Shear-acting structural fuses are steel plates with cutouts subjected to in-plane lateral displacements during extreme loading events such as earthquakes, that dissipate energy through localized shear or flexural yielding mechanisms. Although previous studies have reported that fuses with specific geometry can develop a stable hysteretic behavior, their small thickness makes them prone to buckling, reducing strength and energy dissipation capacity. In this work, topology optimization using genetic algorithms is performed to find optimized shapes for structural fuses with a square domain and constant thickness. The objective function uses the fuse's shear buckling load VB obtained from a 3D linear buckling analysis, and shear yield load VY obtained from a material nonlinear, but geometrically linear 2D plane-stress analysis. The two analyses are shown to be computationally efficient and viable for use in the optimization routine. The variations VY/VB=0.1,0.2,0.3 are investigated considering a target volume equal to 30%, 40% and 50% the fuse's original volume. A new set of optimized topologies are obtained, interpreted into smooth shapes, and evaluated using finite elements analyses with models subjected to monotonic and cyclic displacements histories. It was found that the drift angle when out-of-plane buckling occurs can be controlled using the VY/VB ratio, with optimized topologies buckling at drift angles (when subjected to a cyclic displacement protocol) as large as 9% as compared to 6% for previously studied fuses. / Master of Science / Shear-acting structural fuses are steel plates with cutouts that dissipate energy during extreme loading events such as earthquakes. These structural fuses have a fixed edge and an opposing edge subjected to in-plane lateral displacements. Although previous studies have reported that fuses with specific geometry have a good cyclic performance, their small thickness makes them prone to bend or buckle, reducing strength and energy dissipation capacity. Considering a structural fuse with a square domain and constant thickness, a mathematical method called topology optimization is implemented to optimize the distribution of material with the goal of controlling the amount of yielding in the structural fuse before it buckles. The optimization routine uses the fuse’s shear buckling capacity (VB) and shear yield strength (VY ) obtained from relative simple and computationally inexpensive procedures that are also valid to characterize the potential for buckling in a structural fuse. The variations VY /VB = 0.1, 0.2, 0.3 are investigated considering a target volume equal to 30%, 40% and 50% the fuse’s original volume. A set of optimized topologies are interpreted into smooth shapes and evaluated using finite elements analyses. It was found that the drift angle when out-of-plane buckling occurs can be controlled by using the VY /VB ratio, with optimized topologies buckling at drift angles (when subjected to a cyclic displacement protocol) as large as 9% as compared to 6% for previously studied fuses.

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Das Thema dieser Dissertation ist die Anwendung von Variationsmethoden auf Evolutionsgleichungen parabolischen und hyperbolischen Typs. Im ersten Teil der Arbeit beschäftigen wir uns mit Reaktions-Diffusions-Systemen, die sich als Gradientensysteme schreiben lassen. Hierbei verstehen wir unter einem Gradientensystem ein Tripel bestehend aus einem Zustandsraum, einem Entropiefunktional und einer Dissipationsmetrik. Wir geben Bedingungen an, die die geodätische Konvexität des Entropiefunktionals sichern. Geodätische Konvexität ist eine wertvolle aber auch starke strukturelle Eigenschaft und schwer zu zeigen. Wir zeigen anhand zahlreicher Beispiele, darunter ein Drift-Diffusions-System, dass dennoch interessante Systeme existieren, die diese Eigenschaft besitzen. Einen weiteren Punkt dieser Arbeit stellt die Anwendung von Gamma-Konvergenz auf Gradientensysteme dar. Wir betrachten hierbei zwei Modellsysteme aus dem Bereich der Mehrskalenprobleme: Erstens, die rigorose Herleitung einer Allen-Cahn-Gleichung mit dynamischen Randbedingungen und zweitens, einer Interface-Bedingung für eine eindimensionale Diffusionsgleichung jeweils aus einem reinen Bulk-System. Im zweiten Teil der Arbeit beschäftigen wir uns mit dem sog. Weighted-Inertia-Dissipation-Energy-Prinzip für Evolutionsgleichungen. Hierbei werden Trajektorien eines Systems als (Grenzwerte von) Minimierer(n) einer parametrisierten Familie von Funktionalen charakterisiert. Dies erlaubt es, Werkzeuge aus der Theorie der Variationsrechung auf Evolutionsprobleme anzuwenden. Wir zeigen, dass Minimierer der WIDE-Funktionale gegen Lösungen des Ausgangsproblems konvergieren. Hierbei betrachten wir getrennt voneinander den Fall des beschränkten und des unbeschränkten Zeitintervalls, die jeweils mit verschiedenen Methoden behandelt werden. / This thesis deals with the application of variational methods to evolution problems governed by partial differential equations. The first part of this work is devoted to systems of reaction-diffusion equations that can be formulated as gradient systems with respect to an entropy functional and a dissipation metric. We provide methods for establishing geodesic convexity of the entropy functional by purely differential methods. Geodesic convexity is beneficial, however, it is a strong structural property of a gradient system that is rather difficult to achieve. Several examples, including a drift-diffusion system, provide a survey on the applicability of the theory. Next, we demonstrate the application of Gamma-convergence, to derive effective limit models for multiscale problems. The crucial point in this investigation is that we rely only on the gradient structure of the systems. We consider two model problems: The rigorous derivation of an Allen-Cahn system with bulk/surface coupling and of an interface condition for a one-dimensional diffusion equation. The second part of this thesis is devoted to the so-called Weighted-Inertia-Dissipation-Energy principle. The WIDE principle is a global-in-time variational principle for evolution equations either of conservative or dissipative type. It relies on the minimization of a specific parameter-dependent family of functionals (WIDE functionals) with minimizers characterizing entire trajectories of the system. We prove that minimizers of the WIDE functional converge, up to subsequences, to weak solutions of the limiting PDE when the parameter tends to zero. The interest for this perspective is that of moving the successful machinery of the Calculus of Variations.

This dissertation investigates dissipation in microelectromechanical (MEMS) resonators via detailed analysis and modeling of the energy loss mechanisms and provides a framework toward creating resonant devices with ultra-low dissipation. Fundamental mechanisms underlying acoustic energy loss are explored, the results of which are applied to understanding the losses in resonant MEMS devices. Losses in the materials, which set the ultimate limits of the achievable quality factor of the devices, are examined. Other sources of loss, which are determined by the design of the resonator, are investigated and applied to example resonant MEMS structures. The most critical of these designable loss mechanisms are thermoelastic dissipation (TED) and support (or anchor) loss of acoustic energy through the attachment of the MEMS device to its external environment. The dissipation estimation framework enables prediction of the quality factor of a MEMS resonator, which were accurate within a factor of close to 2 for high-frequency bulk acoustic wave MEMS resonators, and represents a signficant step forward by closing one of the largest outstanding problems in MEMS devices: how to predict the quality factor for a given device. Dissipation mitigation approaches developed herein address the most critical dominant loss mechanisms identified using the framework outlined above. These approaches include design of 1D phononic crystals (PCs) and novel 3D MEMS structures to trap and isolate vibration energy away from the resonator anchors, optimization of resonator geometry to suppress thermoelastic dissipation, and analysis of required levels of surface polish to reduce surface dissipation. Phononic crystals can be used to manipulate the properties of materials. In the case of the 1D PC linear acoustic bandgap (LAB) structures developed here, this manipulation arises from the formation of frequency stop bands, or bandgapwhich convert silicon from a material capable of supporting acoustic waves to a material which rejects acoustic propagation at frequencies in the bandgap. The careful design of these LAB structures is demonstrated to be able to enhance the quality factor and insertion loss of MEMS resonators without significant detrimental effects on the overall device performance.

Animal cells are often cultured in stirred tank reactors. Having no cell wall, these animal cells are very sensitive to the fluid mechanical stresses that result from agitation by the impeller and from the rising and bursting of bubbles, which are generated within the culture medium in the stirred tank to supply oxygen by mass transfer to the cells. If excessive, these fluid mechanical stresses can result in damage/death of animal cells. Stress due to the rising and bursting of bubbles can be avoided by using a gas-permeable membrane, in the form of a long coiled tube (with air passing through it) within the stirred tank, instead of air-bubbles to oxygenate the culture medium. Fluid mechanical stress due to impeller agitation can be controlled using appropriate impeller rotational speeds. The aim of this study was to lay the foundations for future work in which a correlation would be developed between cell damage/death and the fluid mechanical stresses that result from impeller agitation and bubbling. Such a correlation could be used to design stirred-tank reactors at any scale and to determine appropriate operating conditions that minimise cell damage/death due to fluid mechanical stresses. Firstly, a validated CFD model of a baffled tank stirred with a Rushton turbine was developed to allow fluid mechanical stresses due to impeller agitation to be estimated. In these simulations, special attention was paid to the turbulence energy dissipation rate, which has been closely linked to cell damage/death in the literature. Different turbulence models, including the k-ε, SST, SSG-RSM and the SAS-SST models, were investigated. All the turbulence models tested predicted the mean axial and tangential velocities reasonably well, but under-predicted the decay of mean radial velocity away from the impeller. The k-ε model predicted poorly the generation and dissipation of turbulence in the vicinity of the impeller. This contrasts with the SST model, which properly predicted the appearance of maxima in the turbulence kinetic energy and turbulence energy dissipation rate just off the impeller blades. Curvature correction improved the SST model by allowing a more accurate prediction of the magnitude and location of these maxima. However, neither the k-ε nor the SST models were able to properly capture the chaotic and three-dimensional nature of the trailing vortices that form downstream of the blades of the impeller. In this sense, the SAS-SST model produced more physical predictions. However,this model has some drawbacks for modelling stirred tanks, such as the large number of modelled revolutions required to obtain good statistical averaging for calculating turbulence quantities. Taking into consideration both accuracy and solution time, the SSG-RSM model was the least satisfactory model tested for predicting turbulent flow in a baffled stirred tank with a Rushton turbine. In the second part of the work, experiments to determine suitable oxygen transfer rates for culturing cells were carried out in a stirred tank oxygenated using either a sparger to bubble air through the culture medium or a gas-permeable membrane. Results showed that the oxygen transfer rates for both methods of oxygenation were always above the minimum oxygen requirements for culturing animal cells commonly produced in industry, although the oxygen transfer rate for air-bubbling was at-least 10 times higher compared with using a gas-permeable membrane. These results pave the way for future experiments, in which animal cells would be cultured in the stirred tank using bubbling and (separately) a gas-permeable membrane for oxygenation so that the effect of rising and bursting bubbles on cell damage/death rates can be quantified. The effect of impeller agitation on cell damage/death would be quantified by using the gas permeable membrane for oxygenation (to remove the detrimental effects of bubbling), and changing the impeller speed to observe the effect of agitation intensity. In the third and final part of this work, the turbulent flow in the stirred tank used in the oxygenation experiments was simulated using CFD. The SST turbulence model with curvature correction was used in these simulations, since it was found to be the most accurate model for predicting turbulence energy dissipation rate in a stirred tank. The predicted local maximum turbulence energy dissipation rate of 8.9x10¹ m2/s3 at a rotational speed of 900 rpm was found to be substantially less than the value of 1.98x10⁵ m2/s3 quoted in the literature as a critical value above which cell damage/death becomes significant. However, the critical value for the turbulence energy dissipation rate quoted in the literature was determined in a single-pass flow device, whereas animal cells in a stirred tank experience frequent exposure to high turbulence energy dissipation rates (in the vicinity of the impeller) due to circulation within the stirred tank and long culture times. Future cell-culturing experiments carried out in the stirred tank of this work would aim to determine a more appropriate critical value for the turbulence energy dissipation rate in a stirred tank, above which cell damage/death becomes a problem.

Approved for public release, distribution is unlimited / Ensign, United States Navy

Fundamental aspects of turbulence and turbulent mixing are investigated using direct numerical simulations (DNS) of stationary isotropic turbulence, with Taylor-scale Reynolds numbers ranging from 8 to 650 and Schmidt numbers from 1/8 to 1024. The primary emphasis is on important scaling issues that arise in the study of intermittency, mixing and turbulence under solid-body rotation. Simulations up to 2048^3 in size have been performed using large resource allocations on Terascale computers at leading supercomputing centers. Substantial efforts in algorithmic development have also been undertaken and resulted in a new code based on a two-dimensional domain decomposition which allows the use of very large number of processors.Benchmark tests indicate very good parallel performance for resolutions up to 4096^3 on up to 32768 processors. Investigation of intermittency through the statistics of dissipation and enstrophy in a series of simulations at the same Reynolds number but different resolution indicate that accurate results in high-order moments require a higher degree of fine-scale resolution than commonly practiced. At the highest Reynolds number in our simulations (400 and 650) dissipation and enstrophy exhibit extreme fluctuations of O(1000) the mean which have not been studied in the literature before and suggest a universal scaling of small scales. Simulations at Reynolds number of 650 on 2048^3 grids with scalars at Sc=1/8 and 1 have allowed us to obtain the clearest evidence of attainment of inertial-convective scaling in the scalar spectrum in numerical simulations to date whereas results at high Sc support k^{-1} viscous-convective scaling. Intermittency for scalars as measured by the tail of the PDF of scalar dissipation and moments of scalar gradient fluctuations is found to saturate at high Sc. Persistent departures from isotropy are observed as the Reynolds number increases. However, results suggest a return to isotropy at high Schmidt numbers, a tendency that appears to be stronger at high Reynolds numbers. The effects of the Coriolis force on turbulence under solid-body rotation are investigated using simulations on enlarged solution domains which reduce the effects of periodic boundary conditions.

With the rise in constructing using FRP reinforcement, owing to corrosion problems in steel-reinforced structures, there is a need for a system to resist lateral loads induced from wind and earthquake loads. The present study addressed the applicability of reinforced-concrete shear walls totally reinforced with glass-fiber-reinforced polymer (GFRP) bars to attain reasonable strength and drift requirements as specified in different codes. Four large-scale shear walls - one reinforced with steel bars (as reference specimen) and three totally reinforced with GFRP bars - were constructed and tested to failure under quasi-static reversed cyclic lateral loading. The GFRP-reinforced walls had different aspect ratios covering the range of medium-rise walls. The reported test results clearly showed that properly designed and detailed GFRPreinforced walls could reach their flexural capacities with no strength degradation, and that shear, sliding shear, and anchorage failures were not major problems and could be effectively controlled. The results also showed recoverable and self-centering behavior up to allowable drift limits before moderate damage occurred and achieved a maximum drift meeting the limitation of most building codes. Acceptable levels of energy dissipation accompanied by relatively small residual forces, compared to the steel-reinforced shear wall, were observed. Finite element simulation was conducted and the analyses captured the main features of behavior. Interaction of flexural and shear deformations of the tested shear walls was investigated. It was found that relying on the diagonal transducers tended to overestimate shear distortions by 30% to 50%. Correcting the results based on the use of vertical transducers was assessed and found to produce consistent results. Decoupling the flexural and shear deformations was discussed. Using GFRP bars as elastic material gave uniform distribution of shear strains along the shear region, resulting in shear deformation ranging from 15 to 20% of total deformation. The yielding of the steel bars intensified the shear strains at the yielding location, causing significant degradation in shear deformation ranging from 2 to 40% of total deformation. The results obtained demonstrated significantly high utilization levels of such shear wall type, therefore, primary guidelines for seismic design of GFRP-reinforced shear wall in moderate earthquakes regions was presented, as no design guidelines for lateral load resistance for GFRP-reinforced walls are available in codes. The ultimate limit state was addressed by providing strength capacity that limit ductility demand to their safe flexural displacement capacity. The strength demands were derived from ground motion spectra using modification factors that depend on both the strength and energy absorption of the structure. Deformation capacity was derived by proposing new definitions for elastic (virtual yield) displacement and maximum allowable displacement. Strength modification factor was proposed based on the test results. The occurrence of "virtual plastic hinge" for GFRP-reinforced shear walls was described providing new definitions convenient with the behavior of the GFRP-reinforced shear walls. "Virtual plastic hinge" length was estimated based on observations and calculations. Subsequently, the experimental results were used to justify the proposed design procedure. The promising results could provide impetus for constructing shear walls reinforced with GFRP bars and constitute a step toward using GFRP reinforcement in such lateral-resisting systems.

Cette thèse présente les résultats de travaux visant à étudier les interactions entre les conditions hydrodynamiques et le comportement bactérien en bioréacteur. En s'intéressant plus particulièrement aux phénomènes agissant aux petites échelles, nous avons cherché à identifier, caractériser et quantifier les couplages hydro-bio à l'échelle de la cellule. Ici, la souche Lactococcus lactis a été choisie comme modèle microbiologique, alors qu’un réacteur de type Couette a été préféré afin d’engendrer des contraintes hydrodynamiques connues et définies. Il a été démontré que dans des conditions spécifiques d’écoulement (Modulated Wavy Vortex Flow), les bactéries lactiques s’agrègent au sein d’une matrice riche en polysaccharides. Le lien entre ce phénotype atypique et les contraintes locales liées à l’écoulement a été étudié { l’aide de simulation numérique directe de l’écoulement combiné { un suivi de particule. Cette approche permet d’établir les profils temporels des contraintes subies et de comparer la nature des forces disruptives subies au mécanisme d’agrégation séparation des cellules bactériennes au sein de leur matrice. Ce travail de recherche donne ainsi d’autres exemples d’interactions cellule – environement en bioréacteurs, mettant en exergue des effets mécaniques / The aim of this work is to reach a better understanding of environmental effects on bacterial behaviour in bioreactors. Particular attention has been paid to hydrodynamically-induced stresses at the cell scale, with a view to characterizing and quantifying these local interactions. As a “model experiment”, Lactococcus lactis NCDO2118 has been cultivated in a CouetteBioreactor, a device generating a known and defined flow field. Under specific flow regime (Modulated Wavy Vortex Flow), the cells end up being entrapped in a polysaccharidic matrix. The phenotype of the cells has been demonstrated to be strongly affected by the flow conditions. The stress signal encountered by the cells has been characterized, through umerical simulation (Direct Numerical Simulation) and lagrangian particle tracking, and linked to the phenotypic expression. These studies provide further examples of bacterial response to local hydrodynamic conditions

Submitted by Regina Correa (rehecorrea@gmail.com) on 2016-09-19T19:31:52Z No. of bitstreams: 1 TeseHS.pdf: 6507848 bytes, checksum: 467139021a2d6e49272a3197b75c3216 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-21T12:29:38Z (GMT) No. of bitstreams: 1 TeseHS.pdf: 6507848 bytes, checksum: 467139021a2d6e49272a3197b75c3216 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-21T12:29:45Z (GMT) No. of bitstreams: 1 TeseHS.pdf: 6507848 bytes, checksum: 467139021a2d6e49272a3197b75c3216 (MD5) / Made available in DSpace on 2016-09-21T12:29:53Z (GMT). No. of bitstreams: 1 TeseHS.pdf: 6507848 bytes, checksum: 467139021a2d6e49272a3197b75c3216 (MD5) Previous issue date: 2016-03-28 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Taylor-Vortex reactor (TVB) is fast becoming the next bioreactor to culture animal cells due to milder shear and homogeneous flow structures through-out the bioreactor in comparison to the traditional stirred vessels. However, there is little information in the literature for the TVB on the viscous energy dissipation rate (VEDR), which is considered the ideal parameter to characterize the cell death, and its geometrical aspects, which may affect the culture of animal cells resulting in poor efficiency. Consequently, this work focuses on: the estimation of the VEDR of mean flow and turbulent kinetic energy (TKE) using an experimental 2D particle image velocimetry (PIV) method and a computational fluid dynamics (CFD) method using different turbulence models, principally the direct numerical simulation (DNS) model; and, the impact of the off-bottom clearance area and the external cylinder’s bottom shape on the flow structures of TVB. Both numerical and experimental methods confirm that the bulk zone comprising of the 80 % of the gap-width, where the cell cultures will spend most of the time, has a near constant velocity magnitude of around 50 % of the tip velocity and VEDR values which are around 10 times lower than at the walls. Qualitatively, the DNS model predicted well the flow structure of both mean and turbulence parameters in comparison with the experimental PIV predictions. However, quantitatively only the mean velocity predictions are in good agreement with the PIV data with certain amount of under-estimation of the turbulence parameters. Among different turbulence models, the large eddy simulation (LES) - wall adapting local eddy-viscosity (WALE) model presented best comparison with the DNS model data for all the flow parameters; while, the Reynolds stress model and the LES-Smagorinsky models were the poorest. On the other hand, the Reynolds averaged Navier-Stokes (RANS) based two equation models estimated well the mean velocity components in comparison with the DNS model data, but could not capture well the flow structures of the turbulence components. The geometrical features of curved surface of outer bottom and off-bottom clearance area which are of practical importance in stirred vessels, impact adversely the flow structures in the TVB due to poor axial velocity component. In comparison with the spinner vessel, a stirred tank type bioeactor but with lower shear, for similar Re/ReT ratio, the maximum and mean VEDR were always found to be of lower magnitude values, and due to much less difference between the maximum and the mean values, the TVB presents more uniform structures in comparison to the spinner vessel. / O biorreator de Vórtices de Taylor (TVB) está se tornando uma nova descoberta, devido ao seu cisalhamento mais suave e fluxo homogêneo em comparações com os biorreatores de tanque agitados. Na literatura acadêmica há pouca informação sobre este biorreator quanto a taxa de dissipação de energia viscosa (VEDR), que é o parâmetro ideal para caracterizar a morte celular, e seus aspectos geométricos, que afetam o cultivo das células animais, resultando em baixa eficiência. A presente pesquisa, portanto, objetivou focar na estimativa da VEDR de fluxo médio e de energia cinética turbulenta (TKE) no TVB usando os métodos: experimental de 2D de velocimetria das partículas por imagem (PIV) e numérico de dinâmica de fluídos computacional (CFD) com diferentes modelos de turbulência, principalmente a simulação numérica direta (DNS). E focar nos aspectos geométricos do impacto da área de apuramento entre o cilindro interno e externo e na forma da base do cilindro externo na estrutura de fluxo do TVB. Os dois métodos experimental e numérico demonstraram que, em aproximadamente 80 % da área lateral entre os cilindros interno e externo onde as células vão passar a maior parte do tempo, a magnitude de velocidade é de cerca de 50 % da máxima e os valores de VEDR são 10 vezes menores do que nas paredes. Qualitativamente, o DNS mostrou boas comparações dos fluxos médios e dos parâmetros turbulentos em relação aos resultados apresentados pelo PIV para o TVB. No entanto, quantitativamente, apenas as previsões médias de velocidade estão em boa concordância com os dados do PIV, pois os parâmetros turbulentos foram sub-estimados. Entre os diferentes modelos de turbulência utilizados, o modelo simulação de grande escala (LES) - Wall Adapting Local Eddy-Viscosity apresentou a melhor comparação com os dados do DNS para todos os parâmetros do fluxo. O modelo de estresse Reynolds e LES - Smagorinsky, por sua vez, apresentaram as piores comparações. Os modelos de duas equações de RANS, entretanto, apesar de estimarem bem os componentes de velocidade média em comparação com os dados do modelo DNS, não captaram bem as estruturas de fluxo dos componentes de turbulência. Quanto aos aspectos geométricos, as alterações nas características da área de apuramento entre o cilindro interno e externo e a estrutura curva da base do cilindro externo, que são de importância prática em tanque agitados, neste estudo, afetaram negativamente o fluxo no TVB devido ao seu baixo componente de velocidade axial. Por fim, a comparação entre o TVB e o Spinner Flask, considerado também um biorreator com baixo cisalhamento, demostrou que para Re/ReT semelhante, os valores máximo e médio do VEDR foram sempre inferiores, e devido à diferença muito menor entre o os valores máximo e médio, o TVB apresenta estruturas mais uniformes em comparação com o Spinner Flask. / processo nº 140756/2012-4 ; processo nº - 241739/2012-8)