Modelli non lineari statici e dinamici su dati microeconomici: analisi delle condizioni finanziarie delle famiglie italiane

The thesis studies the economic and financial conditions of Italian households, by using microeconomic data of the Survey on Household Income and Wealth (SHIW) over the period 1998-2006. It develops along two lines of enquiry. First it studies the determinants of households holdings of assets and liabilities and estimates their correlation degree. After a review of the literature, it estimates two non-linear multivariate models on the interactions between assets and liabilities with repeated cross-sections. Second, it analyses households financial difficulties. It defines a quantitative measure of financial distress and tests, by means of non-linear dynamic probit models, whether the probability of experiencing financial difficulties is persistent over time. Chapter 1 provides a critical review of the theoretical and empirical literature on the estimation of assets and liabilities holdings, on their interactions and on households net wealth. The review stresses the fact that a large part of the literature explain households debt holdings as a function, among others, of net wealth, an assumption that runs into possible endogeneity problems. Chapter 2 defines two non-linear multivariate models to study the interactions between assets and liabilities held by Italian households. Estimation refers to a pooling of cross-sections of SHIW. The first model is a bivariate tobit that estimates factors affecting assets and liabilities and their degree of correlation with results coherent with theoretical expectations. To tackle the presence of non normality and heteroskedasticity in the error term, generating non consistent tobit estimators, semi-parametric estimates are provided that confirm the results of the tobit model. The second model is a quadrivariate probit on three different assets (safe, risky and real) and total liabilities; the results show the expected patterns of interdependence suggested by theoretical considerations. Chapter 3 reviews the methodologies for estimating non-linear dynamic panel data models, drawing attention to the problems to be dealt with to obtain consistent estimators. Specific attention is given to the initial condition problem raised by the inclusion of the lagged dependent variable in the set of explanatory variables. The advantage of using dynamic panel data models lies in the fact that they allow to simultaneously account for true state dependence, via the lagged variable, and unobserved heterogeneity via individual effects specification. Chapter 4 applies the models reviewed in Chapter 3 to analyse financial difficulties of Italian households, by using information on net wealth as provided in the panel component of the SHIW. The aim is to test whether households persistently experience financial difficulties over time. A thorough discussion is provided of the alternative approaches proposed by the literature (subjective/qualitative indicators versus quantitative indexes) to identify households in financial distress. Households in financial difficulties are identified as those holding amounts of net wealth lower than the value corresponding to the first quartile of net wealth distribution. Estimation is conducted via four different methods: the pooled probit model, the random effects probit model with exogenous initial conditions, the Heckman model and the recently developed Wooldridge model. Results obtained from all estimators accept the null hypothesis of true state dependence and show that, according with the literature, less sophisticated models, namely the pooled and exogenous models, over-estimate such persistence.

Metodi di ottimizzazione morfologica nel progetto preliminare di propulsori aeronautici avanzati

The aim of this Doctoral Thesis is to develop a genetic algorithm based optimization methods to find the best conceptual design architecture of an aero-piston-engine, for given design specifications. Nowadays, the conceptual design of turbine airplanes starts with the aircraft specifications, then the most suited turbofan or turbo propeller for the specific application is chosen. In the aeronautical piston engines field, which has been dormant for several decades, as interest shifted towards turboaircraft, new materials with increased performance and properties have opened new possibilities for development. Moreover, the engine’s modularity given by the cylinder unit, makes it possible to design a specific engine for a given application. In many real engineering problems the amount of design variables may be very high, characterized by several non-linearities needed to describe the behaviour of the phenomena. In this case the objective function has many local extremes, but the designer is usually interested in the global one. The stochastic and the evolutionary optimization techniques, such as the genetic algorithms method, may offer reliable solutions to the design problems, within acceptable computational time. The optimization algorithm developed here can be employed in the first phase of the preliminary project of an aeronautical piston engine design. It’s a mono-objective genetic algorithm, which, starting from the given design specifications, finds the engine propulsive system configuration which possesses minimum mass while satisfying the geometrical, structural and performance constraints. The algorithm reads the project specifications as input data, namely the maximum values of crankshaft and propeller shaft speed and the maximal pressure value in the combustion chamber. The design variables bounds, that describe the solution domain from the geometrical point of view, are introduced too. In the Matlab® Optimization environment the objective function to be minimized is defined as the sum of the masses of the engine propulsive components. Each individual that is generated by the genetic algorithm is the assembly of the flywheel, the vibration damper and so many pistons, connecting rods, cranks, as the number of the cylinders. The fitness is evaluated for each individual of the population, then the rules of the genetic operators are applied, such as reproduction, mutation, selection, crossover. In the reproduction step the elitist method is applied, in order to save the fittest individuals from a contingent mutation and recombination disruption, making it undamaged survive until the next generation. Finally, as the best individual is found, the optimal dimensions values of the components are saved to an Excel® file, in order to build a CAD-automatic-3D-model for each component of the propulsive system, having a direct pre-visualization of the final product, still in the engine’s preliminary project design phase. With the purpose of showing the performance of the algorithm and validating this optimization method, an actual engine is taken, as a case study: it’s the 1900 JTD Fiat Avio, 4 cylinders, 4T, Diesel. Many verifications are made on the mechanical components of the engine, in order to test their feasibility and to decide their survival through generations. A system of inequalities is used to describe the non-linear relations between the design variables, and is used for components checking for static and dynamic loads configurations. The design variables geometrical boundaries are taken from actual engines data and similar design cases. Among the many simulations run for algorithm testing, twelve of them have been chosen as representative of the distribution of the individuals. Then, as an example, for each simulation, the corresponding 3D models of the crankshaft and the connecting rod, have been automatically built. In spite of morphological differences among the component the mass is almost the same. The results show a significant mass reduction (almost 20% for the crankshaft) in comparison to the original configuration, and an acceptable robustness of the method have been shown. The algorithm here developed is shown to be a valid method for an aeronautical-piston-engine preliminary project design optimization. In particular the procedure is able to analyze quite a wide range of design solutions, rejecting the ones that cannot fulfill the feasibility design specifications. This optimization algorithm could increase the aeronautical-piston-engine development, speeding up the production rate and joining modern computation performances and technological awareness to the long lasting traditional design experiences.

Collective effects for the LHC injectors: non-ultrarelativistic approaches

The upgrade of the CERN accelerator complex has been planned in order to further increase the LHC performances in exploring new physics frontiers. One of the main limitations to the upgrade is represented by the collective instabilities. These are intensity dependent phenomena triggered by electromagnetic fields excited by the interaction of the beam with its surrounding. These fields are represented via wake fields in time domain or impedances in frequency domain. Impedances are usually studied assuming ultrarelativistic bunches while we mainly explored low and medium energy regimes in the LHC injector chain. In a non-ultrarelativistic framework we carried out a complete study of the impedance structure of the PSB which accelerates proton bunches up to 1.4 GeV. We measured the imaginary part of the impedance which creates betatron tune shift. We introduced a parabolic bunch model which together with dedicated measurements allowed us to point to the resistive wall impedance as the source of one of the main PSB instability. These results are particularly useful for the design of efficient transverse instability dampers. We developed a macroparticle code to study the effect of the space charge on intensity dependent instabilities. Carrying out the analysis of the bunch modes we proved that the damping effects caused by the space charge, which has been modelled with semi-analytical method and using symplectic high order schemes, can increase the bunch intensity threshold. Numerical libraries have been also developed in order to study, via numerical simulations of the bunches, the impedance of the whole CERN accelerator complex. On a different note, the experiment CNGS at CERN, requires high-intensity beams. We calculated the interpolating Hamiltonian of the beam for highly non-linear lattices. These calculations provide the ground for theoretical and numerical studies aiming to improve the CNGS beam extraction from the PS to the SPS.

Mapping the elastic response of epithelial apical cell membranes suspended across porous array

As the elastic response of cell membranes to mechanical stimuli plays a key role in various cellular processes, novel biophysical strategies to quantify the elasticity of native membranes under physiological conditions at a nanometer scale are gaining interest. In order to investigate the elastic response of apical membranes, elasticity maps of native membrane sheets, isolated from MDCK II (Madine Darby Canine kidney strain II) epithelial cells, were recorded by local indentation with an Atomic Force Microscope (AFM). To exclude the underlying substrate effect on membrane indentation, a highly ordered gold coated porous array with a pore diameter of 1.2 μm was used to support apical membranes. Overlays of fluorescence and AFM images show that intact apical membrane sheets are attached to poly-D-lysine coated porous substrate. Force indentation measurements reveal an extremely soft elastic membrane response if it is indented at the center of the pore in comparison to a hard repulsion on the adjacent rim used to define the exact contact point. A linear dependency of force versus indentation (-dF/dh) up to 100 nm penetration depth enabled us to define an apparent membrane spring constant (kapp) as the slope of a linear fit with a stiffness value of for native apical membrane in PBS. A correlation between fluorescence intensity and kapp is also reported. Time dependent hysteresis observed with native membranes is explained by a viscoelastic solid model of a spring connected to a Kelvin-Voight solid with a time constant of 0.04 s. No hysteresis was reported with chemically fixated membranes. A combined linear and non linear elastic response is suggested to relate the experimental data of force indentation curves to the elastic modulus and the membrane thickness. Membrane bending is the dominant contributor to linear elastic indentation at low loads, whereas stretching is the dominant contributor for non linear elastic response at higher loads. The membrane elastic response was controlled either by stiffening with chemical fixatives or by softening with F-actin disrupters. Overall, the presented setup is ideally suitable to study the interactions of the apical membrane with the underlying cytoskeleton by means of force indentation elasticity maps combined with fluorescence imaging.

Analysis of cumulative effects of multiple stressors on saltmarshes and consideration of management options

Natural systems face pressures exerted by natural physical-chemical forcings and a myriad of co-occurring human stressors that may interact to cause larger than expected effects, thereby presenting a challenge to ecosystem management. This thesis aimed to develop new information that can contribute to reduce the existing knowledge gaps hampering the holistic management of multiple stressors. I undertook a review of the state-of-the-art methods to detect, quantify and predict stressor interactions, identifying techniques that could be applied in this thesis research. Then, I conducted a systematic review of saltmarsh multiple stressor studies in conjunction with a multiple stressor mapping exercise for the study system in order to infer potential important synergistic stressor interactions. This analysis identified key stressors that are affecting the study system, but also pointed to data gaps in terms of driver and pressure data and raised issues for potentially overlooked stressors. Using field mesocosms, I explored how a local stressor (nutrient availability) affects the responses of saltmarsh vegetation to a global stressor (increased inundation) in different soil types. Results indicate that saltmarsh vegetation would be more drastically affected by increased inundation in low than in medium organic matter soils, and especially in estuaries already under high nutrient availability. In another field experiment, I examined the challenges of managing co-occurring and potentially interacting local stressors on saltmarsh vegetation: recreational trampling and smothering by deposition of excess macroalgal wrack due to high nutrient loads. Trampling and wrack prevention had interacting effects, causing non-linear responses of the vegetation to simulated management of these stressors, such that vegetation recovered only in those treatments simulating the combined prevention of both stressors. During this research I detected, using molecular genetic methods, a widespread presence of S. anglica (and to a lesser extent S. townsendii), two previously unrecorded non-native Spartinas in the study areas.

Experimental and modeling study of the filtration and oxidation characteristics of a diesel oxidation catalyst and a catalyzed particulate filter

A diesel oxidation catalyst (DOC) with a catalyzed diesel particulate filter (CPF) is an effective exhaust aftertreatment device that reduces particulate emissions from diesel engines, and properly designed DOC-CPF systems provide passive regeneration of the filter by the oxidation of PM via thermal and NO2/temperature-assisted means under various vehicle duty cycles. However, controlling the backpressure on engines caused by the addition of the CPF to the exhaust system requires a good understanding of the filtration and oxidation processes taking place inside the filter as the deposition and oxidation of solid particulate matter (PM) change as functions of loading time. In order to understand the solid PM loading characteristics in the CPF, an experimental and modeling study was conducted using emissions data measured from the exhaust of a John Deere 6.8 liter, turbocharged and after-cooled engine with a low-pressure loop EGR system and a DOC-CPF system (or a CCRT® - Catalyzed Continuously Regenerating Trap®, as named by Johnson Matthey) in the exhaust system. A series of experiments were conducted to evaluate the performance of the DOC-only, CPF-only and DOC-CPF configurations at two engine speeds (2200 and 1650 rpm) and various loads on the engine ranging from 5 to 100% of maximum torque at both speeds. Pressure drop across the DOC and CPF, mass deposited in the CPF at the end of loading, upstream and downstream gaseous and particulate emissions, and particle size distributions were measured at different times during the experiments to characterize the pressure drop and filtration efficiency of the DOCCPF system as functions of loading time. Pressure drop characteristics measured experimentally across the DOC-CPF system showed a distinct deep-bed filtration region characterized by a non-linear pressure drop rise, followed by a transition region, and then by a cake-filtration region with steadily increasing pressure drop with loading time at engine load cases with CPF inlet temperatures less than 325 °C. At the engine load cases with CPF inlet temperatures greater than 360 °C, the deep-bed filtration region had a steep rise in pressure drop followed by a decrease in pressure drop (due to wall PM oxidation) in the cake filtration region. Filtration efficiencies observed during PM cake filtration were greater than 90% in all engine load cases. Two computer models, i.e., the MTU 1-D DOC model and the MTU 1-D 2-layer CPF model were developed and/or improved from existing models as part of this research and calibrated using the data obtained from these experiments. The 1-D DOC model employs a three-way catalytic reaction scheme for CO, HC and NO oxidation, and is used to predict CO, HC, NO and NO2 concentrations downstream of the DOC. Calibration results from the 1-D DOC model to experimental data at 2200 and 1650 rpm are presented. The 1-D 2-layer CPF model uses a ‘2-filters in series approach’ for filtration, PM deposition and oxidation in the PM cake and substrate wall via thermal (O2) and NO2/temperature-assisted mechanisms, and production of NO2 as the exhaust gas mixture passes through the CPF catalyst washcoat. Calibration results from the 1-D 2-layer CPF model to experimental data at 2200 rpm are presented. Comparisons of filtration and oxidation behavior of the CPF at sample load-cases in both configurations are also presented. The input parameters and selected results are also compared with a similar research work with an earlier version of the CCRT®, to compare and explain differences in the fundamental behavior of the CCRT® used in these two research studies. An analysis of the results from the calibrated CPF model suggests that pressure drop across the CPF depends mainly on PM loading and oxidation in the substrate wall, and also that the substrate wall initiates PM filtration and helps in forming a PM cake layer on the wall. After formation of the PM cake layer of about 1-2 µm on the wall, the PM cake becomes the primary filter and performs 98-99% of PM filtration. In all load cases, most of PM mass deposited was in the PM cake layer, and PM oxidation in the PM cake layer accounted for 95-99% of total PM mass oxidized during loading. Overall PM oxidation efficiency of the DOC-CPF device increased with increasing CPF inlet temperatures and NO2 flow rates, and was higher in the CCRT® configuration compared to the CPF-only configuration due to higher CPF inlet NO2 concentrations. Filtration efficiencies greater than 90% were observed within 90-100 minutes of loading time (starting with a clean filter) in all load cases, due to the fact that the PM cake on the substrate wall forms a very efficient filter. A good strategy for maintaining high filtration efficiency and low pressure drop of the device while performing active regeneration would be to clean the PM cake filter partially (i.e., by retaining a cake layer of 1-2 µm thickness on the substrate wall) and to completely oxidize the PM deposited in the substrate wall. The data presented support this strategy.

Model to describe the mode I fracture of steel fiber reinforced ultra-high performance concrete

Ultra-high performance fiber reinforced concrete (UHPFRC) has arisen from the implementation of a variety of concrete engineering and materials science concepts developed over the last century. This material offers superior strength, serviceability, and durability over its conventional counterparts. One of the most important differences for UHPFRC over other concrete materials is its ability to resist fracture through the use of randomly dispersed discontinuous fibers and improvements to the fiber-matrix bond. Of particular interest is the materials ability to achieve higher loads after first crack, as well as its high fracture toughness. In this research, a study of the fracture behavior of UHPFRC with steel fibers was conducted to look at the effect of several parameters related to the fracture behavior and to develop a fracture model based on a non-linear curve fit of the data. To determine this, a series of three-point bending tests were performed on various single edge notched prisms (SENPs). Compression tests were also performed for quality assurance. Testing was conducted on specimens of different cross-sections, span/depth (S/D) ratios, curing regimes, ages, and fiber contents. By comparing the results from prisms of different sizes this study examines the weakening mechanism due to the size effect. Furthermore, by employing the concept of fracture energy it was possible to obtain a comparison of the fracture toughness and ductility. The model was determined based on a fit to P-w fracture curves, which was cross referenced for comparability to the results. Once obtained the model was then compared to the models proposed by the AFGC in the 2003 and to the ACI 544 model for conventional fiber reinforced concretes.

Some past decision theory models for euro construction model codes and for road drainage in Spain, and modest hints with multi-criteria methods for agro and environmental assurance

The authors are from UPM and are relatively grouped, and all have intervened in different academic or real cases on the subject, at different times as being of different age. With precedent from E. Torroja and A. Páez in Madrid Spain Safety Probabilistic models for concrete about 1957, now in ICOSSAR conferences, author J.M. Antón involved since autumn 1967 for euro-steel construction in CECM produced a math model for independent load superposition reductions, and using it a load coefficient pattern for codes in Rome Feb. 1969, practically adopted for European constructions, giving in JCSS Lisbon Feb. 1974 suggestion of union for concrete-steel-al.. That model uses model for loads like Gumbel type I, for 50 years for one type of load, reduced to 1 year to be added to other independent loads, the sum set in Gumbel theories to 50 years return period, there are parallel models. A complete reliability system was produced, including non linear effects as from buckling, phenomena considered somehow in actual Construction Eurocodes produced from Model Codes. The system was considered by author in CEB in presence of Hydraulic effects from rivers, floods, sea, in reference with actual practice. When redacting a Road Drainage Norm in MOPU Spain an optimization model was realized by authors giving a way to determine the figure of Return Period, 10 to 50 years, for the cases of hydraulic flows to be considered in road drainage. Satisfactory examples were a stream in SE of Spain with Gumbel Type I model and a paper of Ven Te Chow with Mississippi in Keokuk using Gumbel type II, and the model can be modernized with more varied extreme laws. In fact in the MOPU drainage norm the redacting commission acted also as expert to set a table of return periods for elements of road drainage, in fact as a multi-criteria complex decision system. These precedent ideas were used e.g. in wide Codes, indicated in symposia or meetings, but not published in journals in English, and a condensate of contributions of authors is presented. The authors are somehow involved in optimization for hydraulic and agro planning, and give modest hints of intended applications in presence of agro and environment planning as a selection of the criteria and utility functions involved in bayesian, multi-criteria or mixed decision systems. Modest consideration is made of changing in climate, and on the production and commercial systems, and on others as social and financial.

A simulation method to estimate closing forces in car-sealing rubber elements

The door-closing process can reinforce the impression of a solid, rock-proof, car body or of a rather cheap, flimsy vehicle. As there are no real prototypes during rubber profile bidding-out stages, engineers need to carry out non-linear numerical simulations that involve complex phenomena as well as static and dynamic loads for several profile candidates. This paper presents a structured virtual design tool based on FEM, including constitutive laws and incompressibility constraints allowing to predict more realistically the final closing forces and even to estimate sealing overpressure as an additional guarantee of noise insulation. Comparisons with results of physical tests are performed.

Low-cost retrofitting solutions for RC frames using masonry infill panels

A large number of reinforced concrete (RC) frame structures built in earthquake-prone areas such as Haiti are vulnerable to strong ground motions. Structures in developing countries need low-cost seismic retrofit solutions to reduce their vulnerability. This paper investigates the feasibility of using masonry infill walls to reduce deformations and damage caused by strong ground motions in brittle and weak RC frames designed only for gravity loads. A numerical experiment was conducted in which several idealized prototypes representing RC frame structures of school buildings damaged during the Port-au-Prince earthquake (Haiti, 2010) were strengthened by adding elements representing masonry infill walls arranged in different configurations. Each configuration was characterized by the ratio Rm of the area of walls in the direction of the ground motion (in plan) installed in each story to the total floor area. The numerical representations of these idealized RC frame structures with different values of Rm were (hypothetically) subjected to three major earthquakes with peak ground accelerations of approximately 0.5g. The results of the non-linear dynamic response analyses were summarized in tentative relationships between Rm and four parameters commonly used to characterize the seismic response of structures: interstory drift, Park and Ang indexes of damage, and total amount of energy dissipated by the main frame. It was found that Rm=4% is a reasonable minimum design value for seismic retrofitting purposes in cases in which available resources are not sufficient to afford conventional retrofit measures.

Flutter margin with non-linearities: real-time prediction of flutter onset speed

The present article shows a procedure to predict the flutter speed based on real-time tuning of a quasi non-linear aeroelastic model. A two-dimensional non-linear (freeplay) aeroeslastic model is implemented inMatLab/Simulink with incompressible aerodynamic conditions. A comparison with real compressible conditions is provided. Once the numerical validation is accomplished, a parametric aeroelastic model is built in order to describe the proposed procedure and contribute to reduce the number of flight hours needed to expand the flutter envelope.

Fracture behaviour of notched round bars made of PMMA subjected to torsion at -60 °C

This paper presents seventy new experimental results from PMMA notched specimens tested under torsion at 60 C. The notch root radius ranges from 0.025 to 7.0 mm. At this temperature the non-linear effects previously observed on specimens of the same material tested at room temperature strongly reduce. The averaged value of the strain energy density over a control volume is used to assess the critical loads to failure. The radius of the control volume and the critical strain energy density are evaluated a priori by using in combination the mode III critical stress intensity factor from cracked-like specimens and the critical stress to failure detected from semicircular notches with a large notch root radius

Moment transfer and influence of transverse beams in interior waffle flat plate-column connections under lateral loading

This paper addresses two aspects of the behavior of interior reinforced concrete waffle flat plate?column connections under lateral loads: the share of the unbalanced moment between flexure and excentric shear, and the effect of the transverse beams. A non-linear finite element model (benchmark model) was developed and calibrated with the results of quasi-static cyclic tests conducted on a 3/5 scale specimen. First, from this numerical model, the portion cv of the unbalanced moment transferred by the excentricity of shear about the centroid of the critical sections defined by Eurocode 2 (EC-2) and by ACI 318-11 was calculated and compared with the share-out prescribed by these codes. It is found that while the critical section of EC-2 is consistent with the cv provided by this code, in the case of ACI 318-11, the value assigned to cv is far below (about 50% smaller) the actual one obtained with the numerical simulations. Second, from the benchmark model, seven additional models were developed by varying the depth D of the transverse beam over the thickness h of the plate. It was found that the ductility of the connection and the effective width of the plate can respectively be increased up to 50% and 10% by raising D/h to 2 and 1.5.

Discontinuous solutions and boundary value problems for non-linearly elastic fibre-reinforced materials

En este trabajo se han analizado varios problemas en el contexto de la elasticidad no lineal basándose en modelos constitutivos representativos. En particular, se han analizado problemas relacionados con el fenómeno de perdida de estabilidad asociada con condiciones de contorno en el caso de material reforzados con fibras. Cada problema se ha formulado y se ha analizado por separado en diferentes capítulos. En primer lugar se ha mostrado el análisis del gradiente de deformación discontinuo para un material transversalmente isótropo, en particular, el modelo del material considerado consiste de una base neo-Hookeana isótropa incrustada con fibras de refuerzo direccional caracterizadas con un solo parámetro. La solución de este problema se vincula con instabilidades que dan lugar al mecanismo de fallo conocido como banda de cortante. La perdida de elipticidad de las ecuaciones diferenciales de equilibrio es una condición necesaria para que aparezca este tipo de soluciones y por tanto las inestabilidades asociadas. En segundo lugar se ha analizado una deformación combinada de extensión, inación y torsión de un tubo cilíndrico grueso donde se ha encontrado que la deformación citada anteriormente puede ser controlada solo para determinadas direcciones de las fibras refuerzo. Para entender el comportamiento elástico del tubo considerado se ha ilustrado numéricamente los resultados obtenidos para las direcciones admisibles de las fibras de refuerzo bajo la deformación considerada. En tercer lugar se ha estudiado el caso de un tubo cilíndrico grueso reforzado con dos familias de fibras sometido a cortante en la dirección azimutal para un modelo de refuerzo especial. En este problema se ha encontrado que las inestabilidades que aparecen en el material considerado están asociadas con lo que se llama soluciones múltiples de la ecuación diferencial de equilibrio. Se ha encontrado que el fenómeno de instabilidad ocurre en un estado de deformación previo al estado de deformación donde se pierde la elipticidad de la ecuación diferencial de equilibrio. También se ha demostrado que la condición de perdida de elipticidad y ^W=2 = 0 (la segunda derivada de la función de energía con respecto a la deformación) son dos condiciones necesarias para la existencia de soluciones múltiples. Finalmente, se ha analizado detalladamente en el contexto de elipticidad un problema de un tubo cilíndrico grueso sometido a una deformación combinada en las direcciones helicoidal, axial y radial para distintas geotermias de las fibras de refuerzo . In the present work four main problems have been addressed within the framework of non-linear elasticity based on representative constitutive models. Namely, problems related to the loss of stability phenomena associated with boundary value problems for fibre-reinforced materials. Each of the considered problems is formulated and analysed separately in different chapters. We first start with the analysis of discontinuous deformation gradients for a transversely isotropic material under plane deformation. In particular, the material model is an augmented neo-Hookean base with a simple unidirectional reinforcement characterised by a single parameter. The solution of this problem is related to material instabilities and it is associated with a shear band-type failure mode. The loss of ellipticity of the governing differential equations is a necessary condition for the existence of these material instabilities. The second problem involves a detailed analysis of the combined non-linear extension, inflation and torsion of a thick-walled circular cylindrical tube where it has been found that the aforementioned deformation is controllable only for certain preferred directions of transverse isotropy. Numerical results have been illustrated to understand the elastic behaviour of the tube for the admissible preferred directions under the considered deformation. The third problem deals with the analysis of a doubly fibre-reinforced thickwalled circular cylindrical tube undergoing pure azimuthal shear for a special class of the reinforcing model where multiple non-smooth solutions emerge. The associated instability phenomena are found to occur prior to the point where the nominal stress tensor changes monotonicity in a particular direction. It has been also shown that the loss of ellipticity condition that arises from the equilibrium equation and ^W=2 = 0 (the second derivative of the strain-energy function with respect to the deformation) are equivalent necessary conditions for the emergence of multiple solutions for the considered material. Finally, a detailed analysis in the basis of the loss of ellipticity of the governing differential equations for a combined helical, axial and radial elastic deformations of a fibre-reinforced circular cylindrical tube is carried out.

Cálculo de pilas con aparatos de apoyo tipo POT y tablero con punto fijo

In recent years a great number of high speed railway bridges have been constructed within the Spanish borders. Due to the demanding high speed trains route's geometrical requirements, bridges frequently show remarkable lengths. This fact is the main reason why railway bridges are overall longer than roadway bridges. In the same line, it is also worth highlighting the importance of high speed trains braking forces compared to vehicles. While vehicles braking forces can be tackled easily, the railway braking forces demand the existence of a fixed-point. It is generally located at abutments where the no-displacements requirement can be more easily achieved. In some other cases the fixed-point is placed in one of the interior columns. As a consequence of these bridges' length and the need of a fixed-point, temperature, creep and shrinkage strains lead to fairly significant deck displacements, which become greater with the distance to the fixed-point. These displacements need to be accommodated by the piers and bearings deformation. Regular elastomeric bearings are not able to allow such displacements and therefore are not suitable for this task. For this reason, the use of sliding PTFE POT bearings has been an extensive practice mainly because they permit sliding with low friction. This is not the only reason of the extensive use of these bearings to high-speed railways bridges. The value of the vertical loads at each bent is significantly higher than in roadway bridges. This is so mainly because the live loads due to trains traffic are much greater than vehicles. Thus, gravel rails foundation represents a non-negligible permanent load at all. All this together increases the value of vertical loads to be withstood. This high vertical load demand discards the use of conventional bearings for excessive compressions. The PTFE POT bearings' higher technology allows to accommodate this level of compression thanks to their design. The previously explained high-speed railway bridge configuration leads to a key fact regarding longitudinal horizontal loads (such as breaking forces) which is the transmission of these loads entirely to the fixed-point alone. Piers do not receive these longitudinal horizontal loads since PTFE POT bearings displayed are longitudinally free-sliding. This means that longitudinal horizontal actions on top of piers will not be forces but imposed displacements. This feature leads to the need to approach these piers design in a different manner that when piers are elastically linked to superstructure, which is the case of elastomeric bearings. In response to the previous, the main goal of this Thesis is to present a Design Method for columns displaying either longitudinally fixed POT bearings or longitudinally free PTFE POT bearings within bridges with fixed-point deck configuration, applicable to railway and road vehicles bridges. The method was developed with the intention to account for all major parameters that play a role in these columns behavior. The long process that has finally led to the method's formulation is rooted in the understanding of these column's behavior. All the assumptions made to elaborate the formulations contained in this method have been made in benefit of conservatives results. The singularity of the analysis of columns with this configuration is due to a combination of different aspects. One of the first steps of this work was to study they of these design aspects and understand the role each plays in the column's response. Among these aspects, special attention was dedicated to the column's own creep due to permanent actions such us rheological deck displacements, and also to the longitudinally guided PTFE POT bearings implications in the design of the column. The result of this study is the Design Method presented in this Thesis, that allows to work out a compliant vertical reinforcement distribution along the column. The design of horizontal reinforcement due to shear forces is not addressed in this Thesis. The method's formulations are meant to be applicable to the greatest number of cases, leaving to the engineer judgement many of the different parameters values. In this regard, this method is a helpful tool for a wide range of cases. The widespread use of European standards in the more recent years, in particular the so-called Eurocodes, has been one of the reasons why this Thesis has been developed in accordance with Eurocodes. Same trend has been followed for the bearings design implications, which are covered by the rather recent European code EN-1337. One of the most relevant aspects that this work has taken from the Eurocodes is the non-linear calculations security format. The biaxial bending simplified approach that shows the Design Method presented in this work also lies on Eurocodes recommendations. The columns under analysis are governed by a set of dimensionless parameters that are presented in this work. The identification of these parameters is a helpful for design purposes for two columns with identical dimensionless parameters may be designed together. The first group of these parameters have to do with the cross-sectional behavior, represented in the bending-curvature diagrams. A second group of parameters define the columns response. Thanks to this identification of the governing dimensionless parameters, it has been possible what has been named as Dimensionless Design Curves, which basically allows to obtain in a reduced time a preliminary vertical reinforcement column distribution. These curves are of little use nowadays, firstly because each family of curves refer to specific values of many different parameters and secondly because the use of computers allows for extremely quick and accurate calculations.