite element software package is presented in Chapter 8 which models the behaviour of cold formed stainless steel lipped channel section columns of short-to-medium length subject to pure axial compression loading and also combined bending and axial compression loading. Chapter 9 presents the experimental findings showing the relationship between material hardness and material yield strength for cold-formed areas. The results are then compared to the theoretical results from Chapter 6 to determine their accuracy in prediction of the structural behaviour of full cold formed structural member cross-sections. The load capacity obtained for axially compressed steel and stainless steel struts from experiments are compared to those obtained from the various design code predictions described in Chapter 6. Also presented are the experimental findings, design code recommendations and finite element predictions for the load capacity of stainless steel columns. Chapter 10 concludes on the work by discussing the various issues arising from the experiments, from the design code recommendations and from finite element analysis 11 M. Macdonald

Lai, Kim Fung = 幼樑之振動與力學特性 / 黎劍鋒. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 99-102). / Abstracts in English and Chinese. / Lai, Kim Fung = You liang zhi zhen dong yu li xue te xing / Li, Jianfeng. / Chapter I --- Vibrations of Timoshenko Beams --- p.1 / Chapter 1 --- Introduction --- p.2 / Chapter 1.1 --- Overview --- p.2 / Chapter 1.2 --- Simple theory of static beam bending --- p.6 / Chapter 1.3 --- Foundation of problem --- p.7 / Chapter 1.4 --- Literature review --- p.12 / Chapter 1.4.1 --- Euler-Bernoulli Beam Theory (EBBT) --- p.12 / Chapter 1.4.2 --- Timoshenko Beam Theory (TBT) --- p.16 / Chapter 1.5 --- Preview of our results --- p.20 / Chapter 2 --- 3-D problem --- p.22 / Chapter 2.1 --- Elastic theory --- p.23 / Chapter 2.2 --- Boundary conditions --- p.24 / Chapter 2.3 --- Plane waves in uniform thin beams --- p.25 / Chapter 2.4 --- Solving order-by-order analytically --- p.26 / Chapter 2.5 --- Minimization approach --- p.36 / Chapter 3 --- 2-D problem --- p.50 / Chapter 3.1 --- Boundary conditions and effective moduli --- p.51 / Chapter 3.2 --- Expansion for thin beams --- p.54 / Chapter 3.3 --- Plane waves in uniform thin beam --- p.56 / Chapter 3.4 --- Boundary conditions --- p.57 / Chapter 3.5 --- Truncation --- p.58 / Chapter 3.6 --- Numerical solution --- p.58 / Chapter 3.7 --- Analytic results for soft mode --- p.60 / Chapter 3.8 --- EBBT and TBT for 2-D problem --- p.62 / Chapter 3.9 --- Analytic results for hard mode at q = 0 --- p.64 / Chapter 3.10 --- Higher-order corrections for hard mode --- p.66 / Chapter 4 --- Summary --- p.71 / Chapter II --- Vibrations of Single-Walled Carbon nanotubes --- p.73 / Chapter 5 --- Introduction --- p.74 / Chapter 5.1 --- General properties --- p.74 / Chapter 5.2 --- Graphene sheet --- p.76 / Chapter 5.3 --- Rolling up a graphene sheet --- p.78 / Chapter 5.4 --- Foundation of problem --- p.79 / Chapter 5.5 --- Literature review --- p.79 / Chapter 5.6 --- Preview of our results --- p.80 / Chapter 6 --- Structure and strain energy under zero stress --- p.81 / Chapter 6.1 --- Description of the structure --- p.81 / Chapter 6.2 --- Description of the strain energy --- p.83 / Chapter 6.3 --- Minimization of energy --- p.86 / Chapter 7 --- SWCNT under strain --- p.89 / Chapter 7.1 --- Subject to an axial strain --- p.89 / Chapter 7.2 --- Subject to a radial strain --- p.94 / Chapter 7.3 --- Subject to a torsional strain --- p.95 / Chapter 8 --- Summary --- p.98 / Bibliography --- p.99 / Chapter A --- "Expressing elastic moduli G, λ and M in terms of Y andv" --- p.103 / Chapter B --- Simplification of the functional E to a neat expression --- p.105 / Chapter C --- Expressing effective elastic moduli G' and M' in terms of Y' and v' --- p.106 / Chapter D --- Illustration of the lowest non-trivial truncation --- p.107 / Chapter E --- The proof of Self-adjointness of H(q) --- p.109 / Chapter F --- Proof of the identity KeVec= KeVel --- p.112

The aim of this thesis is to establish the extent to which materials can be deformed under shear-dominant loadings. Custom Al-6061-T6 tubular specimens are loaded under radial and corner paths of tension and shear to failure. During the experiments, the deformation is monitored in a test section designed to have nearly uniform stress and deformation at large strains while providing minimum constraint to the development of localization that precedes failure. The recorded shear stress-rotation and axial stress-displacement responses exhibit maxima beyond which deformation localizes in a narrow band that is of the order of the 1 mm wall thickness of the test section. For the mainly shear dominated stress paths followed, deformation remained nearly planar allowing for the establishment of both the true stresses and the local deformation strictly from measurements. Results from thirteen radial path experiments as well as from four corner path experiments show the strain at failure to monotonically increase as the mean stress decreases, a result that is in contrast with previously reported results for Al alloys. Also, the measured failure strains are significantly larger than previously reported values. Analysis of corner stress paths investigates the path dependence of localization and failure. Results show little path dependence on the failure strains, but some path dependence on stress maxima and failure stresses. Furthermore, statistical grain-level strain estimates from five of the stress paths revealed a significant variation in strain across the macroscopically observed localization zone. In the neighborhood of the crack tip strains with 25-100% higher levels than the macroscopic values were recorded. This indicates that localization also occurs at a smaller scale than hitherto understood. The difference between the macro strain at failure and the average grain level values increased as the axial/shear stress ratio increased. / text

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Thesis (M.S.)--Mississippi State University. Department of Mechanical Engineering. / Title from title screen. Includes bibliographical references.

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It is reasonable to assume that an aircraft might experience some in-flight discrete source damage caused by various incidents. It is, thus, necessary to evaluate the impact of such damage on the performance of the aircraft. This study is focused on evaluating the effect of a simple discrete damage in an aircraft wing on its static and dynamic response. The damaged wing is modeled by a thin-walled beam with a longitudinal crack the response of which can be obtained analytically. As uncertainties are present in the location and size of the crack as well as in the applied loads, their effects are incorporated into the framework consisting of structural response, crack propagation and aeroelasticity. The first objective of this study is to examine the effect of damage represented by a crack on the wing flexibility that influences its deformation and aero-elastic divergence characteristics. To study this, the thin-walled beam is modeled by Benscoter thin-walled beam theory combined with Gunnlaugsson and Pedersen compatibility conditions to accurately account for the discontinuity at the interface of the cracked and uncracked beam segments. Instead of conducting a detailed finite element analysis, the solution is obtained in an exact sense for general distributed loads representing the wind pressure effects. This analytical approach is shown to provide very accurate values for the global beam response compared with the detailed finite element shell analysis. This analytical solution is, then, used to study the beam response probabilistically. The crack location and size are assumed to be uncertain and are, thus, characterized by random variable. For a specified limit state, the probability of failure can be conveniently calculated by the first order second moment analysis using the safety index approach. The same analytical solution is also used to study the aero-elastic divergence characteristics of a wing, the inner structure of which is represented by a thin-walled beam with a crack of uncertain size and position along the beam. The second objective of this study is to examine the time growth of a crack under dynamic gust type of loading to which a wing is likely to be exposed during flight. Damage propagating during operation further deteriorates the safety of the aircraft and it is necessary to study its time growth so that its impact on the performance can be evaluated before it reaches its unstable state. The proposed framework for the crack growth analysis is based on classical fracture mechanics where the remaining flight time is obtained by Monte Carlo simulation in which various uncertainties are taken into account. To obtain equivalent cyclic loading required for crack growth analysis, random vibration analysis of the thin-walled beam is conducted for stochastic wind load defined by a gust load spectral density function. The probability of failure represented by the crack size approaching the critical crack size within the flight duration or the remaining flight time before a crack reaches its limiting value are obtained. This study with a simple representation of a wing and damage is anticipated to provide initial guidance for future studies to examine the impact of discrete source damage on the in-flight performance of the aircrafts, with the ultimate goal of minimizing the adverse effect and enhancing the safety of aircrafts experiencing damage. / Ph. D.