Analysis by finite element calculations of light scattering in laser-textured AZO films for PV thin-film solar cells

In the thin-film photovoltaic industry, to achieve a high light scattering in one or more of the cell interfaces is one of the strategies that allow an enhancement of light absorption inside the cell and, therefore, a better device behavior and efficiency. Although chemical etching is the standard method to texture surfaces for that scattering improvement, laser light has shown as a new way for texturizing different materials, maintaining a good control of the final topography with a unique, clean, and quite precise process. In this work AZO films with different texture parameters are fabricated. The typical parameters used to characterize them, as the root mean square roughness or the haze factor, are discussed and, for deeper understanding of the scattering mechanisms, the light behavior in the films is simulated using a finite element method code. This method gives information about the light intensity in each point of the system, allowing the precise characterization of the scattering behavior near the film surface, and it can be used as well to calculate a simulated haze factor that can be compared with experimental measurements. A discussion of the validation of the numerical code, based in a comprehensive comparison with experimental data is included.

An algorithm for graphical computer results in shells

A Finite Element technique to interpolate general data (function values and its derivatives) has been developped. The technique can be considered as a generalized solution of the classical polynomial interpolation, because the condition for the interpolating function to be a polynomial is replaced by a minimizing condition of a given “smoothing” functional. In this way it is possible to find interpolating functions with a given level of continuity according to the class of finite elements used. Examples have been presented in order to assess the accuracy and efficiency of the procedure.

Dynamic analysis using finite elements to calculate the critical wear section of the contact wire in suburban railway overhead conductor rails

The purpose of this study is to determine the critical wear levels of the contact wire of the catenary on metropolitan lines. The study has focussed on the zones of contact wire where localised wear is produced, normally associated with the appearance of electric arcs. To this end, a finite element model has been developed to study the dynamics of pantograph-catenary interaction. The model includes a zone of localised wear and a singularity in the contact wire in order to simulate the worst case scenario from the point of view of stresses. In order to consider the different stages in the wire wear process, different depths and widths of the localised wear zone were defined. The results of the dynamic simulations performed for each stage of wear let the area of the minimum resistant section of the contact wire be determined for which stresses are greater than the allowable stress. The maximum tensile stress reached in the contact wire shows a clear sensitivity to the size of the local wear zone, defined by its width and depth. In this way, if the wear measurements taken with an overhead line recording vehicle are analysed, it will be possible to calculate the potential breakage risk of the wire. A strong dependence of the tensile forces of the contact wire has also been observed. These results will allow priorities to be set for replacing the most critical sections of wire, thereby making maintenance much more efficient. The results obtained show that the wire replacement criteria currently borne in mind have turned out to be appropriate, although in some wear scenarios these criteria could be adjusted even more, and so prolong the life cycle of the contact wire.

Respuesta sísmica de un edificio de estructuras metálica con aisladores : alternativas de diseño

El presente trabajo es un estudio teórico – experimental para la implementación de un edificio metálico de cuatro plantas con dispositivos disipadores de energía. Este estudio presenta una técnica para la generación de un registro sísmico artificial, que sea compatible con los espectros de diseño de las normas chilena y española. Este acelerograma se crea con una herramienta computacional denominada SIMQKE. La simulación de la estructura sometida al terremoto artificial se realizará en el programa de elementos finitos SAP200. El trabajo se encuentra dividido en cuatro capítulos, cuyos contenidos son los siguientes. En el capitulo uno, o estado del arte, se revisan las diferentes técnicas de aislamiento sísmico, se describe el dispositivo a utilizar, sus bases teóricas y formulación matemática, se revisan las normas NCh.2745 Of.2003 [12], NCSE-02 [18] y se presenta la técnica para la generación de un registro sintético compatible. El capítulo dos aborda el análisis experimental para un edificio real: una edificación de estructura metálica implementada con disipadores de energía metálicos y que será sometida a tres terremotos de diferente magnitud. El capítulo tres expone los resultados de los desplazamientos medidos para la estructura sin disipadores y con ellos, se presentan los porcentajes de disminución de desplazamientos relativos por planta y por tipo de estructura. Por último, el capítulo cuatro presenta las principales conclusiones y una breve discusión de los resultados. The present work is a theoretical and experimental study for the implementation of a fourstorey building with energy dissipating devices. This study presents a technique for generation an artificial seismic record, which is compatible with the design spectra Chilean and Spanish standards. This accelerogram is created with a computational tool called SIMQKE. The simulation of the structure subjected to artificial earthquake will take place in the finite element program SAP2000. This work is divided into four chapters whose contents are as follows. In chapter one, or state of the art, reviews the different seismic isolation techniques, describes the device used, theoretical and mathematical formulation, NCh2745 Of.2003 [12] and NCSE-02 [18] standards are checked, and presents the technique for generating a synthetic record compatible. Chapter two explains the experimental analysis to a real building: a building of steel structure implemented with metallic energy dissipators and will be submitted to three different earthquakes of magnitude. Chapter three presents the results of measured displacements for the structure without dissipators and with them, the percentages of decline relative displacements per plant and type of structure. Finally, chapter four presents the main conclusions and a brief discussion of the results.

A mathematical framework for finite strain elastoplastic consolidation. Part 1: Balance laws, variational formulation, and linearization

A mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented. Strong and weak forms of the boundary-value problem are derived using both the material and spatial descriptions. The algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the Kirchhoff pore water pressure. Balance laws are written for the soil-water mixture following the motion of the soil matrix alone. It is shown that the motion of the fluid phase only affects the Jacobian of the solid phase motion, and therefore can be characterized completely by the motion of the soil matrix. Furthermore, it is shown from energy balance consideration that the effective, or intergranular, stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil-water mixture. Finally, it is shown that the mathematical model is amenable to consistent linearization, and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method.

Análisis de la influencia de distintos diseños de paraguas de micropilotes, pantalla de micropilotes, paraguas de jet grouting y pantallas de jet grouting en los asientos en superficie durante la ejecución de túneles perforados superficialmente

Ya en el informe acerca del estado de la tecnología en la excavación profunda y en la construcción de túneles en terreno duro presentado en la 7ª Conferencia en Mecánica de Suelos e Ingeniería de la Cimentación, Peck (1969) introdujo los tres temas a ser tenidos en cuenta para el diseño de túneles en terrenos blandos: o Estabilidad de la cavidad durante la construcción, con particular atención a la estabilidad del frente del túnel; o Evaluación de los movimientos del terreno inducidos por la construcción del túnel y de la incidencia de los trabajos subterráneos a poca profundidad sobre los asentamientos en superficie; o Diseño del sistema de sostenimiento del túnel a instalar para asegurar la estabilidad de la estructura a corto y largo plazo. Esta Tesis se centra en los problemas señalados en el segundo de los puntos, analizando distintas soluciones habitualmente proyectadas para reducir los movimientos inducidos por la excavación de los túneles. El objeto de la Tesis es el análisis de la influencia de distintos diseños de paraguas de micropilotes, pantalla de micropilotes, paraguas de jet grouting y pantallas de jet grouting en los asientos en superficie durante la ejecución de túneles ejecutados a poca profundidad, con objeto de buscar el diseño que optimice los medios empleados para una determinada reducción de asientos. Para ello se establecen unas premisas para los proyectistas con objeto de conocer a priori cuales son los tratamientos más eficientes (de los propuestos en la Tesis) para la reducción de asientos en superficie cuando se ha de proyectar un túnel, de tal manera que pueda tener datos cualitativos y algunos cuantitativos sobre los diseños más óptimos, utilizando para ello un programa de elementos finitos de última generación que permite realizara la simulación tensodeformación del terreno mediante el modelo de suelo con endurecimiento (Hardening Soil Small model), que es una variante elastoplástica del modelo hiperbólico, similar al Hardening Soil Model. Además, este modelo incorpora una relación entre deformación y el modulo de rigidez, simulando el diferente comportamiento del suelo para pequeñas deformaciones (por ejemplo vibraciones con deformaciones por debajo de 10-5 y grandes deformaciones (deformaciones > 10-3). Para la realización de la Tesis se han elegido cinco secciones de túnel, dos correspondiente a secciones tipo de túnel ejecutado con tuneladora y tres secciones ejecutados mediante convencionales (dos correspondientes a secciones que han utilizado el método Belga y una que ha utilizado el NATM). Para conseguir los objetivos marcados, primeramente se ha analizado mediante una correlación entre modelos tridimensionales y bidimensionales el valor de relajación usado en estos últimos, y ver su variación al cambio de parámetros como la sección del túnel, la cobertera, el procedimiento constructivo, longitud de pase (métodos convencionales) o presión del frente (tuneladora) y las características geotécnicas de los materiales donde se ejecuta el túnel. Posteriormente se ha analizado que diseño de pantalla de protección tiene mejor eficacia respecto a la reducción de asientos, variando distintos parámetros de las características de la misma, como son el empotramiento, el tipo de micropilotes o pilote, la influencia del arriostramiento de las pantallas de protección en cabeza, la inclinación de la pantalla, la separación de la pantalla al eje del túnel y la disposición en doble fila de la pantalla de pantalla proyectada. Para finalizar el estudio de la efectividad de pantalla de protección para la reducción de asiento, se estudiará la influencia de la sobrecarga cercanas (simulación de edificios) tiene en la efectividad de la pantalla proyectada (desde el punto de vista de reducción de movimientos en superficie). Con objeto de poder comparar la efectividad de la pantalla de micropilotes respecto a la ejecución de un paraguas de micropilotes se ha analizado distintos diseños de paraguas, comparando el movimiento obtenido con el obtenido para el caso de pantalla de micropilotes, comparando ambos resultados con los medidos en obras ya ejecutadas. En otro apartado se ha realizado una comparación entre tratamientos similar, comparándolos en este caso con un paraguas de jet grouting y pantallas de jet grouting. Los resultados obtenidos se han con valores de asientos medidos en distintas obras ya ejecutadas y cuyas secciones se corresponden a los empleados en los modelos numéricos. Since the report on the state of technology in deep excavation and tunnelling in hard ground presented at the 7th Conference on Soil Mechanics and Foundation Engineering, Peck (1969) introduced the three issues to be taken into account for the design of tunnels in soft ground: o Cavity Stability during construction, with particular attention to the stability of the tunnel face; o Evaluation of ground movements induced by tunnelling and the effect of shallow underground workings on surface settlement; o Design of the tunnel support system to be installed to ensure short and long term stability of the structure. This thesis focuses on the issues identified in the second point, usually analysing different solutions designed to reduce the movements induced by tunnelling. The aim of the thesis is to analyse the influence of different micropile forepole umbrellas, micropile walls, jet grouting umbrellas and jet grouting wall designs on surface settlements during near surface tunnelling in order to use the most optimal technique to achieve a determined reduction in settlement. This will establish some criteria for designers to know a priori which methods are most effective (of those proposed in the thesis) to reduce surface settlements in tunnel design, so that it is possible to have qualitative and some quantitative data on the optimal designs, using the latest finite element modelling software that allows simulation of the ground’s infinitesimal strain behaviour using the Hardening Soil Small Model, which is a variation on the elasto-plastic hyperbolic model, similar to Hardening Soil model. In addition, this model incorporates a relationship between strain and the rigidity modulus, simulating different soil behaviour for small deformations (eg deformation vibrations below 10-5 and large deformations (deformations > 10-3). For the purpose of this thesis five tunnel sections have been chosen, two sections corresponding to TBM tunnels and three sections undertaken by conventional means (two sections corresponding to the Belgian method and one corresponding to the NATM). To achieve the objectives outlined, a correlation analysis of the relaxation values used in the 2D and 3D models was undertaken to verify them against parameters such as the tunnel cross-section, the depth of the tunnel, the construction method, the length of step (conventional method) or face pressure (TBM) and the geotechnical characteristics of the ground where the tunnel is constructed. Following this, the diaphragm wall design with the greatest efficiency regarding settlement reduction was analysed, varying parameters such as the toe depth, type of micropiles or piles, the influence of bracing of the head protection diaphragm walls, the inclination of the diaphragm wall, the separation between the diaphragm wall and the tunnel axis and the double diaphragm wall design arrangement. In order to complete the study into the effectiveness of protective diaphragm walls ofn the reduction of settlements, the influence of nearby imposed loads (simulating buildings) on the effectiveness of the designed diaphragm walls (from the point of view of reducing surface movements) will be studied. In order to compare the effectiveness of micropile diaphragm walls regarding the installation of micropile forepole umbrellas, different designs of these forepole umbrellas have been analysed comparing the movement obtained with that obtained for micropiled diaphragm walls, comparing both results with those measured from similar completed projects. In another section, a comparison between similar treatments has been completed, comparing the treatments with a forepole umbrella by jet grouting and jet grouting walls. The results obtained compared with settlement values measured in various projects already completed and whose sections correspond to those used in the numerical models.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

Contribución al desarrollo de técnicas CAD para el diseño de antenas impresas y dispositivos pasivos de microondas basadas en el método de elementos finitos

El objetivo principal de esta tesis es el desarrollo de herramientas numéricas basadas en técnicas de onda completa para el diseño asistido por ordenador (Computer-Aided Design,‘CAD’) de dispositivos de microondas. En este contexto, se desarrolla una herramienta numérica basada en el método de los elementos finitos para el diseño y análisis de antenas impresas mediante algoritmos de optimización. Esta técnica consiste en dividir el análisis de una antena en dos partes. Una parte de análisis 3D que se realiza sólo una vez en cada punto de frecuencia de la banda de funcionamiento donde se sustituye una superficie que contiene la metalización del parche por puertas artificiales. En una segunda parte se inserta entre las puertas artificiales en la estructura 3D la superficie soportando una metalización y se procede un análisis 2D para caracterizar el comportamiento de la antena. La técnica propuesta en esta tesis se puede implementar en un algoritmo de optimización para definir el perfil de la antena que permite conseguir los objetivos del diseño. Se valida experimentalmente dicha técnica empleándola en el diseño de antenas impresas de banda ancha para diferentes aplicaciones mediante la optimización del perfil de los parches. También, se desarrolla en esta tesis un procedimiento basado en el método de descomposición de dominio y el método de los elementos finitos para el diseño de dispositivos pasivos de microonda. Se utiliza este procedimiento en particular para el diseño y sintonía de filtros de microondas. En la primera etapa de su aplicación se divide la estructura que se quiere analizar en subdominios aplicando el método de descomposición de dominio, este proceso permite analizar cada segmento por separado utilizando el método de análisis adecuado dado que suele haber subdominios que se pueden analizar mediante métodos analíticos por lo que el tiempo de análisis es más reducido. Se utilizan métodos numéricos para analizar los subdominios que no se pueden analizar mediante métodos analíticos. En esta tesis, se utiliza el método de los elementos finitos para llevar a cabo el análisis. Además de la descomposición de dominio, se aplica un proceso de barrido en frecuencia para reducir los tiempos del análisis. Como método de orden reducido se utiliza la técnica de bases reducidas. Se ha utilizado este procedimiento para diseñar y sintonizar varios ejemplos de filtros con el fin de comprobar la validez de dicho procedimiento. Los resultados obtenidos demuestran la utilidad de este procedimiento y confirman su rigurosidad, precisión y eficiencia en el diseño de filtros de microondas. ABSTRACT The main objective of this thesis is the development of numerical tools based on full-wave techniques for computer-aided design ‘CAD’ of microwave devices. In this context, a numerical technique based on the finite element method ‘FEM’ for the design and analysis of printed antennas using optimization algorithms has been developed. The proposed technique consists in dividing the analysis of the antenna in two stages. In the first stage, the regions of the antenna which do not need to be modified during the CAD process are initially characterized only once from their corresponding matrix transfer function (Generalized Admittance matrix, ‘GAM’). The regions which will be modified are defined as artificial ports, precisely the regions which will contain the conducting surfaces of the printed antenna. In a second stage, the contour shape of the conducting surfaces of the printed antenna is iteratively modified in order to achieve a desired electromagnetic performance of the antenna. In this way, a new GAM of the radiating device which takes into account each printed antenna shape is computed after each iteration. The proposed technique can be implemented with a genetic algorithm to achieve the design objectives. This technique is validated experimentally and applied to the design of wideband printed antennas for different applications by optimizing the shape of the radiating device. In addition, a procedure based on the domain decomposition method and the finite element method has been developed for the design of microwave passive devices. In particular, this procedure can be applied to the design and tune of microwave filters. In the first stage of its implementation, the structure to be analyzed is divided into subdomains using the domain decomposition method; this process allows each subdomains can be analyzed separately using suitable analysis method, since there is usually subdomains that can be analyzed by analytical methods so that the time of analysis is reduced. For analyzing the subdomains that cannot be analyzed by analytical methods, we use the numerical methods. In this thesis, the FEM is used to carry out the analysis. Furthermore the decomposition of the domain, a frequency sweep process is applied to reduce analysis times. The reduced order model as the reduced basis technique is used in this procedure. This procedure is applied to the design and tune of several examples of microwave filters in order to check its validity. The obtained results allow concluding the usefulness of this procedure and confirming their thoroughness, accuracy and efficiency for the design of microwave filters.

Elastostatics

In this chapter, we are going to describe the main features as well as the basic steps of the Boundary Element Method (BEM) as applied to elastostatic problems and to compare them with other numerical procedures. As we shall show, it is easy to appreciate the adventages of the BEM, but it is also advisable to refrain from a possible unrestrained enthusiasm, as there are also limitations to its usefulness in certain types of problems. The number of these problems, nevertheless, is sufficient to justify the interest and activity that the new procedure has aroused among researchers all over the world. Briefly speaking, the most frequently used version of the BEM as applied to elastostatics works with the fundamental solution, i.e. the singular solution of the governing equations, as an influence function and tries to satisfy the boundary conditions of the problem with the aid of a discretization scheme which consists exclusively of boundary elements. As in other numerical methods, the BEM was developed thanks to the computational possibilities offered by modern computers on totally "classical" basis. That is, the theoretical grounds are based on linear elasticity theory, incorporated long ago into the curricula of most engineering schools. Its delay in gaining popularity is probably due to the enormous momentum with which Finite Element Method (FEM) penetrated the professional and academic media. Nevertheless, the fact that these methods were developed before the BEM has been beneficial because de BEM successfully uses those results and techniques studied in past decades. Some authors even consider the BEM as a particular case of the FEM while others view both methods as special cases of the general weighted residual technique. The first paper usually cited in connection with the BEM as applied to elastostatics is that of Rizzo, even though the works of Jaswon et al., Massonet and Oliveira were published at about the same time, the reason probably being the attractiveness of the "direct" approach over the "indirect" one. The work of Tizzo and the subssequent work of Cruse initiated a fruitful period with applicatons of the direct BEM to problems of elastostacs, elastodynamics, fracture, etc. The next key contribution was that of Lachat and Watson incorporating all the FEM discretization philosophy in what is sometimes called the "second BEM generation". This has no doubt, led directly to the current developments. Among the various researchers who worked on elastostatics by employing the direct BEM, one can additionallly mention Rizzo and Shippy, Cruse et al., Lachat and Watson, Alarcón et al., Brebbia el al, Howell and Doyle, Kuhn and Möhrmann and Patterson and Sheikh, and among those who used the indirect BEM, one can additionally mention Benjumea and Sikarskie, Butterfield, Banerjee et al., Niwa et al., and Altiero and Gavazza. An interesting version of the indirct method, called the Displacement Discontinuity Method (DDM) has been developed by Crounh. A comprehensive study on various special aspects of the elastostatic BEM has been done by Heisse, while review-type articles on the subject have been reported by Watson and Hartmann. At the present time, the method is well established and is being used for the solution of variety of problems in engineering mechanics. Numerous introductory and advanced books have been published as well as research-orientated ones. In this sense, it is worth noting the series of conferences promoted by Brebbia since 1978, wich have provoked a continuous research effort all over the world in relation to the BEM. In the following sections, we shall concentrate on developing the direct BEM as applied to elastostatics.

The Boundary Element Method in elastodynamics

As is well known B.E.M. is obtained as a mixture of the integral representation formula of classical elasticity and the discretization philosophy of the finite element method (F.E.M.). The paper presents the application of B.E.M. to elastodynamic problems. Both the transient and steady state solutions are presented as well as some techniques to simplify problems with a free-stress boundary.

Experimental and numerical study of cw green laser crystallization of a-Si:H thin films

Crystallization and grain growth technique of thin film silicon are among the most promising methods for improving efficiency and lowering cost of solar cells. A major advantage of laser crystallization and annealing over conventional heating methods is its ability to limit rapid heating and cooling to thin surface layers. Laser energy is used to heat the amorphous silicon thin film, melting it and changing the microstructure to polycrystalline silicon (poly-Si) as it cools. Depending on the laser density, the vaporization temperature can be reached at the center of the irradiated area. In these cases ablation effects are expected and the annealing process becomes ineffective. The heating process in the a-Si thin film is governed by the general heat transfer equation. The two dimensional non-linear heat transfer equation with a moving heat source is solve numerically using the finite element method (FEM), particularly COMSOL Multiphysics. The numerical model help to establish the density and the process speed range needed to assure the melting and crystallization without damage or ablation of the silicon surface. The samples of a-Si obtained by physical vapour deposition were irradiated with a cw-green laser source (Millennia Prime from Newport-Spectra) that delivers up to 15 W of average power. The morphology of the irradiated area was characterized by confocal laser scanning microscopy (Leica DCM3D) and Scanning Electron Microscopy (SEM Hitachi 3000N). The structural properties were studied by micro-Raman spectroscopy (Renishaw, inVia Raman microscope).

Inestabilidad de pórticos planos metálicos de edificación con inclusión de la flexibilidad de las uniones y elementos no prismáticos : un enfoque para la optimización

En esta tesis se aborda el problema de la modelización, análisis y optimización de pórticos metálicos planos de edificación frente a los estados límites último y de servicio. El objetivo general es presentar una técnica secuencial ordenada de optimización discreta para obtener el coste mínimo de pórticos metálicos planos de edificación, teniendo en cuenta las especificaciones del EC-3, incorporando las uniones semirrígidas y elementos no prismáticos en el proceso de diseño. Asimismo se persigue valorar su grado de influencia sobre el diseño final. El horizonte es extraer conclusiones prácticas que puedan ser de utilidad y aplicación simple para el proyecto de estructuras metálicas. La cantidad de publicaciones técnicas y científicas sobre la respuesta estructural de entramados metálicos es inmensa; por ello se ha hecho un esfuerzo intenso en recopilar el estado actual del conocimiento, sobre las líneas y necesidades actuales de investigación. Se ha recabado información sobre los métodos modernos de cálculo y diseño, sobre los factores que influyen sobre la respuesta estructural, sobre técnicas de modelización y de optimización, al amparo de las indicaciones que algunas normativas actuales ofrecen sobre el tema. En esta tesis se ha desarrollado un procedimiento de modelización apoyado en el método de los elementos finitos implementado en el entorno MatLab; se han incluido aspectos claves tales como el comportamiento de segundo orden, la comprobación ante inestabilidad y la búsqueda del óptimo del coste de la estructura frente a estados límites, teniendo en cuenta las especificaciones del EC-3. También se ha modelizado la flexibilidad de las uniones y se ha analizado su influencia en la respuesta de la estructura y en el peso y coste final de la misma. Se han ejecutado algunos ejemplos de aplicación y se ha contrastado la validez del modelo con resultados de algunas estructuras ya analizadas en referencias técnicas conocidas. Se han extraído conclusiones sobre el proceso de modelización y de análisis, sobre la repercusión de la flexibilidad de las uniones en la respuesta de la estructura. El propósito es extraer conclusiones útiles para la etapa de proyecto. Una de las principales aportaciones del trabajo en su enfoque de optimización es la incorporación de una formulación de elementos no prismáticos con uniones semirrígidas en sus extremos. Se ha deducido una matriz de rigidez elástica para dichos elementos. Se ha comprobado su validez para abordar el análisis no lineal; para ello se han comparado los resultados con otros obtenidos tras aplicar otra matriz deducida analíticamente existente en la literatura y también mediante el software comercial SAP2000. Otra de las aportaciones de esta tesis es el desarrollo de un método de optimización del coste de pórticos metálicos planos de edificación en el que se tienen en cuenta aspectos tales como las imperfecciones, la posibilidad de incorporar elementos no prismáticos y la caracterización de las uniones semirrígidas, valorando la influencia de su flexibilidad sobre la respuesta de la estructura. Así, se han realizado estudios paramétricos para valorar la sensibilidad y estabilidad de las soluciones obtenidas, así como rangos de validez de las conclusiones obtenidas. This thesis deals with the problems of modelling, analysis and optimization of plane steel frames with regard to ultimate and serviceability limit states. The objective of this work is to present an organized sequential technique of discrete optimization for achieving the minimum cost of plane steel frames, taking into consideration the EC-3 specifications as well as including effects of the semi-rigid joints and non-prismatic elements in the design process. Likewise, an estimate of their influence on the final design is an aim of this work. The final objective is to draw practical conclusions which can be handful and easily applicable for a steel-structure project. An enormous amount of technical and scientific publications regarding steel frames is currently available, thus making the achievement of a comprehensive and updated knowledge a considerably hard task. In this work, a large variety of information has been gathered and classified, especially that related to current research lines and needs. Thus, the literature collected encompasses references related to state-of-the-art design methods, factors influencing the structural response, modelling and optimization techniques, as well as calculation and updated guidelines of some steel Design Codes about the subject. In this work a modelling procedure based on the finite element implemented within the MatLab programming environment has been performed. Several keys aspects have been included, such as second order behaviour, the safety assessment against structural instability and the search for an optimal cost considering the limit states according to EC-3 specifications. The flexibility of joints has been taken into account in the procedure hereby presented; its effects on the structural response, on the optimum weight and on the final cost have also been analysed. In order to confirm the validity and adequacy of this procedure, some application examples have been carried out. The results obtained were compared with those available from other authors. Several conclusions about the procedure that comprises modelling, analysis and design stages, as well as the effect of the flexibility of connections on the structural response have been drawn. The purpose is to point out some guidelines for the early stages of a project. One of the contributions of this thesis is an attempt for optimizing plane steel frames in which both non-prismatic beam-column-type elements and semi-rigid connections have been considered. Thus, an elastic stiffness matrix has been derived. Its validity has been tested through comparing its accuracy with other analytically-obtained matrices available in the literature, and with results obtained by the commercial software SAP2000. Another achievement of this work is the development of a method for cost optimization of plane steel building frames in which some relevant aspects have been taken in consideration. These encompass geometric imperfections, non-prismatic beam elements and the numerical characterization of semi-rigid connections, evaluating the effect of its flexibility on the structural response. Hence, some parametric analyses have been performed in order to assess the sensitivity, the stability of the outcomes and their range of applicability as well.

Experimental and numerical study of cracking of concrete due to reinforcement corrosion

La corrosión del acero es una de las patologías más importantes que afectan a las estructuras de hormigón armado que están expuestas a ambientes marinos o al ataque de sales fundentes. Cuando se produce corrosión, se genera una capa de óxido alrededor de la superficie de las armaduras, que ocupa un volumen mayor que el acero inicial; como consecuencia, el óxido ejerce presiones internas en el hormigón circundante, que lleva a la fisuración y, ocasionalmente, al desprendimiento del recubrimiento de hormigón. Durante los últimos años, numerosos estudios han contribuido a ampliar el conocimiento sobre el proceso de fisuración; sin embargo, aún existen muchas incertidumbres respecto al comportamiento mecánico de la capa de óxido, que es fundamental para predecir la fisuración. Por ello, en esta tesis se ha desarrollado y aplicado una metodología, para mejorar el conocimiento respecto al comportamiento del sistema acero-óxido-hormigón, combinando experimentos y simulaciones numéricas. Se han realizado ensayos de corrosión acelerada en condiciones de laboratorio, utilizando la técnica de corriente impresa. Con el objetivo de obtener información cercana a la capa de acero, como muestras se seleccionaron prismas de hormigón con un tubo de acero liso como armadura, que se diseñaron para conseguir la formación de una única fisura principal en el recubrimiento. Durante los ensayos, las muestras se equiparon con instrumentos especialmente diseñados para medir la variación de diámetro y volumen interior de los tubos, y se midió la apertura de la fisura principal utilizando un extensómetro comercial, adaptado a la geometría de las muestras. Las condiciones de contorno se diseñaron cuidadosamente para que los campos de corriente y deformación fuesen planos durante los ensayos, resultando en corrosión uniforme a lo largo del tubo, para poder reproducir los ensayos en simulaciones numéricas. Se ensayaron series con varias densidades de corriente y varias profundidades de corrosión. De manera complementaria, el comportamiento en fractura del hormigón se caracterizó en ensayos independientes, y se midió la pérdida gravimétrica de los tubos siguiendo procedimientos estándar. En todos los ensayos, la fisura principal creció muy despacio durante las primeras micras de profundidad de corrosión, pero después de una cierta profundidad crítica, la fisura se desarrolló completamente, con un aumento rápido de su apertura; la densidad de corriente influye en la profundidad de corrosión crítica. Las variaciones de diámetro interior y de volumen interior de los tubos mostraron tendencias diferentes entre sí, lo que indica que la deformación del tubo no fue uniforme. Después de la corrosión acelerada, las muestras se cortaron en rebanadas, que se utilizaron en ensayos post-corrosión. El patrón de fisuración se estudió a lo largo del tubo, en rebanadas que se impregnaron en vacío con resina y fluoresceína para mejorar la visibilidad de las fisuras bajo luz ultravioleta, y se estudió la presencia de óxido dentro de las grietas. En todas las muestras, se formó una fisura principal en el recubrimiento, infiltrada con óxido, y varias fisuras secundarias finas alrededor del tubo; el número de fisuras varió con la profundidad de corrosión de las muestras. Para muestras con la misma corrosión, el número de fisuras y su posición fue diferente entre muestras y entre secciones de una misma muestra, debido a la heterogeneidad del hormigón. Finalmente, se investigó la adherencia entre el acero y el hormigón, utilizando un dispositivo diseñado para empujar el tubo en el hormigón. Las curvas de tensión frente a desplazamiento del tubo presentaron un pico marcado, seguido de un descenso constante; la profundidad de corrosión y la apertura de fisura de las muestras influyeron notablemente en la tensión residual del ensayo. Para simular la fisuración del hormigón causada por la corrosión de las armaduras, se programó un modelo numérico. Éste combina elementos finitos con fisura embebida adaptable que reproducen la fractura del hormigón conforme al modelo de fisura cohesiva estándar, y elementos de interfaz llamados elementos junta expansiva, que se programaron específicamente para reproducir la expansión volumétrica del óxido y que incorporan su comportamiento mecánico. En el elemento junta expansiva se implementó un fenómeno de despegue, concretamente de deslizamiento y separación, que resultó fundamental para obtener localización de fisuras adecuada, y que se consiguió con una fuerte reducción de la rigidez tangencial y la rigidez en tracción del óxido. Con este modelo, se realizaron simulaciones de los ensayos, utilizando modelos bidimensionales de las muestras con elementos finitos. Como datos para el comportamiento en fractura del hormigón, se utilizaron las propiedades determinadas en experimentos. Para el óxido, inicialmente se supuso un comportamiento fluido, con deslizamiento y separación casi perfectos. Después, se realizó un ajuste de los parámetros del elemento junta expansiva para reproducir los resultados experimentales. Se observó que variaciones en la rigidez normal del óxido apenas afectaban a los resultados, y que los demás parámetros apenas afectaban a la apertura de fisura; sin embargo, la deformación del tubo resultó ser muy sensible a variaciones en los parámetros del óxido, debido a la flexibilidad de la pared de los tubos, lo que resultó fundamental para determinar indirectamente los valores de los parámetros constitutivos del óxido. Finalmente, se realizaron simulaciones definitivas de los ensayos. El modelo reprodujo la profundidad de corrosión crítica y el comportamiento final de las curvas experimentales; se comprobó que la variación de diámetro interior de los tubos está fuertemente influenciada por su posición relativa respecto a la fisura principal, en concordancia con los resultados experimentales. De la comparación de los resultados experimentales y numéricos, se pudo extraer información sobre las propiedades del óxido que de otra manera no habría podido obtenerse. Corrosion of steel is one of the main pathologies affecting reinforced concrete structures exposed to marine environments or to molten salt. When corrosion occurs, an oxide layer develops around the reinforcement surface, which occupies a greater volume than the initial steel; thus, it induces internal pressure on the surrounding concrete that leads to cracking and, eventually, to full-spalling of the concrete cover. During the last years much effort has been devoted to understand the process of cracking; however, there is still a lack of knowledge regarding the mechanical behavior of the oxide layer, which is essential in the prediction of cracking. Thus, a methodology has been developed and applied in this thesis to gain further understanding of the behavior of the steel-oxide-concrete system, combining experiments and numerical simulations. Accelerated corrosion tests were carried out in laboratory conditions, using the impressed current technique. To get experimental information close to the oxide layer, concrete prisms with a smooth steel tube as reinforcement were selected as specimens, which were designed to get a single main crack across the cover. During the tests, the specimens were equipped with instruments that were specially designed to measure the variation of inner diameter and volume of the tubes, and the width of the main crack was recorded using a commercial extensometer that was adapted to the geometry of the specimens. The boundary conditions were carefully designed so that plane current and strain fields were expected during the tests, resulting in nearly uniform corrosion along the length of the tube, so that the tests could be reproduced in numerical simulations. Series of tests were carried out with various current densities and corrosion depths. Complementarily, the fracture behavior of concrete was characterized in independent tests, and the gravimetric loss of the steel tubes was determined by standard means. In all the tests, the main crack grew very slowly during the first microns of corrosion depth, but after a critical corrosion depth it fully developed and opened faster; the current density influenced the critical corrosion depth. The variation of inner diameter and inner volume of the tubes had different trends, which indicates that the deformation of the tube was not uniform. After accelerated corrosion, the specimens were cut into slices, which were used in post-corrosion tests. The pattern of cracking along the reinforcement was investigated in slices that were impregnated under vacuum with resin containing fluorescein to enhance the visibility of cracks under ultraviolet lightening and a study was carried out to assess the presence of oxide into the cracks. In all the specimens, a main crack developed through the concrete cover, which was infiltrated with oxide, and several thin secondary cracks around the reinforcement; the number of cracks diminished with the corrosion depth of the specimen. For specimens with the same corrosion, the number of cracks and their position varied from one specimen to another and between cross-sections of a given specimen, due to the heterogeneity of concrete. Finally, the bond between the steel and the concrete was investigated, using a device designed to push the tubes of steel in the concrete. The curves of stress versus displacement of the tube presented a marked peak, followed by a steady descent, with notably influence of the corrosion depth and the crack width on the residual stress. To simulate cracking of concrete due to corrosion of the reinforcement, a numerical model was implemented. It combines finite elements with an embedded adaptable crack that reproduces cracking of concrete according to the basic cohesive model, and interface elements so-called expansive joint elements, which were specially designed to reproduce the volumetric expansion of oxide and incorporate its mechanical behavior. In the expansive joint element, a debonding effect was implemented consisting of sliding and separation, which was proved to be essential to achieve proper localization of cracks, and was achieved by strongly reducing the shear and the tensile stiffnesses of the oxide. With that model, simulations of the accelerated corrosion tests were carried out on 2- dimensional finite element models of the specimens. For the fracture behavior of concrete, the properties experimentally determined were used as input. For the oxide, initially a fluidlike behavior was assumed with nearly perfect sliding and separation; then the parameters of the expansive joint element were modified to fit the experimental results. Changes in the bulk modulus of the oxide barely affected the results and changes in the remaining parameters had a moderate effect on the predicted crack width; however, the deformation of the tube was very sensitive to variations in the parameters of oxide, due to the flexibility of the tube wall, which was crucial for indirect determination of the constitutive parameters of oxide. Finally, definitive simulations of the tests were carried out. The model reproduced the critical corrosion depth and the final behavior of the experimental curves; it was assessed that the variation of inner diameter of the tubes is highly influenced by its relative position with respect to the main crack, in accordance with the experimental observations. From the comparison of the experimental and numerical results, some properties of the mechanical behavior of the oxide were disclosed that otherwise could not have been measured.

Métodos numéricos y estadísticos de caracterización de uniones tubulares soldadas para su aplicación en modelos de elementos finitos de estructuras de vehículos

El análisis de estructuras mediante modelos de elementos finitos representa una de las metodologías más utilizadas y aceptadas en la industria moderna. Para el análisis de estructuras tubulares de grandes dimensiones similares a las sobrestructuras de autobuses y autocares, los elementos de tipo viga son comúnmente utilizados y recomendados debido a que permiten obtener resultados satisfactorios con recursos computacionales reducidos. No obstante, los elementos de tipo viga presentan importante desventaja ya que las uniones modeladas presentan un comportamiento infinitamente rígido, esto determina un comportamiento mas rígido en las estructuras modeladas lo que se traduce en fuentes de error para las simulaciones estructurales (hasta un 60%). Mediante el modelado de uniones tubulares utilizando elementos de tipo área o volumen, se pueden obtener modelos más realistas, ya que las características topológicas de la unión propiamente dicha pueden ser reproducidas con un mayor nivel de detalle. Evitándose de esta manera los inconvenientes de los elementos de tipo viga. A pesar de esto, la modelización de estructuras tubulares de grandes dimensiones con elementos de tipo área o volumen representa una alternativa poco atractiva debido a la complejidad del proceso de modelados y al gran número de elementos resultantes lo que implica la necesidad de grandes recursos computacionales. El principal objetivo del trabajo de investigación presentado, fue el de obtener un nuevo tipo de elemento capaz de proporcionar estimaciones más exactas en el comportamiento de las uniones modeladas, al mismo tiempo manteniendo la simplicidad del procesos de modelado propio de los elementos de tipo viga regular. Con el fin de alcanzar los objetivos planteados, fueron realizadas diferentes metodologías e investigaciones. En base a las investigaciones realizadas, se obtuvo un modelo de unión viga alternativa en el cual se introdujeron un total seis elementos elásticos al nivel de la unión mediante los cuales es posible adaptar el comportamiento local de la misma. Adicionalmente, para la estimación de las rigideces correspondientes a los elementos elásticos se desarrollaron dos metodologías, una primera basada en la caracterización del comportamiento estático de uniones simples y una segunda basada en la caracterización del comportamiento dinámico a través de análisis modales. Las mejoras obtenidas mediante la implementación del modelo de unión alternativa fueron analizadas mediante simulaciones y validación experimental en una estructura tubular compleja representativa de sobrestructuras de autobuses y autocares. En base a los análisis comparativos realizados con la uniones simples modeladas y los experimentos de validación, se determinó que las uniones modeladas con elementos de tipo viga son entre un 5-60% más rígidas que uniones equivalentes modeladas con elementos área o volumen. También se determinó que las uniones área y volumen modeladas son entre un 5 a un 10% mas rígidas en comparación a uniones reales fabricadas. En los análisis realizados en la estructura tubular compleja, se obtuvieron mejoras importantes mediante la implementación del modelo de unión alternativa, las estimaciones del modelo viga se mejoraron desde un 49% hasta aproximadamente un 14%. ABSTRACT The analysis of structures with finite elements models represents one of the most utilized an accepted technique in the modern industry. For the analysis of large tubular structures similar to buses and coaches upper structures, beam type elements are utilized and recommended due to the fact that these elements provide satisfactory results at relatively reduced computational performances. However, the beam type elements have a main disadvantage determined by the fact that the modeled joints have an infinite rigid behavior, this shortcoming determines a stiffer behavior of the modeled structures which translates into error sources for the structural simulations (up to 60%). By modeling tubular junctions with shell and volume elements, more realistic models can be obtained, because the topological characteristics of the junction at the joint level can be reproduced more accurately. This way, the shortcoming that the beam type elements present can be solved. Despite this fact, modeling large tubular structures with shell or volume type elements represents an unattractive alternative due to the complexity of the modeling process and the large number of elements that result which imply the necessity of vast computational performances. The main objective of the research presented in this thesis was to develop a new beam type element that would be able to provide more accurate estimations for the local behavior of the modeled junctions at the same time maintaining the simplicity of the modeling process the regular beam type elements have. In order to reach the established objectives of the research activities, a series of different methodologies and investigations have been necessary. From these investigations an alternative beam T-junction model was obtained, in which a total of six elastic elements at the joint level were introduced, the elastic elements allowed us to adapt the local behavior of the modeled junctions. Additionally, for the estimation of the stiffness values corresponding to the elastic elements two methodologies were developed, one based on the T-junction’s static behavior and a second one based on the T-junction’s dynamic behavior by means of modal analysis. The improvements achieved throughout the implementation of this alternative T-junction model were analyzed though mechanical validation in a complex tubular structures that had a representative configuration for buses and coaches upper structures. From the comparative analyses of the finite element modeled T-junctions and mechanical experimental analysis, was determined that the beam type modeled T-junctions have a stiffer behavior compared to equivalent shell and volume modeled T-junctions with average differences ranging from 5-60% based on the profile configurations. It was also determined that the shell and volume models have a stiffer behavior compared to real T-junctions varying from 5 to 10% depending on the profile configurations. Based on the analysis of the complex tubular structure, significant improvements were obtained by the implementation of the alternative beam T-junction model, the model estimations were improved from a 49% to approximately 14%.