Fluid-structure interaction by a coupled lattice Boltzmann-finite element approach

In this thesis, a strategy to model the behavior of fluids and their interaction with deformable bodies is proposed. The fluid domain is modeled by using the lattice Boltzmann method, thus analyzing the fluid dynamics by a mesoscopic point of view. It has been proved that the solution provided by this method is equivalent to solve the Navier-Stokes equations for an incompressible flow with a second-order accuracy. Slender elastic structures idealized through beam finite elements are used. Large displacements are accounted for by using the corotational formulation. Structural dynamics is computed by using the Time Discontinuous Galerkin method. Therefore, two different solution procedures are used, one for the fluid domain and the other for the structural part, respectively. These two solvers need to communicate and to transfer each other several information, i.e. stresses, velocities, displacements. In order to guarantee a continuous, effective, and mutual exchange of information, a coupling strategy, consisting of three different algorithms, has been developed and numerically tested. In particular, the effectiveness of the three algorithms is shown in terms of interface energy artificially produced by the approximate fulfilling of compatibility and equilibrium conditions at the fluid-structure interface. The proposed coupled approach is used in order to solve different fluid-structure interaction problems, i.e. cantilever beams immersed in a viscous fluid, the impact of the hull of the ship on the marine free-surface, blood flow in a deformable vessels, and even flapping wings simulating the take-off of a butterfly. The good results achieved in each application highlight the effectiveness of the proposed methodology and of the C++ developed software to successfully approach several two-dimensional fluid-structure interaction problems.

A Trans-dimensional inversion algorithm to model deformation sources with unconstrained shape in finite element domains

Ground deformation provides valuable insights on subsurface processes with pattens reflecting the characteristics of the source at depth. In active volcanic sites displacements can be observed in unrest phases; therefore, a correct interpretation is essential to assess the hazard potential. Inverse modeling is employed to obtain quantitative estimates of parameters describing the source. However, despite the robustness of the available approaches, a realistic imaging of these reservoirs is still challenging. While analytical models return quick but simplistic results, assuming an isotropic and elastic crust, more sophisticated numerical models, accounting for the effects of topographic loads, crust inelasticity and structural discontinuities, require much higher computational effort and information about the crust rheology may be challenging to infer. All these approaches are based on a-priori source shape constraints, influencing the solution reliability. In this thesis, we present a new approach aimed at overcoming the aforementioned limitations, modeling sources free of a-priori shape constraints with the advantages of FEM simulations, but with a cost-efficient procedure. The source is represented as an assembly of elementary units, consisting in cubic elements of a regular FE mesh loaded with a unitary stress tensors. The surface response due to each of the six stress tensor components is computed and linearly combined to obtain the total displacement field. In this way, the source can assume potentially any shape. Our tests prove the equivalence of the deformation fields due to our assembly and that of corresponding cavities with uniform boundary pressure. Our ability to simulate pressurized cavities in a continuum domain permits to pre-compute surface responses, avoiding remeshing. A Bayesian trans-dimensional inversion algorithm implementing this strategy is developed. 3D Voronoi cells are used to sample the model domain, selecting the elementary units contributing to the source solution and those remaining inactive as part of the crust.

Finite element models of coseismic deformation due to the 2009 L'Aquila (Italy) and 2008 Wenchuan(China) earthquakes

The topic of my Ph.D. thesis is the finite element modeling of coseismic deformation imaged by DInSAR and GPS data. I developed a method to calculate synthetic Green functions with finite element models (FEMs) and then use linear inversion methods to determine the slip distribution on the fault plane. The method is applied to the 2009 L’Aquila Earthquake (Italy) and to the 2008 Wenchuan earthquake (China). I focus on the influence of rheological features of the earth's crust by implementing seismic tomographic data and the influence of topography by implementing Digital Elevation Models (DEM) layers on the FEMs. Results for the L’Aquila earthquake highlight the non-negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. Regarding the 2008 Wenchuan earthquake, the very steep topographic relief of Longmen Shan Range is implemented in my FE model. A large number of DEM layers corresponding to East China is used to achieve the complete coverage of the FE model. My objective was to explore the influence of the topography on the retrieved coseismic slip distribution. The inversion results reveals significant differences between the flat and topographic model. Thus, the flat models frequently adopted are inappropriate to represent the earth surface topographic features and especially in the case of the 2008 Wenchuan earthquake.

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Study of the circulation processes in the northern Adriatic sea - coastal area and Venice lagoon inlets

This work is a detailed study of hydrodynamic processes in a defined area, the littoral in front of the Venice Lagoon and its inlets, which are complex morphological areas of interconnection. A finite element hydrodynamic model of the Venice Lagoon and the Adriatic Sea has been developed in order to study the coastal current patterns and the exchanges at the inlets of the Venice Lagoon. This is the first work in this area that tries to model the interaction dynamics, running together a model for the lagoon and the Adriatic Sea. First the barotropic processes near the inlets of the Venice Lagoon have been studied. Data from more than ten tide gauges displaced in the Adriatic Sea have been used in the calibration of the simulated water levels. To validate the model results, empirical flux data measured by ADCP probes installed inside the inlets of Lido and Malamocco have been used and the exchanges through the three inlets of the Venice Lagoon have been analyzed. The comparison between modelled and measured fluxes at the inlets outlined the efficiency of the model to reproduce both tide and wind induced water exchanges between the sea and the lagoon. As a second step, also small scale processes around the inlets that connect the Venice lagoon with the Northern Adriatic Sea have been investigated by means of 3D simulations. Maps of vorticity have been produced, considering the influence of tidal flows and wind stress in the area. A sensitivity analysis has been carried out to define the importance of the advection and of the baroclinic pressure gradients in the development of vortical processes seen along the littoral close to the inlets. Finally a comparison with real data measurements, surface velocity data from HF Radar near the Venice inlets, has been performed, which allows for a better understanding of the processes and their seasonal dynamics. The results outline the predominance of wind and tidal forcing in the coastal area. Wind forcing acts mainly on the mean coastal current inducing its detachment offshore during Sirocco events and an increase of littoral currents during Bora events. The Bora action is more homogeneous on the whole coastal area whereas the Sirocco strengthens its impact in the South, near Chioggia inlet. Tidal forcing at the inlets is mainly barotropic. The sensitivity analysis shows how advection is the main physical process responsible for the persistent vortical structures present along the littoral between the Venice Lagoon inlets. The comparison with measurements from HF Radar not only permitted a validation the model results, but also a description of different patterns in specific periods of the year. The success of the 2D and the 3D simulations on the reproduction both of the SSE, inside and outside the Venice Lagoon, of the tidal flow, through the lagoon inlets, and of the small scale phenomena, occurring along the littoral, indicates that the finite element approach is the most suitable tool for the investigation of coastal processes. For the first time, as shown by the flux modeling, the physical processes that drive the interaction between the two basins were reproduced.

Reduced-order modelling, circuit-level design and SOI fabrication of microelectromechanical resonators

This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

Active fibre-reinforced composites with embedded shape memory alloys

This dissertation concerns active fibre-reinforced composites with embedded shape memory alloy wires. The structural application of active materials allows to develop adaptive structures which actively respond to changes in the environment, such as morphing structures, self-healing structures and power harvesting devices. In particular, shape memory alloy actuators integrated within a composite actively control the structural shape or stiffness, thus influencing the composite static and dynamic properties. Envisaged applications include, among others, the prevention of thermal buckling of the outer skin of air vehicles, shape changes in panels for improved aerodynamic characteristics and the deployment of large space structures. The study and design of active composites is a complex and multidisciplinary topic, requiring in-depth understanding of both the coupled behaviour of active materials and the interaction between the different composite constituents. Both fibre-reinforced composites and shape memory alloys are extremely active research topics, whose modelling and experimental characterisation still present a number of open problems. Thus, while this dissertation focuses on active composites, some of the research results presented here can be usefully applied to traditional fibre-reinforced composites or other shape memory alloy applications. The dissertation is composed of four chapters. In the first chapter, active fibre-reinforced composites are introduced by giving an overview of the most common choices available for the reinforcement, matrix and production process, together with a brief introduction and classification of active materials. The second chapter presents a number of original contributions regarding the modelling of fibre-reinforced composites. Different two-dimensional laminate theories are derived from a parent three-dimensional theory, introducing a procedure for the a posteriori reconstruction of transverse stresses along the laminate thickness. Accurate through the thickness stresses are crucial for the composite modelling as they are responsible for some common failure mechanisms. A new finite element based on the First-order Shear Deformation Theory and a hybrid stress approach is proposed for the numerical solution of the two-dimensional laminate problem. The element is simple and computationally efficient. The transverse stresses through the laminate thickness are reconstructed starting from a general finite element solution. A two stages procedure is devised, based on Recovery by Compatibility in Patches and three-dimensional equilibrium. Finally, the determination of the elastic parameters of laminated structures via numerical-experimental Bayesian techniques is investigated. Two different estimators are analysed and compared, leading to the definition of an alternative procedure to improve convergence of the estimation process. The third chapter focuses on shape memory alloys, describing their properties and applications. A number of constitutive models proposed in the literature, both one-dimensional and three-dimensional, are critically discussed and compared, underlining their potential and limitations, which are mainly related to the definition of the phase diagram and the choice of internal variables. Some new experimental results on shape memory alloy material characterisation are also presented. These experimental observations display some features of the shape memory alloy behaviour which are generally not included in the current models, thus some ideas are proposed for the development of a new constitutive model. The fourth chapter, finally, focuses on active composite plates with embedded shape memory alloy wires. A number of di®erent approaches can be used to predict the behaviour of such structures, each model presenting different advantages and drawbacks related to complexity and versatility. A simple model able to describe both shape and stiffness control configurations within the same context is proposed and implemented. The model is then validated considering the shape control configuration, which is the most sensitive to model parameters. The experimental work is divided in two parts. In the first part, an active composite is built by gluing prestrained shape memory alloy wires on a carbon fibre laminate strip. This structure is relatively simple to build, however it is useful in order to experimentally demonstrate the feasibility of the concept proposed in the first part of the chapter. In the second part, the making of a fibre-reinforced composite with embedded shape memory alloy wires is investigated, considering different possible choices of materials and manufacturing processes. Although a number of technological issues still need to be faced, the experimental results allow to demonstrate the mechanism of shape control via embedded shape memory alloy wires, while showing a good agreement with the proposed model predictions.

Numerical simulations of magma chamber dynamics at Campi Flegrei, and associated seismicity, deformation and gravity changes

Understanding the complex relationships between quantities measured by volcanic monitoring network and shallow magma processes is a crucial headway for the comprehension of volcanic processes and a more realistic evaluation of the associated hazard. This question is very relevant at Campi Flegrei, a volcanic quiescent caldera immediately north-west of Napoli (Italy). The system activity shows a high fumarole release and periodic ground slow movement (bradyseism) with high seismicity. This activity, with the high people density and the presence of military and industrial buildings, makes Campi Flegrei one of the areas with higher volcanic hazard in the world. In such a context my thesis has been focused on magma dynamics due to the refilling of shallow magma chambers, and on the geophysical signals detectable by seismic, deformative and gravimetric monitoring networks that are associated with this phenomenologies. Indeed, the refilling of magma chambers is a process frequently occurring just before a volcanic eruption; therefore, the faculty of identifying this dynamics by means of recorded signal analysis is important to evaluate the short term volcanic hazard. The space-time evolution of dynamics due to injection of new magma in the magma chamber has been studied performing numerical simulations with, and implementing additional features in, the code GALES (Longo et al., 2006), recently developed and still on the upgrade at the Istituto Nazionale di Geofisica e Vulcanologia in Pisa (Italy). GALES is a finite element code based on a physico-mathematical two dimensional, transient model able to treat fluids as multiphase homogeneous mixtures, compressible to incompressible. The fundamental equations of mass, momentum and energy balance are discretised both in time and space using the Galerkin Least-Squares and discontinuity-capturing stabilisation technique. The physical properties of the mixture are computed as a function of local conditions of magma composition, pressure and temperature.The model features enable to study a broad range of phenomenologies characterizing pre and sin-eruptive magma dynamics in a wide domain from the volcanic crater to deep magma feeding zones. The study of displacement field associated with the simulated fluid dynamics has been carried out with a numerical code developed by the Geophysical group at the University College Dublin (O’Brien and Bean, 2004b), with whom we started a very profitable collaboration. In this code, the seismic wave propagation in heterogeneous media with free surface (e.g. the Earth’s surface) is simulated using a discrete elastic lattice where particle interactions are controlled by the Hooke’s law. This method allows to consider medium heterogeneities and complex topography. The initial and boundary conditions for the simulations have been defined within a coordinate project (INGV-DPC 2004-06 V3_2 “Research on active volcanoes, precursors, scenarios, hazard and risk - Campi Flegrei”), to which this thesis contributes, and many researchers experienced on Campi Flegrei in volcanological, seismic, petrological, geochemical fields, etc. collaborate. Numerical simulations of magma and rock dynamis have been coupled as described in the thesis. The first part of the thesis consists of a parametric study aimed at understanding the eect of the presence in magma of carbon dioxide in magma in the convection dynamics. Indeed, the presence of this volatile was relevant in many Campi Flegrei eruptions, including some eruptions commonly considered as reference for a future activity of this volcano. A set of simulations considering an elliptical magma chamber, compositionally uniform, refilled from below by a magma with volatile content equal or dierent from that of the resident magma has been performed. To do this, a multicomponent non-ideal magma saturation model (Papale et al., 2006) that considers the simultaneous presence of CO2 and H2O, has been implemented in GALES. Results show that the presence of CO2 in the incoming magma increases its buoyancy force promoting convection ad mixing. The simulated dynamics produce pressure transients with frequency and amplitude in the sensitivity range of modern geophysical monitoring networks such as the one installed at Campi Flegrei . In the second part, simulations more related with the Campi Flegrei volcanic system have been performed. The simulated system has been defined on the basis of conditions consistent with the bulk of knowledge of Campi Flegrei and in particular of the Agnano-Monte Spina eruption (4100 B.P.), commonly considered as reference for a future high intensity eruption in this area. The magmatic system has been modelled as a long dyke refilling a small shallow magma chamber; magmas with trachytic and phonolitic composition and variable volatile content of H2O and CO2 have been considered. The simulations have been carried out changing the condition of magma injection, the system configuration (magma chamber geometry, dyke size) and the resident and refilling magma composition and volatile content, in order to study the influence of these factors on the simulated dynamics. Simulation results allow to follow each step of the gas-rich magma ascent in the denser magma, highlighting the details of magma convection and mixing. In particular, the presence of more CO2 in the deep magma results in more ecient and faster dynamics. Through this simulations the variation of the gravimetric field has been determined. Afterward, the space-time distribution of stress resulting from numerical simulations have been used as boundary conditions for the simulations of the displacement field imposed by the magmatic dynamics on rocks. The properties of the simulated domain (rock density, P and S wave velocities) have been based on data from literature on active and passive tomographic experiments, obtained through a collaboration with A. Zollo at the Dept. of Physics of the Federici II Univeristy in Napoli. The elasto-dynamics simulations allow to determine the variations of the space-time distribution of deformation and the seismic signal associated with the studied magmatic dynamics. In particular, results show that these dynamics induce deformations similar to those measured at Campi Flegrei and seismic signals with energies concentrated on the typical frequency bands observed in volcanic areas. The present work shows that an approach based on the solution of equations describing the physics of processes within a magmatic fluid and the surrounding rock system is able to recognise and describe the relationships between geophysical signals detectable on the surface and deep magma dynamics. Therefore, the results suggest that the combined study of geophysical data and informations from numerical simulations can allow in a near future a more ecient evaluation of the short term volcanic hazard.

The port-Hamiltonian framework as a comprehensive approach to model and simulate complex systems

This thesis describes modelling tools and methods suited for complex systems (systems that typically are represented by a plurality of models). The basic idea is that all models representing the system should be linked by well-defined model operations in order to build a structured repository of information, a hierarchy of models. The port-Hamiltonian framework is a good candidate to solve this kind of problems as it supports the most important model operations natively. The thesis in particular addresses the problem of integrating distributed parameter systems in a model hierarchy, and shows two possible mechanisms to do that: a finite-element discretization in port-Hamiltonian form, and a structure-preserving model order reduction for discretized models obtainable from commercial finite-element packages.

A model for diffusive and displacive phase transitions in steels

Heat treatment of steels is a process of fundamental importance in tailoring the properties of a material to the desired application; developing a model able to describe such process would allow to predict the microstructure obtained from the treatment and the consequent mechanical properties of the material. A steel, during a heat treatment, can undergo two different kinds of phase transitions [p.t.]: diffusive (second order p.t.) and displacive (first order p.t.); in this thesis, an attempt to describe both in a thermodynamically consistent framework is made; a phase field, diffuse interface model accounting for the coupling between thermal, chemical and mechanical effects is developed, and a way to overcome the difficulties arising from the treatment of the non-local effects (gradient terms) is proposed. The governing equations are the balance of linear momentum equation, the Cahn-Hilliard equation and the balance of internal energy equation. The model is completed with a suitable description of the free energy, from which constitutive relations are drawn. The equations are then cast in a variational form and different numerical techniques are used to deal with the principal features of the model: time-dependency, non-linearity and presence of high order spatial derivatives. Simulations are performed using DOLFIN, a C++ library for the automated solution of partial differential equations by means of the finite element method; results are shown for different test-cases. The analysis is reduced to a two dimensional setting, which is simpler than a three dimensional one, but still meaningful.

Modeling, design and experimental characterization of Micro-Electro-Mechanical-Systems for gas chromatographic applications

Design parameters, process flows, electro-thermal-fluidic simulations and experimental characterizations of Micro-Electro-Mechanical-Systems (MEMS) suited for gas-chromatographic (GC) applications are presented and thoroughly described in this thesis, whose topic belongs to the research activities the Institute for Microelectronics and Microsystems (IMM)-Bologna is involved since several years, i.e. the development of micro-systems for chemical analysis, based on silicon micro-machining techniques and able to perform analysis of complex gaseous mixtures, especially in the field of environmental monitoring. In this regard, attention has been focused on the development of micro-fabricated devices to be employed in a portable mini-GC system for the analysis of aromatic Volatile Organic Compounds (VOC) like Benzene, Toluene, Ethyl-benzene and Xylene (BTEX), i.e. chemical compounds which can significantly affect environment and human health because of their demonstrated carcinogenicity (benzene) or toxicity (toluene, xylene) even at parts per billion (ppb) concentrations. The most significant results achieved through the laboratory functional characterization of the mini-GC system have been reported, together with in-field analysis results carried out in a station of the Bologna air monitoring network and compared with those provided by a commercial GC system. The development of more advanced prototypes of micro-fabricated devices specifically suited for FAST-GC have been also presented (silicon capillary columns, Ultra-Low-Power (ULP) Metal OXide (MOX) sensor, Thermal Conductivity Detector (TCD)), together with the technological processes for their fabrication. The experimentally demonstrated very high sensitivity of ULP-MOX sensors to VOCs, coupled with the extremely low power consumption, makes the developed ULP-MOX sensor the most performing metal oxide sensor reported up to now in literature, while preliminary test results proved that the developed silicon capillary columns are capable of performances comparable to those of the best fused silica capillary columns. Finally, the development and the validation of a coupled electro-thermal Finite Element Model suited for both steady-state and transient analysis of the micro-devices has been described, and subsequently implemented with a fluidic part to investigate devices behaviour in presence of a gas flowing with certain volumetric flow rates.

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.

Experimental Analysis and Numerical Simulation of Quench in Superconducting HTS Tapes and Coils

The quench characteristics of second generation (2 G) YBCO Coated Conductor (CC) tapes are of fundamental importance for the design and safe operation of superconducting cables and magnets based on this material. Their ability to transport high current densities at high temperature, up to 77 K, and at very high fields, over 20 T, together with the increasing knowledge in their manufacturing, which is reducing their cost, are pushing the use of this innovative material in numerous system applications, from high field magnets for research to motors and generators as well as for cables. The aim of this Ph. D. thesis is the experimental analysis and numerical simulations of quench in superconducting HTS tapes and coils. A measurements facility for the characterization of superconducting tapes and coils was designed, assembled and tested. The facility consist of a cryostat, a cryocooler, a vacuum system, resistive and superconducting current leads and signal feedthrough. Moreover, the data acquisition system and the software for critical current and quench measurements were developed. A 2D model was developed using the finite element code COMSOL Multiphysics R . The problem of modeling the high aspect ratio of the tape is tackled by multiplying the tape thickness by a constant factor, compensating the heat and electrical balance equations by introducing a material anisotropy. The model was then validated both with the results of a 1D quench model based on a non-linear electric circuit coupled to a thermal model of the tape, to literature measurements and to critical current and quench measurements made in the cryogenic facility. Finally the model was extended to the study of coils and windings with the definition of the tape and stack homogenized properties. The procedure allows the definition of a multi-scale hierarchical model, able to simulate the windings with different degrees of detail.

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.