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.

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.

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.

In this thesis, hybrid stress finite element is formulated for the analysis of the isotropic, thin walled, open section beams with variable cross sections. The beam element has two nodes each having seven degrees of freedom. Assumption of stress field is sufficient to determine the element stiffness matrix. Axial, flexural and torsional effects are taken into account in the analysis. The methodology can be applied both to the tapered and the uniform beams. Throughout this study, firstly element cross-sectional properties are computed using the flow analogy of the inter-connected elements which may have different thicknesses. Then another computer program calculates the displacements and stresses at the nodes along the beam. The results obtained are compared to the results taken from literature and commercial FEM program Nastran.

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.

<p>U ovoj disertaciji, izvršena su teorijska i eksperimentalna istraživanja dinamičkog onašanja jezgra visokih zgrada. Model je zasnovan na Vlasovoj teoriji tankozidnih nosača, kao i na metodi prenosnih matrica. Jezgro se tretira kao tankozidni nosač otvorenog poprečnog preseka, koji je na dnu uklješten u temeljnu ploču, dok je na vrhu&nbsp; slobodan.&nbsp; Duž&nbsp; ose&nbsp; smicanja,&nbsp; jezgro&nbsp; je&nbsp; podeljeno&nbsp; na&nbsp; čvorove&nbsp; u&nbsp; nivoima spratova&nbsp; u&nbsp; kojima&nbsp; su&nbsp; redukovane&nbsp; mase.&nbsp; Poseban&nbsp; naglasak&nbsp; je&nbsp; stavljen&nbsp; na&nbsp; analizu uticaja poprečnih greda, međuspratnih ploča, kao i načinu oslanjanja međuspratnih ploča po spoljašnjoj konturi na dinamičke karakteristike jezgra. Razvijeni&nbsp; numerički&nbsp; postupak&nbsp; je&nbsp; primenjen&nbsp; na&nbsp; armiranobetonskom&nbsp; jezgru petnaestospratne zgrade, koja je analizirana ranijeu radovima mnogih autora. U tu svrhu korišćen je računarski program TWBEIG, napisan primenom Visual Fortran programskog jezika. Analize su urađene i MKE, a dobijeni rezultati su upoređeni. Vrednosti sopstvenih frekvencija pokazuju dobro slaganje.<br />Ovaj rad daje detalje i o eksperimentalnoj studiji&nbsp; u kojoj se primenjuje pleksiglas model u cilju pružanja eksperimentalnih podataka zaproveru tačnosti i pouzdanosti numeričkih&nbsp; rezultata.&nbsp; Dobijeni&nbsp; rezultati&nbsp; su&nbsp; takođe&nbsp; upoređeni&nbsp; sa&nbsp; rezultatima dobijenim TWBEIG računarskim programom, kao i MKE.<br />Predstavljeni&nbsp; numerički&nbsp; metod&nbsp; nudi&nbsp; solidnu&nbsp; osnovu&nbsp; za&nbsp; formiranje&nbsp; jednostavnog modela&nbsp; proračuna,&nbsp; a&nbsp; ipak&nbsp; obezbeđuje&nbsp; odgovarajući&nbsp; nivo&nbsp; preciznosti.&nbsp; Predloženi postupak&nbsp; može&nbsp; biti&nbsp; korišćen&nbsp; i&nbsp; u&nbsp; fazi&nbsp; prethodne&nbsp; analize&nbsp; zgrade,&nbsp; kao&nbsp; i&nbsp; u&nbsp; fazi konačnog projektovanja.</p> / <p>In this dissertation, a theoretical and experimental study of the dynamic behaviour<br />of&nbsp; the&nbsp; tall&nbsp; buildings&nbsp; core&nbsp; was&nbsp; carried&nbsp; out.&nbsp; The&nbsp; model&nbsp; is&nbsp; based&nbsp; on&nbsp; the&nbsp; Vlasov&#39;s<br />theory of thin-walled beams and the transfer matrixmethod. The core is treated as<br />a thin&nbsp; wall-walled, open cross section cantilever beam. Along the shear axis the<br />core&nbsp; is&nbsp; divided&nbsp; into&nbsp; nodes,&nbsp; in&nbsp; the&nbsp; level&nbsp; of&nbsp; the&nbsp; floors,&nbsp; in&nbsp; which&nbsp; the&nbsp; masses&nbsp; are<br />reduced.&nbsp; Special&nbsp; emphasis&nbsp; was&nbsp; given&nbsp; to&nbsp; the&nbsp; analysis of&nbsp; the&nbsp; influence,&nbsp; of&nbsp; lintel<br />beams,&nbsp; floor&nbsp; slabs,&nbsp; as&nbsp; well&nbsp; as&nbsp; the&nbsp; type&nbsp; of&nbsp; restraints&nbsp; along&nbsp; the&nbsp; outer&nbsp; edge&nbsp; of&nbsp; the<br />floor slabs, on the dynamic characteristics of the core.<br />The&nbsp; developed&nbsp; numerical&nbsp; procedure&nbsp; was&nbsp; applied&nbsp; to&nbsp; the&nbsp; fifteen-storey&nbsp; reinforced<br />concrete core tall building, analyzed previously inthe papers of many authors. For<br />this&nbsp; purpose,&nbsp; the&nbsp; computer&nbsp; program&nbsp; TWBEIG&nbsp; was&nbsp; used, written&nbsp; using&nbsp; Visual<br />Fortran programming language. The analyses were also performed with FEM and<br />subsequently the results were compared. The values&nbsp; of natural frequencies show<br />significant agreement. This&nbsp; paper&nbsp; presents&nbsp; details&nbsp; about&nbsp; the&nbsp; experimental&nbsp; study&nbsp; which&nbsp; applies&nbsp; the plexiglas model in order to provide experimental data to verify the accuracy and reliability of the numerical results. The results are also compared with the results obtained with the TWBEIG computer program, as well&nbsp; as with FEM. The values of frequencies show reasonable agreement.<br />The proposed numerical&nbsp; method offers a solid base&nbsp; for the creation of a&nbsp; simple<br />calculation model, yet provides the appropriate level of precision. It can be either<br />used for preliminary analysis or for the final design.</p>

The aging infrastructure worldwide and the typical increase in service loads relative to original design loads make it essential to develop effective techniques for strengthening and rehabilitating existing structures, to enhance their resistance. An effective method for strengthening existing steel I-beams is to weld either one or two cover plates to the flange(s). In many cases, it is not feasible to completely unload the beam before carrying out the strengthening procedure. In these conditions, operators resort to strengthen beams while under loading. In such scenarios, it becomes a challenging task to assess the lateral torsional buckling (LTB) capacity of the member under present steel design standards (e.g., CAN/CSA-S16 2019 and ANSI/AISC360 2022) which do not consider the effect of pre-strengthening loads on LTB resistance. Within this context, the present study investigates the effects of pre-strengthening loads on the critical moment capacity by developing a series of solutions, ranging from elaborate and accurate to simplified but approximate, to predict the elastic LTB capacity of beams strengthened with cover plate(s) while under load. In this respect, the study contributes to the existing body of knowledge through four aspects: In the first contribution, a shell-based finite element (FE) study is developed to analyze the effect of various geometric and loading parameters on the LTB capacity of doubly symmetric beams strengthened symmetrically with two cover plates. The study carefully simulates the entire history, including the application of pre-existing loads, clamping forces to align the initially straight steel cover plates with the bent beam configuration, the rebound effect arising after clamping force removal, the contact at the interfaces between cover plates and flanges induced by welding, and the application of post-strengthening loads up to the point of elastic LTB initiation for the strengthened system, as determined by eigenvalue analysis. A simplified design equation is then proposed to quantify the post-strengthening critical moment capacity. The validity of the equation is assessed against FE results and its merits and limitations are discussed. The study shows that web distortional effects play a crucial role in reducing the elastic critical moment capacity. Practical recommendations are provided to mitigate such distortional effects and hence maximize the elastic critical moment capacity of the strengthened beams. The second contribution formulates a variational principle for the LTB analysis of doubly symmetric beams strengthened symmetrically with identical steel cover plates. The formulation considers the full sequence of loading and strengthening and captures the effects of pre-strengthening loads and the beneficial effects of pre-buckling deformation (PBD). The study examines the effect of geometry, partial strengthening schemes, presence of different pre- and post-strengthening load patterns, and load height effects. The variational principle is subsequently used to develop a FE formulation, culminating in a quadratic eigenvalue problem. The validity of the FE formulation is assessed through comparisons with other numerical techniques predictions as well as experimental results by others, and subsequently used to conduct a parametric study to characterize the gain in elastic critical moment capacity attained by cover plate strengthening. For beams partly strengthened with cover plates along their spans, the study identifies the optimum locations for cover plates that maximize the critical moments. The third contribution builds upon the variational principle developed by formulating a simple and approximate energy-based design-oriented solution to quantify the LTB resistance of simply supported I-beams strengthened with cover plates. The solution captures the detrimental effect of loads acting on the beam before strengthening and the beneficial effects resulting from PBD, pre- and post-strengthening load heights, as well as moment gradient effects. The potential use of the equations developed in practical applications involving beam strengthening is illustrated through design examples. The fourth contribution expands the variational formulation to include beams with monosymmetric cross-sections and/or symmetric beams with unsymmetric cover plate geometries. The modified variational principle is used to develop a thin-walled beam FE formulation, which is subsequently employed to predict the non-distortional LTB capacity of monosymmetric strengthened beams. Comparative analyses with shell models confirm the validity of the proposed solutions, and practical design recommendations for suppressing web distortion are provided. The effects of various design parameters on the total elastic critical moment capacity are evaluated in a systematic parametric study. The study identifies the loading conditions under which the magnitude of pre-strengthening loads significantly influences the predicted total critical moments. The solutions developed in the present study equip structural designers and analysts with novel techniques that reliably quantify the LTB strength of steel beams strengthened with cover plates, thus enabling them to optimize strengthening strategies for beams whose strengths are governed by LTB modes of failure.

Dans le cadre linéaire, les modèles de Mindlin-Reissner pour les plaques épaisses et de Naghdi pour les coques épaisses sont les plus utilisés. Il est connu que la discrétisation par éléments finis de ces modèles conduit à un phénomène de verrouillage numérique quand l’épaisseur tend vers zéro. Il s’agit du verrouillage en cisaillement dans le cas des plaques et du verrouillage en cisaillement et en membrane dans le cas des coques. Il existe quelques éléments finis qui permettent d’éviter ces difficultés ou du moins de les réduire. L’élément DKMQ pour les plaques et sa version DKMQ24 pour les coques, sont des éléments de bas ordre, basés sur une formulation mixte, qui ont été proposés il y a quelques années afin d’éviter ces phénomènes de verrouillage. Dans cette thèse, on s’est attaché à évaluer numériquement les performances de ces éléments. Outre les cas tests classiques, on s’est focalisé sur l’analyse de la condition inf-sup discrète pour l’élément DKMQ. Nous avons étudié également le test de la s-norme proposé par Bathe, pour l’élément DKMQ24. Enfin, nous avons effectué une analyse d’erreur a posteriori pour les éléments DKMQ et DKMQ24, en utilisant l’estimateur d’erreur Z2 (dû à Zienkiewicz et Zhu), associé aux techniques de recouvrement de la moyenne, de projection ou encore SPR. Les résultats obtenus ont permis de quantifier les performances de ces deux éléments finis pour les problèmes de verrouillage, et d’en dégager les limites. Deux applications importantes de ces éléments DKMQ et DKMQ24 ont été ensuite présentées, la première concerne la simulation des poutres à parois minces à section ouverte et la seconde le calcul des plaques composites. / In the linear case, the Mindlin-Reissner model for thick plates and the Naghdi model for thick shells are commonly used. The finite element discretization of these models leads to numerical locking phenomenon when the thickness approaches zero : shear locking for plates and both shear and membrane locking for shells. There are some finite elements that could reduce or even eliminate this phenomenon. DKMQ element for plates or DKMQ24 element for shells, are low-order elements, based on a mixed formulation, introduced a few years ago to prevent the numerical locking phenomenon. In this thesis, we concentrated on numerical evaluation of the performance of these elements. Besides the classical benchmark tests, we also focused on the analysis of discrete inf-sup condition for DKMQ element. We studied the s-norm test proposed by Bathe for DKMQ24 element. Finally, we performed a posteriori error estimation for DKMQ and DKMQ24 elements, using the error estimator Z2 (proposed by Zienkiewicz and Zhu), associated with the averaging, projection or SPR recovery methods. The results obtained have enabled us to quantify the performance of these two finite elements for locking problems, and to identify their limits. Two important applications of these elements DKMQ and DKMQ24 were then presented ; the first one concerns thin-walled beams with open cross-section and the second one composite plates.