Modelli semplificati per valutazione di vulnerabilità sismica di strutture in muratura

L'obiettivo della tesi è stato quello di indagare il complesso problema della vulnerabilità sismica dei ponte in muratura ad arco utilizzando modelli semplificati. Dopo una descrizione dei materiali da costruzione impiegati nella realizzazione e dei principali elementi dei un ponti in muratura, si è indirizzato lo studio di un ponte ad arco situato nel comune di San Marcello Pistoiese. Viene mostrato un modello numerico che permette di descrivere il comportamento strutturale del ponte sotto azione sismica e di valutare la capacità di carico del ponte sottoposto ad una azione trasversale. In un secondo momento viene descritta la realizzazione di un modello in scala del ponte, che è stato sottoposto a prove distruttive effettuate per valutare la capacità di carico del ponte rispetto ad un ipotetica azione orizzontale. Si è cercato poi di inquadrare il problema in un modello teorico che faccia riferimento all'analisi limite. Esso descrive un cinematismo di collasso a telaio che prende spunto dal quadro fessurativo del modello in muratura. Infine sono stati presentati modelli FEM numerici in ordine di complessità crescente, cercando di inquadrare il comportamento meccanico del prototipo del ponte. Tre tipi di modelli sono rappresentati: un telaio incernierato alle estremità costituito da elementi beam con resistenza alla flessione . Il secondo tipo è costituito da una reticolare equivalente che mima lo schema del ponte ed è formato solo da bielle. Infine, il terzo tipo cerca di descrivere l'intero modello con elementi tridimensionali.

Numerical methods for the dispersion analysis of Guided Waves

The use of guided ultrasonic waves (GUW) has increased considerably in the fields of non-destructive (NDE) testing and structural health monitoring (SHM) due to their ability to perform long range inspections, to probe hidden areas as well as to provide a complete monitoring of the entire waveguide. Guided waves can be fully exploited only once their dispersive properties are known for the given waveguide. In this context, well stated analytical and numerical methods are represented by the Matrix family methods and the Semi Analytical Finite Element (SAFE) methods. However, while the former are limited to simple geometries of finite or infinite extent, the latter can model arbitrary cross-section waveguides of finite domain only. This thesis is aimed at developing three different numerical methods for modelling wave propagation in complex translational invariant systems. First, a classical SAFE formulation for viscoelastic waveguides is extended to account for a three dimensional translational invariant static prestress state. The effect of prestress, residual stress and applied loads on the dispersion properties of the guided waves is shown. Next, a two-and-a-half Boundary Element Method (2.5D BEM) for the dispersion analysis of damped guided waves in waveguides and cavities of arbitrary cross-section is proposed. The attenuation dispersive spectrum due to material damping and geometrical spreading of cavities with arbitrary shape is shown for the first time. Finally, a coupled SAFE-2.5D BEM framework is developed to study the dispersion characteristics of waves in viscoelastic waveguides of arbitrary geometry embedded in infinite solid or liquid media. Dispersion of leaky and non-leaky guided waves in terms of speed and attenuation, as well as the radiated wavefields, can be computed. The results obtained in this thesis can be helpful for the design of both actuation and sensing systems in practical application, as well as to tune experimental setup.

Non-Linear Analysis and Design of Synchronous Bearingless Multiphase Permanent Magnet Machines and Drives

A two-dimensional model to analyze the distribution of magnetic fields in the airgap of a PM electrical machines is studied. A numerical algorithm for non-linear magnetic analysis of multiphase surface-mounted PM machines with semi-closed slots is developed, based on the equivalent magnetic circuit method. By using a modular structure geometry, whose the basic element can be duplicated, it allows to design whatever typology of windings distribution. In comparison to a FEA, permits a reduction in computing time and to directly changing the values of the parameters in a user interface, without re-designing the model. Output torque and radial forces acting on the moving part of the machine can be calculated. In addition, an analytical model for radial forces calculation in multiphase bearingless Surface-Mounted Permanent Magnet Synchronous Motors (SPMSM) is presented. It allows to predict amplitude and direction of the force, depending on the values of torque current, of levitation current and of rotor position. It is based on the space vectors method, letting the analysis of the machine also during transients. The calculations are conducted by developing the analytical functions in Fourier series, taking all the possible interactions between stator and rotor mmf harmonic components into account and allowing to analyze the effects of electrical and geometrical quantities of the machine, being parametrized. The model is implemented in the design of a control system for bearingless machines, as an accurate electromagnetic model integrated in a three-dimensional mechanical model, where one end of the motor shaft is constrained to simulate the presence of a mechanical bearing, while the other is free, only supported by the radial forces developed in the interactions between magnetic fields, to realize a bearingless system with three degrees of freedom. The complete model represents the design of the experimental system to be realized in the laboratory.

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

The calcite(10-14) surface: a versatile substrate for molecular self-assembly

This thesis presents a detailed and successful study of molecular self-assembly on the calcite CaCO3(10-14) surface. One reason for the superior applicability of this particular surface is given by reflecting the well-known growth modes. Layer-by-layer growth, which is a necessity for the formation of templated two-dimensional (2D) molecular structures, is particularly favoured on substrates with a high surface energy. The CaCO3(10-14) surface is among those substrates and, thus, most promising. rnrnAll experiments in this thesis were performed using the non-contact atomic force microscope (NC-AFM) under ultra-high vacuum conditions. The acquisition of drift-free data became in this thesis possible owing to the herein newly developed atom-tracking system. This system features a lateral tip-positioning precision of at least 50pm. Furthermore, a newly developed scan protocol was implemented in this system, which allows for the acquisition of dense three-dimensional (3D) data under room-temperature conditions. An entire 3D data set from a CaCO3(10-14) surface consisting of 85x85x500 pixel is discussed. rnrnThe row-pairing and (2x1) reconstructions of the CaCO3(10-14) surface constitute most interesting research subjects. For both reconstructions, the NC-AFM imaging was classified to a total of 12 contrast modes. Eight of these modes were observed within this thesis, some of them for the first time. Together with literature findings, a total of 10 modes has been observed experimentally to this day. Some contrast modes presented themselves as highly distance-dependent and at least for one contrast mode, a severe tip-termination influence was found. rnrnMost interestingly, the row-pairing reconstruction was found to break a symmetry element of the CaCO3(10-14) surface. With the presence of this reconstruction, the calcite (10-14) surface becomes chiral. From high-resolution NC-AFM data, the identification of the enantiomers is here possible and is presented for one enantiomer in this thesis. rnrnFive studies of self-assembled molecular structures on calcite (10-14) surfaces are presented. Only for one system, namely HBC/CaCO3(10-14), the formation of a molecular bulk structure was observed. This well-known occurence of weak molecule-insulator interaction hinders the investigation of two-dimensional molecular self-assembly. It was, however, possible to force the formation of an island phase for this system upon following a variable-temperature preparation. rnFor the C60/CaCO3(10-14) system it is most notably that no branched island morphologies were found. Instead, the first C60 layer appeared to wet the calcite surface. rnrnIn all studies, the molecules arranged themselves in ordered superstructures. A templating effect due to the underlying calcite substrate was evident for all systems. This templating strikingly led either to the formation of large commensurate superstructures, such as (2x15) with a 14 molecule basis for the C60/CaCO3(10-14) system, or prevented the vast growth of incommensurate molecular motifs, such as the chicken-wire structure in the trimesic acid (TMA)/CaCO3(10-14) system. rnrnThe molecule-molecule and the molecule-substrate interaction was increased upon choosing molecules with carboxylic acid moieties in the third, fourth and fifth study, using terephthalic acid, TMA and helicene molecules. In all these experiments, hydrogen-bonded assemblies were created. rnrnDirected hydrogen bond formation combined with intermolecular pi-pi interaction is employed in the fifth study, where the formation of uni-directional molecular "wires" from single helicene molecules succeeded. Each "wire" is composed of heterochiral helicene pairs, well-aligned along the [01-10] substrate direction and stabilised by pi-pi interaction.

Modelling and analysis of thin-walled beams in the context of the Generalized Beam Theory

In this work, the Generalized Beam Theory (GBT) is used as the main tool to analyze the mechanics of thin-walled beams. After an introduction to the subject and a quick review of some of the most well-known approaches to describe the behaviour of thin-walled beams, a novel formulation of the GBT is presented. This formulation contains the classic shear-deformable GBT available in the literature and contributes an additional description of cross-section warping that is variable along the wall thickness besides along the wall midline. Shear deformation is introduced in such a way that the classical shear strain components of the Timoshenko beam theory are recovered exactly. According to the new kinematics proposed, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition. Later, a procedure for a posteriori reconstruction of all the three-dimensional stress components in the finite element analysis of thin-walled beams using the GBT is presented. The reconstruction is simple and based on the use of three-dimensional equilibrium equations and of the RCP procedure. Finally, once the stress reconstruction procedure is presented, a study of several existing issues on the constitutive relations in the GBT is carried out. Specifically, a constitutive law based on mirroring the kinematic constraints of the GBT model into a specific stress field assumption is proposed. It is shown that this method is equally valid for isotropic and orthotropic beams and coincides with the conventional GBT approach available in the literature. Later on, an analogous procedure is presented for the case of laminated beams. Lastly, as a way to improve an inherently poor description of shear deformability in the GBT, the introduction of shear correction factors is proposed. Throughout this work, numerous examples are provided to determine the validity of all the proposed contributions to the field.

Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Comparison of three optical tracking systems in a complex navigation scenario

Three-dimensional rotational X-ray imaging with the SIREMOBIL Iso-C3D (Siemens AG, Medical Solutions, Erlangen, Germany) has become a well-established intra-operative imaging modality. In combination with a tracking system, the Iso-C3D provides inherently registered image volumes ready for direct navigation. This is achieved by means of a pre-calibration procedure. The aim of this study was to investigate the influence of the tracking system used on the overall navigation accuracy of direct Iso-C3D navigation. Three models of tracking system were used in the study: Two Optotrak 3020s, a Polaris P4 and a Polaris Spectra system, with both Polaris systems being in the passive operation mode. The evaluation was carried out at two different sites using two Iso-C3D devices. To measure the navigation accuracy, a number of phantom experiments were conducted using an acrylic phantom equipped with titanium spheres. After scanning, a special pointer was used to pinpoint these markers. The difference between the digitized and navigated positions served as the accuracy measure. Up to 20 phantom scans were performed for each tracking system. The average accuracy measured was 0.86 mm and 0.96 mm for the two Optotrak 3020 systems, 1.15 mm for the Polaris P4, and 1.04 mm for the Polaris Spectra system. For the Polaris systems a higher maximal error was found, but all three systems yielded similar minimal errors. On average, all tracking systems used in this study could deliver similar navigation accuracy. The passive Polaris system showed ? as expected ? higher maximal errors; however, depending on the application constraints, this might be negligible.

Stress and Strain Adaptation in Load-Dependent Remodeling of the Embryonic Left Ventricle

Altered pressure in the developing left ventricle (LV) results in altered morphology and tissue material properties. Mechanical stress and strain may play a role in the regulating process. This study showed that confocal microscopy, three-dimensional reconstruction, and finite element analysis can provide a detailed model of stress and strain in the trabeculated embryonic heart. The method was used to test the hypothesis that end-diastolic strains are normalized after altered loading of the LV during the stages of trabecular compaction and chamber formation. Stage-29 chick LVs subjected to pressure overload and underload at stage 21 were reconstructed with full trabecular morphology from confocal images and analyzed with finite element techniques. Measured material properties and intraventricular pressures were specified in the models. The results show volume-weighted end-diastolic von Mises stress and strain averaging 50–82% higher in the trabecular tissue than in the compact wall. The volume-weighted-average stresses for the entire LV were 115, 64, and 147Pa in control, underloaded, and overloaded models, while strains were 11, 7, and 4%; thus, neither was normalized in a volume-weighted sense. Localized epicardial strains at mid-longitudinal level were similar among the three groups and to strains measured from high-resolution ultrasound images. Sensitivity analysis showed changes in material properties are more significant than changes in geometry in the overloaded strain adaptation, although resulting stress was similar in both types of adaptation. These results emphasize the importance of appropriate metrics and the role of trabecular tissue in evaluating the evolution of stress and strain in relation to pressure-induced adaptation.

Diagnostic microchip to assay 3D colony-growth potential of captured circulating tumor cells

Microfluidic technology has been successfully applied to isolate very rare tumor-derived epithelial cells (circulating tumor cells, CTCs) from blood with relatively high yield and purity, opening up exciting prospects for early detection of cancer. However, a major limitation of state-of-the-art CTC-chips is their inability to characterize the behavior and function of captured CTCs, for example to obtain information on proliferative and invasive properties or, ultimately, tumor re-initiating potential. Although CTCs can be efficiently immunostained with markers reporting phenotype or fate (e.g. apoptosis, proliferation), it has not yet been possible to reliably grow captured CTCs over long periods of time and at single cell level. It is challenging to remove CTCs from a microchip after capture, therefore such analyses should ideally be performed directly on-chip. To address this challenge, we merged CTC capture with three-dimensional (3D) tumor cell culture on the same microfluidic platform. PC3 prostate cancer cells were isolated from spiked blood on a transparent PDMS CTC-chip, encapsulated on-chip in a biomimetic hydrogel matrix (QGel™) that was formed in situ, and their clonal 3D spheroid growth potential was assessed by microscopy over one week in culture. The possibility to clonally expand a subset of captured CTCs in a near-physiological in vitro model adds an important element to the expanding CTC-chip toolbox that ultimately should improve prediction of treatment responses and disease progression.

Assessing the Validity of Brain Glucose Concentration Measurement Using Microdialysis

Brain functions, such as learning, orchestrating locomotion, memory recall, and processing information, all require glucose as a source of energy. During these functions, the glucose concentration decreases as the glucose is being consumed by brain cells. By measuring this drop in concentration, it is possible to determine which parts of the brain are used during specific functions and consequently, how much energy the brain requires to complete the function. One way to measure in vivo brain glucose levels is with a microdialysis probe. The drawback of this analytical procedure, as with many steadystate fluid flow systems, is that the probe fluid will not reach equilibrium with the brain fluid. Therefore, brain concentration is inferred by taking samples at multiple inlet glucose concentrations and finding a point of convergence. The goal of this thesis is to create a three-dimensional, time-dependent, finite element representation of the brainprobe system in COMSOL 4.2 that describes the diffusion and convection of glucose. Once validated with experimental results, this model can then be used to test parameters that experiments cannot access. When simulations were run using published values for physical constants (i.e. diffusivities, density and viscosity), the resulting glucose model concentrations were within the error of the experimental data. This verifies that the model is an accurate representation of the physical system. In addition to accurately describing the experimental brain-probe system, the model I created is able to show the validity of zero-net-flux for a given experiment. A useful discovery is that the slope of the zero-net-flux line is dependent on perfusate flow rate and diffusion coefficients, but it is independent of brain glucose concentrations. The model was simplified with the realization that the perfusate is at thermal equilibrium with the brain throughout the active region of the probe. This allowed for the assumption that all model parameters are temperature independent. The time to steady-state for the probe is approximately one minute. However, the signal degrades in the exit tubing due to Taylor dispersion, on the order of two minutes for two meters of tubing. Given an analytical instrument requiring a five μL aliquot, the smallest brain process measurable for this system is 13 minutes.

Do women have impaired regional systolic function in hypertensive heart disease? A 3-dimensional echocardiography study

AIMS: In pressure overload left ventricular (LV) hypertrophy, gender-related differences in global LV systolic function have been previously reported. The goal of this study was to determine regional systolic function of the left ventricle in male and female patients with hypertensive heart disease. METHODS AND RESULTS: Regional LV function was analyzed from multiplane transesophageal echocardiography with three-dimensional (3D) reconstruction of the left ventricle. In 24 patients (13 males and 11 females), four parallel (2 basal and 2 apical) equidistant short axis cross-sections from base to apex were obtained from the reconstructed LV. In each short axis 24 wall-thickness measurements were carried out at 15 degrees intervals at end-diastole and end-systole. Thus, a total of 192 measurements were obtained in each patient. Wall thickening was calculated as difference of end-diastolic and end-systolic wall thickness, and fractional thickening as thickening divided by end-diastolic thickness. Fractional thickening and wall stress were inversely related to end-diastolic wall thickness in both, males and females. Females showed less LV systolic function when compared to males (p<0.001). However, when corrected for wall stress, which was higher in females, there was no gender difference in systolic function. CONCLUSION: There are regional differences in LV systolic function in females and males which are directly related to differences in wall stress. Thus, gender-related differences in LV regional function are load-dependent and not due to structural differences.

Integration of computational models and experimental characterization to study internal frost damage in cementitious materials

The objective of this doctoral research is to investigate the internal frost damage due to crystallization pore pressure in porous cement-based materials by developing computational and experimental characterization tools. As an essential component of the U.S. infrastructure system, the durability of concrete has significant impact on maintenance costs. In cold climates, freeze-thaw damage is a major issue affecting the durability of concrete. The deleterious effects of the freeze-thaw cycle depend on the microscale characteristics of concrete such as the pore sizes and the pore distribution, as well as the environmental conditions. Recent theories attribute internal frost damage of concrete is caused by crystallization pore pressure in the cold environment. The pore structures have significant impact on freeze-thaw durability of cement/concrete samples. The scanning electron microscope (SEM) and transmission X-ray microscopy (TXM) techniques were applied to characterize freeze-thaw damage within pore structure. In the microscale pore system, the crystallization pressures at sub-cooling temperatures were calculated using interface energy balance with thermodynamic analysis. The multi-phase Extended Finite Element Modeling (XFEM) and bilinear Cohesive Zone Modeling (CZM) were developed to simulate the internal frost damage of heterogeneous cement-based material samples. The fracture simulation with these two techniques were validated by comparing the predicted fracture behavior with the captured damage from compact tension (CT) and single-edge notched beam (SEB) bending tests. The study applied the developed computational tools to simulate the internal frost damage caused by ice crystallization with the two dimensional (2-D) SEM and three dimensional (3-D) reconstructed SEM and TXM digital samples. The pore pressure calculated from thermodynamic analysis was input for model simulation. The 2-D and 3-D bilinear CZM predicted the crack initiation and propagation within cement paste microstructure. The favorably predicted crack paths in concrete/cement samples indicate the developed bilinear CZM techniques have the ability to capture crack nucleation and propagation in cement-based material samples with multiphase and associated interface. By comparing the computational prediction with the actual damaged samples, it also indicates that the ice crystallization pressure is the main mechanism for the internal frost damage in cementitious materials.

Three members of the connective tissue growth factor family CCN are differentially regulated by mechanical stress

Expression of connective tissue growth factor (CTGF), a member of the CCN gene family, is known to be significantly induced by mechanical stress. We have therefore investigated whether other members of the CCN gene family, including Cyr61 and Nov, might reveal a similar stress-dependent regulation. Fibroblasts growing under stressed conditions within a three-dimensional collagen gel showed at least a 15 times higher level of Cyr61 mRNA than cells growing under relaxed conditions. Upon relaxation, the decline of the Cyr61 mRNA to a lower level occurred within 2 h, and was thus quicker than the response of CTGF. The regulation was fully reversible when stress was reapplied. Thus, Cyr61 represents another typical example of a stress-responsive gene. The level of the Nov mRNA was low in the stressed state, but increased in the relaxed state. This CCN gene therefore shows an inverted regulation relative to that of Cyr61 and CTGF. Inhibition of protein kinases by means of staurosporine suppressed the stress-induced expression of Cyr61 and CTGF. Elevated levels of cAMP induced by forskolin mimicked the effects of relaxation on the regulation of Cyr61, CTGF and Nov. Thus, adenylate cyclase as well as one or several protein kinases might be involved in the mechanoregulation of these CCN genes.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.