<p> A general, consistent, nonlinear theory for open thin-walled elastic beams is presented. The theory takes into account geometric nonlinearities caused by large rotation of the cross section of the beam. The nonlinear differential equations of deformation and response are derived by means of application of Hamilton's principle. It is found that the set of equations reduces to the results obtained by Cullimore and Gregory in the special cases of large uniform torsion of thin-walled members. A solution of a thin-walled beam, subjected to large non-uniform torsional deformation due to application of torques at the ends, is obtained. Comparison is made on the torque - rotation characteristics of a thin-walled beam subjected to large uniform torsion and large non-uniform torsion to show the effect of end constraint from warping.</p> <p> A set of nonlinear equations to study the stability of a thin-walled beam of open cross section, under axial loading (spatial stability) and lateral loading (lateral stability), is presented. Using the derived equations, the dynamic stability of thin-walled beams of symmetrical and monosymmetrical cross sections subjected to axial loads, is investigated. The regions of parametric instability, the steady state amplitudes of oscillations, once parametric instability takes place, and the non-steady state solutions, to show the growth of the parametric oscillations, are carried out.</p> <p> The effect of viscous damping on the steady state amplitude and the growth behaviour of the parametrically excited oscillations is shown. The dynamic stability of a thin-walled beam of symmetrical I section and a monosymmetrical split ring section are worked out in detail as examples.</p> / Thesis / Doctor of Philosophy (PhD)

The objective of this study is to elucidate as much as possible the theory and analysis of BOURDON tubes. Both thick-walled and thin-walled tubes are considered. Three papers, representative of the state-of-the-art of BOURDON tube analysis, are reviewed (References 1, 2, and 6): <p> 1. Wuest, W. "Theory of High-Pressure BOURDON Tubes". </p><p> 2. Andreeva, L. E>, "Elastic Elements of Instruments" </p> <p> 3. Dressler, R., "Elastic Shell-Theory Formulation for BOURDON Tubes" </p><p> Reanalysis of (3) above, with a different approach (Appendix A) checked and completed the general formulation by Dressler. The final forms of all necessary equations, boundary conditions, etc. to the solution of the three governing equations of the BOURDON tube with an elliptical cross-section are given. </p><p> Comparison of results of Andreeva's sensitivity equation with test data of Kardos, Mason and Exline (References 3, 4 and 5) using a qualitative approach as set out by Kardos (References 3 and 17) showed good correlation. </p><p> The study concludes with recommendations for the approach of future research and preliminary design procedures for BOURDON tubes. </p> / Thesis / Master of Engineering (ME)

A dual approach integrating structural tailoring and adaptive materials technology and designed to control the dynamic response of cantilever beams subjected to external excitations is addressed. The cantilevered structure is modeled as a thin-walled beam of arbitrary cross-section and incorporates a number of non-classical effects such as transverse shear, warping restraint, anisotropy of constituent materials and heterogeneity of the construction. Whereas structural tailoring uses the anisotropy properties of advanced composite materials, adaptive materials technology exploits the actuating/sensing capabilities of piezoelectric materials bonded or embedded into the host structure. Various control laws relating the piezoelectrically-induced bending moment with combined kinematical variables characterizing the response at given points of the structure are implemented and their effects on the closed-loop frequencies and dynamic response to external excitations are investigated. The combination of structural tailoring and control by means of adaptive materials proves very effective in damping out vibration. In addition, the influence of a number of non-classical effects characterizing the structural model on the open and closed-loop dynamic responses have been considered and their roles assessed. / Ph. D.

Based on a refined analytical anisotropic thin-walled beam model, aeroelastic instability, dynamic aeroelastic response, active/passive aeroelastic control of advanced aircraft wings modeled as thin-walled beams are systematically addressed. The refined thin-walled beam model is based on an existing framework of the thin-walled beam model and a couple of non-classical effects that are usually also important are incorporated and the model herein developed is validated against the available experimental, Finite Element Anaylsis (FEA), Dynamic Finite Element (DFE), and other analytical predictions. The concept of indicial functions is used to develop unsteady aerodynamic model, which broadly encompasses the cases of incompressible, compressible subsonic, compressible supersonic and hypersonic flows. State-space conversion of the indicial function based unsteady aerodynamic model is also developed. Based on the piezoelectric material technology, a worst case control strategy based on the minimax theory towards the control of aeroelastic systems is further developed. Shunt damping within the aeroelastic tailoring environment is also investigated. The major part of this dissertation is organized in the form of self-contained chapters, each of which corresponds to a paper that has been or will be submitted to a journal for publication. In order to fullfil the requirement of having a continuous presentation of the topics, each chapter starts with the purely structural models and is gradually integrated with the involved interactive field disciplines. / Ph. D.

This dissertation is concerned with a type of energy absorption device made of thin-walled tubes. The tubes will undergo plastic deformation when subjected to an impact loading, and therefore absorb kinetic energy. It has been found that, if the surface of a tube is pre-folded according to an origami pattern, the failure mode of the tube can be altered, leading to a noticeable increase in energy absorption while at the same time, reducing the force needed to initiate plastic deformation within the tube. The main work is presented in four parts. First of all, an experimental study of a type of previously reported thin-walled square tube with pre-manufactured pyramid patterns on the surface has been conducted. Quasi-static axial crushing tests show that the octagonal mode, although numerically proven to be efficient in terms of energy absorption, cannot be consistently triggered. Secondly, a new type of thin-walled tubular energy absorption device, known as the origami tube, which has origami pattern pre-fabricated on the surface, has been studied. A family of origami patterns has been designed for tubes with different profiles. The performances of a series of origami tubes with various configurations subjected to quasi-static axial crushing have been investigated numerically. It is found that a new failure mode, referred to as the complete diamond mode, can be triggered, and both over 50% increase in the mean crushing force and about 30% reduction in the peak force can be achieved in a single tube design in comparison with those of a conventional square tube with identical surface area and wall thickness. A theoretical study of the axial crushing of square origami tubes has been conducted and a mathematical formula has been derived to calculate the mean crushing force. Comparison between theoretical prediction and numerical results shows a good agreement. Quasi-static axial crushing experiments on several square origami tube samples have been carried out. The results show that the complete diamond mode is formed in the samples and both peak force reduction and mean crushing force increase are attained. Thirdly, a new type of curved thin-walled beam with pre-manufactured origami pattern on the surface, known as the origami beam, has been designed and analyzed. A numerical study of a series of origami beams with a variety of configurations subjected to quasi-static lateral bending has been conducted. The results show that two new failure modes, namely, the longitudinal folding mode and the mixed mode, can be induced, and both reduced peak force and increased energy absorption are achieved. Finally, a number of automobile frontal bumpers, which have the origami tube and the origami beam as key components, have been designed and analyzed. Three impact tests have been conducted on each bumper. The numerical results show that both types of origami structures can perform well in realistic loading scenarios, leading to improved energy absorption of the bumpers.

Quick and accurate predictions of equivalent properties for thin-walled composite structures are required in the preliminary design process. Existing literature provides analytical solutions to some structures but is limited to particular cases. No unified approach exists to tackle homogenization of thin-walled structures such as beams, plates, or three-dimensional structures using the thin-walled approximation. In this work, a unified approach is proposed to obtain equivalent properties for beams, plates, and three-dimensional structures for thin-walled composite structures using mechanics of structure genome. The adopted homogenization technique interprets the unit cell associated with the composite structures as an assembly of plates, and the overall strain energy density of the unit cell as a summation of the plate strain energies of these individual plates. The variational asymptotic method is then applied to drop all higher-order terms and the remaining energy is minimized with respect to the unknown fluctuating functions. This has been done by discretizing the two-dimensional unit cell into one-dimensional frame elements in a finite element description. This allows the handling of structures with different levels of complexities and internal geometry within a general framework. Comparisons have been made with other works to show the advantages which the proposed model offers over other methods.

The considerable progress in the research and development of thin-walled beam structures responds to their growing use in engineering construction and to their increased need for efficiency in strength and cost. The result is a structure that exhibits large shear strains and important non uniform warping under different loadings, such as non uniform torsion, shear bending and distortion... A unified approach is formulated in this thesis for 3D thin walled beam structures with arbitrary profile geometries, loading cases and boundary conditions. A single warping function, defined by a linear combination of longitudinal displacements at cross sectional nodes (derived from Prokic work), is enhanced and adapted in order to qualitatively and quantitatively reflect and capture the nature of a widest possible range of behaviors. Constraints are prescribed at the kinematics level in order to enable the study of arbitrary cross sections for general loading. This approach, differing from most published theories, has the advantage of enabling the study of arbitrary cross sections (closed/opened or mixed) without any restrictions or distinctions related to the geometry of the profile. It generates automatic data and characteristic computations from a kinematical discretization prescribed by the profile geometry. The amount of shear bending, torsional and distortional warping and the magnitude of the shear correction factor is computed for arbitrary profile geometries with this single formulation. The proposed formulation is compared to existing theories with respect to the main assumptions and restrictions. The variation of the location of the torsional center, distortional centers and distortional rotational ratio of a profile is discussed in terms of their dependency on the loading cases and on the boundary conditions. A 3D beam finite element model is developed and validated with several numerical applications. The displacements, rotations, amount of warping, normal and shear stresses are compared with reference solutions for general loading cases involving stretching, bending, torsion and/or distortion. Some examples concern the case of beam assemblies with different shaped profiles where the connection type determines the nature of the warping transmission. Other analyses –for which the straightness assumption of Timoshenko theory is relaxed– investigate shear deformation effects on the deflection of short and thin beams by varying the aspect ratio of the beam. Further applications identify the cross sectional distortion and highlight the importance of the distortion on the stresses when compared to bending and torsion even in simple loading cases. Finally, a non linear finite element based on the updated lagrangian formulation is developed by including torsional warping degrees of freedom. An incremental iterative method using the arc length and the Newton-Raphson methods is used to solve the non linear problem. Examples are given to study the flexural, torsional, flexural torsional and lateral torsional buckling problems for which a coupling between the variables describing the flexural and the torsional degrees of freedom occurs. The finite element results are compared to analytical solutions based on different warping functions and commonly used in linear stability for elastic structures having insufficient lateral or torsional stiffnesses that cause an out of plane buckling.

Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / Thin-walled structures are major components in many engineering applications. When a thin-walled slender beam is subjected to lateral loads, causing moments, the beam may buckle by a combined lateral bending and twisting of cross-section, which is called lateral-torsional buckling. A generalized analytical approach for lateral-torsional buckling of anisotropic laminated, thin-walled, rectangular cross-section composite beams under various loading conditions (namely, pure bending and concentrated load) and boundary conditions (namely, simply supported and cantilever) was developed using the classical laminated plate theory (CLPT), with all considered assumptions, as a basis for the constitutive equations. Buckling of such type of members has not been addressed in the literature. Closed form buckling expressions were derived in terms of the lateral, torsional and coupling stiffness coefficients of the overall composite. These coefficients were obtained through dimensional reduction by static condensation of the 6x6 constitutive matrix mapped into an effective 2x2 coupled weak axis bending-twisting relationship. The stability of the beam under different geometric and material parameters, like length/height ratio, ply thickness, and ply orientation, was investigated. The analytical formulas were verified against finite element buckling solutions using ABAQUS for different lamination orientations showing excellent accuracy.

<div>Thin walled structures find wide applications in automotive industry as energy absorption devices. A great deal of research has been conducted to design thin walled structures, where the main objective is to reduce peak crushing forces and increase energy absorption capacity. With the advancement of computers and mathematics, it has been possible to develop 2D patterns which when folded turn into complex 3D structures. This technology can be used to develop patterns for getting structures with desired properties. </div><div>In this study, square origami tubes with folding pattern (Yoshimura pattern) is designed and studied extensively using numerical analysis. An accurate Finite Element Model (FEM) is developed to conduct the numerical analysis. A parametric study was conducted to study the influence of geometric parameters on the mechanical properties like peak crushing force, mean crushing force, load uniformity and maximum intrusion, when subjected to dynamic loading. </div><div>The results from this analysis are studied and various conclusions are drawn. It is found that, when the tube is folded with the pattern having specific dimension, the performance is enhanced significantly, with predictable and stable collapse. It is also found that the stiffness of the module varies with geometrical parameters. With a proper study it is possible to develop origami structures with functionally graded stiffness, the performance of which can be tuned as per requirement, hence, showing promising capabilities as an energy absorption device where progressive collapse from near to end impact end is desired.</div><div><br></div>

Neste trabalho investiga-se o comportamento resistente de vigas de concreto com taxas reduzidas de armadura transversal, analisando-se as possibilidades de melhoria de desempenho pelo reforço do concreto com fibras curtas de aço e polipropileno e pela aplicação da protensão, através de ensaios em vigas de seção quadrada e vigas protendidas de seção duplo-T. Apresenta-se também uma revisão de conhecimentos sobre o comportamento estrutural de elementos de concreto armado ou protendido, com ênfase nas solicitações por força cortante e os principais conceitos sobre os compósitos constituídos de matriz de cimento reforçada com fibras. As principais alterações decorrentes da introdução das fibras foram o aumento da resistência ao cisalhamento, da rigidez após a fissuração e da dutilidade. A protensão aumenta a resistência ao cisalhamento, a resistência à fissuração e a extensão da zona não fissurada, e torna as bielas mais abatidas. Tanto as fibras quanto a protensão proporcionam alívio da tensão nos estribos. / This thesis presents an experimental analysis of the structural behavior of concrete beams with reduced shear reinforcement ratios. Improvements on performance due to prestressing and steel and polypropilene fibers are analized in rectangular and T beam models. A state-of-the-art is presented on shear strength of reinforced and prestressed concrete beams and on fiber reinforced cement-based composites. The main effects due to fiber addition are the increasing of the shear strength, post-cracking stiffiness and ductility. Prestressing helps to increase the shear strength, cracking strength and extension of the non-cracked zone and it turns the struts less inclined. Fibers as well prestressing reduce the stresses on stirrups.