972 resultados para Neumann boundary conditions
Resumo:
In dieser Arbeit werden drei wasserstoffverbrückte Systeme in der kondensierten Phase mit Hilfe von first-principles-Elektronenstruktur-Rechnungen untersucht, die auf der Dichtefunktionaltheorie (DFT) unter periodischen Randbedingungen basieren. Ihre lokalen Konformationen und Wasserstoffbrückenbindungen werden mittels ab-initio Molekulardynamiksimulationen berechnet und weiterhin durch die Bestimmung ihrer spektroskopischen Parameter charakterisiert. Der Schwerpunkt liegt dabei auf lokalen Strukturen und auf schnellen Fluktuationen der Wasserstoffbrückenbindungen, welche von zentraler Bedeutung für die physikalischen und chemischen Eigenschaften der betrachteten Systeme sind. Die für die lokalen, instantanen Konformationen berechneten Spektren werden verwendet, um die physikalischen Prozesse, die hinter den untersuchten Phänomenen stehen, zu erklären: die Wasseradsorption auf metallischen Oberflächen, die Ionensolvatisierung in wässrigen Lösungen und der Protonentransport in protonleitenden Polymeren, welche Prototypen von Membranen für Brennstoffzellen sind. Die Möglichkeit der Vorhersage spektroskopischer Parameter eröffnet vielfältige Möglichkeiten des Dialogs zwischen Experimenten und numerischen Simulationen. Die in dieser Arbeit vorgestellten Ergebnisse zeigen, dass die Zuverlässigkeit dieser theoretischen Berechnungen inzwischen für viele experimentell relevante Systeme ein quantitatives Niveau erreicht hat.
Resumo:
In dieser Arbeit werden Quantum-Hydrodynamische (QHD) Modelle betrachtet, die ihren Einsatz besonders in der Modellierung von Halbleiterbauteilen finden. Das QHD Modell besteht aus den Erhaltungsgleichungen für die Teilchendichte, das Momentum und die Energiedichte, inklusive der Quanten-Korrekturen durch das Bohmsche Potential. Zu Beginn wird eine Übersicht über die bekannten Ergebnisse der QHD Modelle unter Vernachlässigung von Kollisionseffekten gegeben, die aus einem Schrödinger-System für den gemischten-Zustand oder aus der Wigner-Gleichung hergeleitet werden können. Nach der Reformulierung der eindimensionalen QHD Gleichungen mit linearem Potential als stationäre Schrödinger-Gleichung werden die semianalytischen Fassungen der QHD Gleichungen für die Gleichspannungs-Kurve betrachtet. Weiterhin werden die viskosen Stabilisierungen des QHD Modells berücksichtigt, sowie die von Gardner vorgeschlagene numerische Viskosität für das {sf upwind} Finite-Differenzen Schema berechnet. Im Weiteren wird das viskose QHD Modell aus der Wigner-Gleichung mit Fokker-Planck Kollisions-Operator hergeleitet. Dieses Modell enthält die physikalische Viskosität, die durch den Kollision-Operator eingeführt wird. Die Existenz der Lösungen (mit strikt positiver Teilchendichte) für das isotherme, stationäre, eindimensionale, viskose Modell für allgemeine Daten und nichthomogene Randbedingungen wird gezeigt. Die dafür notwendigen Abschätzungen hängen von der Viskosität ab und erlauben daher den Grenzübergang zum nicht-viskosen Fall nicht. Numerische Simulationen der Resonanz-Tunneldiode modelliert mit dem nichtisothermen, stationären, eindimensionalen, viskosen QHD Modell zeigen den Einfluss der Viskosität auf die Lösung. Unter Verwendung des von Degond und Ringhofer entwickelten Quanten-Entropie-Minimierungs-Verfahren werden die allgemeinen QHD-Gleichungen aus der Wigner-Boltzmann-Gleichung mit dem BGK-Kollisions-Operator hergeleitet. Die Herleitung basiert auf der vorsichtige Entwicklung des Quanten-Maxwellians in Potenzen der skalierten Plankschen Konstante. Das so erhaltene Modell enthält auch vertex-Terme und dispersive Terme für die Geschwindigkeit. Dadurch bleibt die Gleichspannungs-Kurve für die Resonanz-Tunneldiode unter Verwendung des allgemeinen QHD Modells in einer Dimension numerisch erhalten. Die Ergebnisse zeigen, dass der dispersive Geschwindigkeits-Term die Lösung des Systems stabilisiert.
Resumo:
Biologische Membranen sind Fettmolekül-Doppelschichten, die sich wie zweidimensionale Flüssigkeiten verhalten. Die Energie einer solchen fluiden Oberfläche kann häufig mit Hilfe eines Hamiltonians beschrieben werden, der invariant unter Reparametrisierungen der Oberfläche ist und nur von ihrer Geometrie abhängt. Beiträge innerer Freiheitsgrade und der Umgebung können in den Formalismus mit einbezogen werden. Dieser Ansatz wird in der vorliegenden Arbeit dazu verwendet, die Mechanik fluider Membranen und ähnlicher Oberflächen zu untersuchen. Spannungen und Drehmomente in der Oberfläche lassen sich durch kovariante Tensoren ausdrücken. Diese können dann z. B. dazu verwendet werden, die Gleichgewichtsposition der Kontaktlinie zu bestimmen, an der sich zwei aneinander haftende Oberflächen voneinander trennen. Mit Ausnahme von Kapillarphänomenen ist die Oberflächenenergie nicht nur abhängig von Translationen der Kontaktlinie, sondern auch von Änderungen in der Steigung oder sogar Krümmung. Die sich ergebenden Randbedingungen entsprechen den Gleichgewichtsbedingungen an Kräfte und Drehmomente, falls sich die Kontaktlinie frei bewegen kann. Wenn eine der Oberflächen starr ist, muss die Variation lokal dieser Fläche folgen. Spannungen und Drehmomente tragen dann zu einer einzigen Gleichgewichtsbedingung bei; ihre Beiträge können nicht mehr einzeln identifiziert werden. Um quantitative Aussagen über das Verhalten einer fluiden Oberfläche zu machen, müssen ihre elastischen Eigenschaften bekannt sein. Der "Nanotrommel"-Versuchsaufbau ermöglicht es, Membraneigenschaften lokal zu untersuchen: Er besteht aus einer porenüberspannenden Membran, die während des Experiments durch die Spitze eines Rasterkraftmikroskops in die Pore gedrückt wird. Der lineare Verlauf der resultierenden Kraft-Abstands-Kurven kann mit Hilfe der in dieser Arbeit entwickelten Theorie reproduziert werden, wenn der Einfluss von Adhäsion zwischen Spitze und Membran vernachlässigt wird. Bezieht man diesen Effekt in die Rechnungen mit ein, ändert sich das Resultat erheblich: Kraft-Abstands-Kurven sind nicht länger linear, Hysterese und nichtverschwindende Trennkräfte treten auf. Die Voraussagen der Rechnungen könnten in zukünftigen Experimenten dazu verwendet werden, Parameter wie die Biegesteifigkeit der Membran mit einer Auflösung im Nanometerbereich zu bestimmen. Wenn die Materialeigenschaften bekannt sind, können Probleme der Membranmechanik genauer betrachtet werden. Oberflächenvermittelte Wechselwirkungen sind in diesem Zusammenhang ein interessantes Beispiel. Mit Hilfe des oben erwähnten Spannungstensors können analytische Ausdrücke für die krümmungsvermittelte Kraft zwischen zwei Teilchen, die z. B. Proteine repräsentieren, hergeleitet werden. Zusätzlich wird das Gleichgewicht der Kräfte und Drehmomente genutzt, um mehrere Bedingungen an die Geometrie der Membran abzuleiten. Für den Fall zweier unendlich langer Zylinder auf der Membran werden diese Bedingungen zusammen mit Profilberechnungen kombiniert, um quantitative Aussagen über die Wechselwirkung zu treffen. Theorie und Experiment stoßen an ihre Grenzen, wenn es darum geht, die Relevanz von krümmungsvermittelten Wechselwirkungen in der biologischen Zelle korrekt zu beurteilen. In einem solchen Fall bieten Computersimulationen einen alternativen Ansatz: Die hier präsentierten Simulationen sagen voraus, dass Proteine zusammenfinden und Membranbläschen (Vesikel) bilden können, sobald jedes der Proteine eine Mindestkrümmung in der Membran induziert. Der Radius der Vesikel hängt dabei stark von der lokal aufgeprägten Krümmung ab. Das Resultat der Simulationen wird in dieser Arbeit durch ein approximatives theoretisches Modell qualitativ bestätigt.
Resumo:
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.
Resumo:
Con gli strumenti informatici disponibili oggi per le industrie, in particolar modo coi software CAE, le possibile simulare in maniera più che soddisfacente i fenomeni fisici presenti in natura. Anche il raffreddamento di un manufatto in polimero può venire simulato, a patto che si conoscano tutti i dati dei materiali e delle condizioni al contorno. Per quanto riguarda i dati dei materiali, i produttori di polimeri sono molto spesso in grado di fornirli, mentre le condizioni al contorno devono essere padroneggiate dal detentore della tecnologia. Nella pratica, tale conoscenza è al più incompleta, quindi si fanno ipotesi per colmare le lacune. Una tra le ipotesi più forti fatte è quella di una perfetta conduzione all'interfaccia tra due corpi. Questo è un vincolo troppo forte, se paragonato alla precisione di tutti gli altri dati necessari alla simulazione, e quindi si è deciso di eseguire una campagna sperimentale per stimare la resistenza al passaggio flusso termico all'interfaccia polimero-stampo ovvero determinare la conduttanza termica di contatto. L'attività svolta in questa tesi di dottorato ha come scopo quello di fornire un contributo significativo allo sviluppo e al miglioramento dell'efficienza termica degli stampi di formatura dei polimeri termoplastici con tecnologia a compressione.
Resumo:
La Comunità Europea, alla luce dei recenti eventi alluvionali occorsi nei Paesi Membri ed al progressivo aumento dei danni economici da essi provocati, ha recentemente emanato una direttiva (Direttiva Europea 2007/60/CE, Flood Directive) per la valutazione e la predisposizione di piani di gestione del rischio idraulico alluvionale. Con riferimento a tale contesto l’attività di ricerca condotta si è concentrata sulla valutazione delle potenzialità offerte dalla modellistica numerico-idraulica mono e bidimensionale quale strumento per l’attuazione della Direttiva 2007/60. Le attività sono state affrontate ponendo particolare attenzione alla valutazione dei termini di incertezza che caratterizzano l’applicazione dei modelli numerico-idraulici, esaminando i possibili effetti di tale incertezza sulla mappatura della pericolosità idraulica. In particolare, lo studio si concentra su diversi tratti fluviali del corso medio inferiore del Fiume Po e si articola in tre parti: 1) analisi dell’incertezza connessa alla definizione delle scale di deflusso in una generica sezione fluviale e valutazione dei suoi effetti sulla calibrazione dei modelli numerici quasi-bidimensionali (quasi-2D); 2) definizione di mappe probabilistiche di allagamento per tratti fluviali arginati in presenza di tre sorgenti di incertezza: incertezza nelle condizioni al contorno di monte, nelle condizioni di valle e nell’identificazione delle eventuali brecce arginali; 3) valutazione dell’applicabilità di un modello quasi-2D per la definizione, a grande scala spaziale, di strategie alternative al tradizionale rialzo dei manufatti arginali per la mitigazione del rischio alluvionale associato a eventi di piena catastrofici. Le analisi condotte, oltre ad aver definito e valutato le potenzialità di metodologie e modelli idraulici a diversa complessità, hanno evidenziato l’entità e l’impatto dei più importanti elementi d’incertezza, sottolineando come la corretta mappatura della pericolosità idraulica debba sempre essere accompagnata da una valutazione della sua incertezza.
Resumo:
In the thesis, we discuss some aspects of 1D quantum systems related to entanglement entropies; in particular, we develop a new numerical method for the detection of crossovers in Luttinger liquids, and we discuss the behaviour of Rényi entropies in open conformal systems, when the boundary conditions preserve their conformal invariance.
Resumo:
In the present work, a multi physics simulation of an innovative safety system for light water nuclear reactor is performed, with the aim to increase the reliability of its main decay heat removal system. The system studied, denoted by the acronym PERSEO (in Pool Energy Removal System for Emergency Operation) is able to remove the decay power from the primary side of the light water nuclear reactor through a heat suppression pool. The experimental facility, located at SIET laboratories (PIACENZA), is an evolution of the Thermal Valve concept where the triggering valve is installed liquid side, on a line connecting two pools at the bottom. During the normal operation, the valve is closed, while in emergency conditions it opens, the heat exchanger is flooded with consequent heat transfer from the primary side to the pool side. In order to verify the correct system behavior during long term accidental transient, two main experimental PERSEO tests are analyzed. For this purpose, a coupling between the mono dimensional system code CATHARE, which reproduces the system scale behavior, with a three-dimensional CFD code NEPTUNE CFD, allowing a full investigation of the pools and the injector, is implemented. The coupling between the two codes is realized through the boundary conditions. In a first analysis, the facility is simulated by the system code CATHARE V2.5 to validate the results with the experimental data. The comparison of the numerical results obtained shows a different void distribution during the boiling conditions inside the heat suppression pool for the two cases of single nodalization and three volume nodalization scheme of the pool. Finaly, to improve the investigation capability of the void distribution inside the pool and the temperature stratification phenomena below the injector, a two and three dimensional CFD models with a simplified geometry of the system are adopted.
Resumo:
Liquids under the influence of external fields exhibit a wide range of intriguing phenomena that can be markedly different from the behaviour of a quiescent system. This work considers two different systems — a glassforming Yukawa system and a colloid-polymer mixture — by Molecular Dynamics (MD) computer simulations coupled to dissipative particle dynamics. The former consists of a 50-50 binary mixture of differently-sized, like-charged colloids interacting via a screened Coulomb (Yukawa) potential. Near the glass transition the influence of an external shear field is studied. In particular, the transition from elastic response to plastic flow is of interest. At first, this model is characterised in equilibrium. Upon decreasing temperature it exhibits the typical dynamics of glassforming liquids, i.e. the structural relaxation time τα grows strongly in a rather small temperature range. This is discussed with respect to the mode-coupling theory of the glass transition (MCT). For the simulation of bulk systems under shear, Lees-Edwards boundary conditions are applied. At constant shear rates γ˙ ≫ 1/τα the relevant time scale is given by 1/γ˙ and the system shows shear thinning behaviour. In order to understand the pronounced differences between a quiescent system and a system under shear, the response to a suddenly commencing or terminating shear flow is studied. After the switch-on of the shear field the shear stress shows an overshoot, marking the transition from elastic to plastic deformation, which is connected to a super-diffusive increase of the mean squared displacement. Since the average static structure only depends on the value of the shear stress, it does not discriminate between those two regimes. The distribution of local stresses, in contrast, becomes broader as soon as the system starts flowing. After a switch-off of the shear field, these additional fluctuations are responsible for the fast decay of stresses, which occurs on a time scale 1/γ˙ . The stress decay after a switch-off in the elastic regime, on the other hand, happens on the much larger time scale of structural relaxation τα. While stresses decrease to zero after a switch-off for temperatures above the glass transition, they decay to a finite value for lower temperatures. The obtained results are important for advancing new theoretical approaches in the framework of mode-coupling theory. Furthermore, they suggest new experimental investigations on colloidal systems. The colloid-polymer mixture is studied in the context of the behaviour near the critical point of phase separation. For the MD simulations a new effective model with soft interaction potentials is introduced and its phase diagram is presented. Here, mainly the equilibrium properties of this model are characterised. While the self-diffusion constants of colloids and polymers do not change strongly when the critical point is approached, critical slowing down of interdiffusion is observed. The order parameter fluctuations can be determined through the long-wavelength limit of static structure factors. For this strongly asymmetric mixture it is shown how the relevant structure factor can be extracted by a diagonalisation of a matrix that contains the partial static structure factors. By presenting first results of this model under shear it is demonstrated that it is suitable for non-equilibrium simulations as well.
Resumo:
Photovoltaic (PV) solar panels generally produce electricity in the 6% to 16% efficiency range, the rest being dissipated in thermal losses. To recover this amount, hybrid photovoltaic thermal systems (PVT) have been devised. These are devices that simultaneously convert solar energy into electricity and heat. It is thus interesting to study the PVT system globally from different point of views in order to evaluate advantages and disadvantages of this technology and its possible uses. In particular in Chapter II, the development of the PVT absorber numerical optimization by a genetic algorithm has been carried out analyzing different internal channel profiles in order to find a right compromise between performance and technical and economical feasibility. Therefore in Chapter III ,thanks to a mobile structure built into the university lab, it has been compared experimentally electrical and thermal output power from PVT panels with separated photovoltaic and solar thermal productions. Collecting a lot of experimental data based on different seasonal conditions (ambient temperature,irradiation, wind...),the aim of this mobile structure has been to evaluate average both thermal and electrical increasing and decreasing efficiency values obtained respect to separate productions through the year. In Chapter IV , new PVT and solar thermal equation based models in steady state conditions have been developed by software Dymola that uses Modelica language. This permits ,in a simplified way respect to previous system modelling softwares, to model and evaluate different concepts about PVT panel regarding its structure before prototyping and measuring it. Chapter V concerns instead the definition of PVT boundary conditions into a HVAC system . This was made trough year simulations by software Polysun in order to finally assess the best solar assisted integrated structure thanks to F_save(solar saving energy)factor. Finally, Chapter VI presents the conclusion and the perspectives of this PhD work.
Resumo:
Dal 1999 presso il laboratorio del Centro Agricoltura Ambiente “G. Nicoli” a Crevalcore (BO) è in corso una sperimentazione finalizzata a verificare la possibilità di attuare la tecnica del maschio sterile (SIT) in Italia contro Aedes albopictus. Alcuni aspetti per migliorare l’efficienza di questa struttura pilota, oggetto della presente ricerca, sono stati: 1) studio degli effetti di determinati costituenti della dieta larvale a) sullo sviluppo larvale stesso, per individuare intervalli limite di densità larvale e di concentrazione di cibo in cui è possibile lo sviluppo di tale specie, e b) sulla qualità dei maschi adulti ottenuti; 2) la valutazione di attrezzatura per l’allevamento massale e 3) la possibilità di migliorare la dieta larvale mediante integrazione di carboidrati. Dalle prove di valutazione della dieta larvale si è potuto osservare che, per quanto riguarda i parametri larvali, le due diete denominate “IAEA” (1 e 2) sono risultate più efficaci rispetto alla dieta standard “CAA”. Tali diete sono perciò da preferirsi nel loro possibile impiego in biofabbriche per l’allevamento massale. Le prove condotte sugli adulti allevati con le diverse diete hanno suggerito la necessità di valutare una possibile integrazione di componenti per migliorarne la longevità. Risulta altresì opportuno continuare la ricerca per ottimizzare la dieta larvale così da ottenere maschi di elevata qualità. Grazie ai risultati ottenuti dalle prove per valutare l’impiego di attrezzatura massale (vassoi di grandi dimensioni e carrello) si è potuto definire un modello per l’allevamento di Ae. albopictus con parametri standardizzati di densità larvale, dose di dieta, temperatura dell’acqua di allevamento, percentuale di maschi passati al setacciamento e rendimento di allevamento. Prove future saranno necessarie per testare altri componenti della dieta ricchi in carboidrati, quali saccarosio, da aggiungere alla dieta larvale per migliorare le qualità degli adulti ottenuti senza provocare effetti negativi sui parametri dello sviluppo larvale.
Resumo:
This thesis is concerned with the adsorption and detachment of polymers at planar, rigid surfaces. We have carried out a systematic investigation of adsorption of polymers using analytical techniques as well as Monte Carlo simulations with a coarse grained off-lattice bead spring model. The investigation was carried out in three stages. In the first stage the adsorption of a single multiblock AB copolymer on a solid surface was investigated by means of simulations and scaling analysis. It was shown that the problem could be mapped onto an effective homopolymer problem. Our main result was the phase diagram of regular multiblock copolymers which shows an increase in the critical adsorption potential of the substrate with decreasing size of blocks. We also considered the adsorption of random copolymers which was found to be well described within the annealed disorder approximation. In the next phase, we studied the adsorption kinetics of a single polymer on a flat, structureless surface in the regime of strong physisorption. The idea of a ’stem-flower’ polymer conformation and the mechanism of ’zipping’ during the adsorption process were used to derive a Fokker-Planck equation with reflecting boundary conditions for the time dependent probability distribution function (PDF) of the number of adsorbed monomers. The numerical solution of the time-dependent PDF obtained from a discrete set of coupled differential equations were shown to be in perfect agreement with Monte Carlo simulation results. Finally we studied force induced desorption of a polymer chain adsorbed on an attractive surface. We approached the problem within the framework of two different statistical ensembles; (i) by keeping the pulling force fixed while measuring the position of the polymer chain end, and (ii) by measuring the force necessary to keep the chain end at fixed distance above the adsorbing plane. In the first case we treated the problem within the framework of the Grand Canonical Ensemble approach and derived analytic expressions for the various conformational building blocks, characterizing the structure of an adsorbed linear polymer chain, subject to pulling force of fixed strength. The main result was the phase diagram of a polymer chain under pulling. We demonstrated a novel first order phase transformation which is dichotomic i.e. phase coexistence is not possible. In the second case, we carried out our study in the “fixed height” statistical ensemble where one measures the fluctuating force, exerted by the chain on the last monomer when a chain end is kept fixed at height h over the solid plane at different adsorption strength ε. The phase diagram in the h − ε plane was calculated both analytically and by Monte Carlo simulations. We demonstrated that in the vicinity of the polymer desorption transition a number of properties like fluctuations and probability distribution of various quantities behave differently, if h rather than the force, f, is used as an independent control parameter.
Resumo:
We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. Within a coarse-grained picture, the properties of fluid interfaces are very well described by an effective capillary wave Hamiltonian which governs both the equilibrium interface configuration and the thermal fluctuations (capillary waves) around this equilibrium (or mean-field) position. As postulated by the Goldstone theorem the capillary waves are long-range correlated. The interface breaks the continuous translational symmetry of the system, and in the limit of vanishing external fields - like gravity - it has to be accompanied by easily excitable long wavelength (Goldstone) modes – precisely the capillary waves. In this system the restriction of the long-ranged interface fluctuations by particles gives rise to fluctuation-induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example for the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuating multipole moments of an auxiliary charge density-like field defined on the area enclosed by the contact lines. These fluctuations are coupled to fluctuations of multipole moments of the contact line position (due to the possible position and orientational fluctuations of the colloids). We obtain explicit expressions for the behavior of the Casimir interaction at large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations are suppressed, the Casimir interaction at large distances is isotropic, attractive and long ranged (double-logarithmic in the distance). If, however, colloid fluctuations are included, the Casimir interaction at large distances changes to a power law in the inverse distance and becomes anisotropic. The leading power is 4 if only vertical fluctuations of the colloid center are allowed, and it becomes 8 if also orientational fluctuations are included.
Resumo:
A 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded conical and cylindrical shells subjected to mechanical loadings. Several types of graded materials are investigated. The functionally graded material consists of ceramic and metallic constituents. A four parameter power law function is used. The UTSDT allows the presence of a finite transverse shear stress at the top and bottom surfaces of the graded shell. In addition, the initial curvature effect included in the formulation leads to the generalization of the present theory (GUTSDT). The Generalized Differential Quadrature (GDQ) method is used to discretize the derivatives in the governing equations, the external boundary conditions and the compatibility conditions. Transverse and normal stresses are also calculated by integrating the three dimensional equations of equilibrium in the thickness direction. In this way, the six components of the stress tensor at a point of the conical or cylindrical shell or panel can be given. The initial curvature effect and the role of the power law functions are shown for a wide range of functionally conical and cylindrical shells under various loading and boundary conditions. Finally, numerical examples of the available literature are worked out.
Resumo:
This work presents a comprehensive methodology for the reduction of analytical or numerical stochastic models characterized by uncertain input parameters or boundary conditions. The technique, based on the Polynomial Chaos Expansion (PCE) theory, represents a versatile solution to solve direct or inverse problems related to propagation of uncertainty. The potentiality of the methodology is assessed investigating different applicative contexts related to groundwater flow and transport scenarios, such as global sensitivity analysis, risk analysis and model calibration. This is achieved by implementing a numerical code, developed in the MATLAB environment, presented here in its main features and tested with literature examples. The procedure has been conceived under flexibility and efficiency criteria in order to ensure its adaptability to different fields of engineering; it has been applied to different case studies related to flow and transport in porous media. Each application is associated with innovative elements such as (i) new analytical formulations describing motion and displacement of non-Newtonian fluids in porous media, (ii) application of global sensitivity analysis to a high-complexity numerical model inspired by a real case of risk of radionuclide migration in the subsurface environment, and (iii) development of a novel sensitivity-based strategy for parameter calibration and experiment design in laboratory scale tracer transport.