A robust numerical framework to the analysis of material failure of fibre reinforced soft tissue

In this work, robustness and stability of continuum damage models applied to material failure in soft tissues are addressed. In the implicit damage models equipped with softening, the presence of negative eigenvalues in the tangent elemental matrix degrades the condition number of the global matrix, leading to a reduction of the computational performance of the numerical model. Two strategies have been adapted from literature to improve the aforementioned computational performance degradation: the IMPL-EX integration scheme [Oliver,2006], which renders the elemental matrix contribution definite positive, and arclength-type continuation methods [Carrera,1994], which allow to capture the unstable softening branch in brittle ruptures. The IMPL-EX integration scheme has as a major drawback the need to use small time steps to keep numerical error below an acceptable value. A convergence study, limiting the maximum allowed increment of internal variables in the damage model, is presented. Finally, numerical simulation of failure problems with fibre reinforced materials illustrates the performance of the adopted methodology.

Common motifs in scientific workflows: An empirical analysis

Workflow technology continues to play an important role as a means for specifying and enacting computational experiments in modern science. Reusing and re-purposing workflows allow scientists to do new experiments faster, since the workflows capture useful expertise from others. As workflow libraries grow, scientists face the challenge of finding workflows appropriate for their task, understanding what each workflow does, and reusing relevant portions of a given workflow.We believe that workflows would be easier to understand and reuse if high-level views (abstractions) of their activities were available in workflow libraries. As a first step towards obtaining these abstractions, we report in this paper on the results of a manual analysis performed over a set of real-world scientific workflows from Taverna, Wings, Galaxy and Vistrails. Our analysis has resulted in a set of scientific workflow motifs that outline (i) the kinds of data-intensive activities that are observed in workflows (Data-Operation motifs), and (ii) the different manners in which activities are implemented within workflows (Workflow-Oriented motifs). These motifs are helpful to identify the functionality of the steps in a given workflow, to develop best practices for workflow design, and to develop approaches for automated generation of workflow abstractions.

Probabilistic Analysis of Tunnel Liners

The use of probabilistic methods to analyse reliability of structures is being applied to a variety of engineering problems due to the possibility of establishing the failure probability on rational grounds. In this paper we present the application of classical reliability theory to analyse the safety of underground tunnels.

Simplified Procedure for the Nonlinear Seismic Analysis of Bridges

The severe accidents suffered by bridges during recent earthquake show that more careful analysis are needed to guarantee their behaviour. In particular simplified non-linear analysis could be useful to bridge the gap between theoretical research and practical applications. This paper presents one of those simplified methods that can be applied for first designs or to retrofitting of groups of bridges.

Computational model for local damage assesment of structures

In the last years many studies have been developed to analyze the seismic behavior throug the damage concept. In fact, the evaluation of the structural damage is important in order to quantify the safety of new and existing structures and, also, to establish a framework for seismic retrofitting decision making of structures. Most proposed models are based on a post-earthquake evaluation in such a way they uncouple the computation of the structural response from that of damage. However, there are other models which include explicity the existing coupling between the degradation and the structural mechanical beaviour. Those models are closer to the physical reality and its formulation is based on the principles of Continuum Damage Mechanics. In the present work, a coupled model is formulated using a simplified application of the Continuum Damage Mechanics to the analysis of frames and allows its representation in standard finite element programs. This work is part of the activities developed by the Structural Mechanics Department (UPM) within ICONS (European Research Project on Innovative Seismic Design Concepts for New and Existing Structures).

Image analysis by moment invariants using a set of step-like basis functions

Moment invariants have been thoroughly studied and repeatedly proposed as one of the most powerful tools for 2D shape identification. In this paper a set of such descriptors is proposed, being the basis functions discontinuous in a finite number of points. The goal of using discontinuous functions is to avoid the Gibbs phenomenon, and therefore to yield a better approximation capability for discontinuous signals, as images. Moreover, the proposed set of moments allows the definition of rotation invariants, being this the other main design concern. Translation and scale invariance are achieved by means of standard image normalization. Tests are conducted to evaluate the behavior of these descriptors in noisy environments, where images are corrupted with Gaussian noise up to different SNR values. Results are compared to those obtained using Zernike moments, showing that the proposed descriptor has the same performance in image retrieval tasks in noisy environments, but demanding much less computational power for every stage in the query chain.

Simulation of the deformation of polycrystalline nanostructured Ti by computational homogenization

Computational homogenization by means of the finite element analysis of a representative volume element of the microstructure is used to simulate the deformation of nanostructured Ti. The behavior of each grain is taken into account using a single crystal elasto-viscoplastic model which includes the microscopic mechanisms of plastic deformation by slip along basal, prismatic and pyramidal systems. Two different representations of the polycrystal were used. Each grain was modeled with one cubic finite element in the first one while many cubic elements were used to represent each grain in the second one, leading to a model which includes the effect of grain shape and size in a limited number of grains due to the computational cost. Both representations were used to simulate the tensile deformation of nanostructured Ti processed by ECAP-C as well as the drawing process of nanostructured Ti billets. It was found that the first representation based in one finite element per grain led to a stiffer response in tension and was not able to predict the texture evolution during drawing because the strain gradient within each grain could not be captured. On the contrary, the second representation of the polycrystal microstructure with many finite elements per grain was able to predict accurately the deformation of nanostructured Ti.

Analysis of pixel-mapping rounding on geometric distortion as a prediction for view synthesis distortion

We analyze the performance of the geometric distortion, incurred when coding depth maps in 3D Video, as an estimator of the distortion of synthesized views. Our analysis is motivated by the need of reducing the computational complexity required for the computation of synthesis distortion in 3D video encoders. We propose several geometric distortion models that capture (i) the geometric distortion caused by the depth coding error, and (ii) the pixel-mapping precision in view synthesis. Our analysis starts with the evaluation of the correlation of geometric distortion values obtained with these models and the actual distortion on synthesized views. Then, the different geometric distortion models are employed in the rate-distortion optimization cycle of depth map coding, in order to assess the results obtained by the correlation analysis. Results show that one of the geometric distortion models is performing consistently better than the other models in all tests. Therefore, it can be used as a reasonable estimator of the synthesis distortion in low complexity depth encoders.

Bayesian scene analysis for multi-camera 3D tracking and camera positioning

Los sistemas de seguimiento mono-cámara han demostrado su notable capacidad para el análisis de trajectorias de objectos móviles y para monitorización de escenas de interés; sin embargo, tanto su robustez como sus posibilidades en cuanto a comprensión semántica de la escena están fuertemente limitadas por su naturaleza local y monocular, lo que los hace insuficientes para aplicaciones realistas de videovigilancia. El objetivo de esta tesis es la extensión de las posibilidades de los sistemas de seguimiento de objetos móviles para lograr un mayor grado de robustez y comprensión de la escena. La extensión propuesta se divide en dos direcciones separadas. La primera puede considerarse local, ya que está orientada a la mejora y enriquecimiento de las posiciones estimadas para los objetos móviles observados directamente por las cámaras del sistema; dicha extensión se logra mediante el desarrollo de un sistema multi-cámara de seguimiento 3D, capaz de proporcionar consistentemente las posiciones 3D de múltiples objetos a partir de las observaciones capturadas por un conjunto de sensores calibrados y con campos de visión solapados. La segunda extensión puede considerarse global, dado que su objetivo consiste en proporcionar un contexto global para relacionar las observaciones locales realizadas por una cámara con una escena de mucho mayor tamaño; para ello se propone un sistema automático de localización de cámaras basado en las trayectorias observadas de varios objetos móviles y en un mapa esquemático de la escena global monitorizada. Ambas líneas de investigación se tratan utilizando, como marco común, técnicas de estimación bayesiana: esta elección está justificada por la versatilidad y flexibilidad proporcionada por dicho marco estadístico, que permite la combinación natural de múltiples fuentes de información sobre los parámetros a estimar, así como un tratamiento riguroso de la incertidumbre asociada a las mismas mediante la inclusión de modelos de observación específicamente diseñados. Además, el marco seleccionado abre grandes posibilidades operacionales, puesto que permite la creación de diferentes métodos numéricos adaptados a las necesidades y características específicas de distintos problemas tratados. El sistema de seguimiento 3D con múltiples cámaras propuesto está específicamente diseñado para permitir descripciones esquemáticas de las medidas realizadas individualmente por cada una de las cámaras del sistema: esta elección de diseño, por tanto, no asume ningún algoritmo específico de detección o seguimiento 2D en ninguno de los sensores de la red, y hace que el sistema propuesto sea aplicable a redes reales de vigilancia con capacidades limitadas tanto en términos de procesamiento como de transmision. La combinación robusta de las observaciones capturadas individualmente por las cámaras, ruidosas, incompletas y probablemente contaminadas por falsas detecciones, se basa en un metodo de asociación bayesiana basado en geometría y color: los resultados de dicha asociación permiten el seguimiento 3D de los objetos de la escena mediante el uso de un filtro de partículas. El sistema de fusión de observaciones propuesto tiene, como principales características, una gran precisión en términos de localización 3D de objetos, y una destacable capacidad de recuperación tras eventuales errores debidos a un número insuficiente de datos de entrada. El sistema automático de localización de cámaras se basa en la observación de múltiples objetos móviles y un mapa esquemático de las áreas transitables del entorno monitorizado para inferir la posición absoluta de dicho sensor. Para este propósito, se propone un novedoso marco bayesiano que combina modelos dinámicos inducidos por el mapa en los objetos móviles presentes en la escena con las trayectorias observadas por la cámara, lo que representa un enfoque nunca utilizado en la literatura existente. El sistema de localización se divide en dos sub-tareas diferenciadas, debido a que cada una de estas tareas requiere del diseño de algoritmos específicos de muestreo para explotar en profundidad las características del marco desarrollado: por un lado, análisis de la ambigüedad del caso específicamente tratado y estimación aproximada de la localización de la cámara, y por otro, refinado de la localización de la cámara. El sistema completo, diseñado y probado para el caso específico de localización de cámaras en entornos de tráfico urbano, podría tener aplicación también en otros entornos y sensores de diferentes modalidades tras ciertas adaptaciones. ABSTRACT Mono-camera tracking systems have proved their capabilities for moving object trajectory analysis and scene monitoring, but their robustness and semantic possibilities are strongly limited by their local and monocular nature and are often insufficient for realistic surveillance applications. This thesis is aimed at extending the possibilities of moving object tracking systems to a higher level of scene understanding. The proposed extension comprises two separate directions. The first one is local, since is aimed at enriching the inferred positions of the moving objects within the area of the monitored scene directly covered by the cameras of the system; this task is achieved through the development of a multi-camera system for robust 3D tracking, able to provide 3D tracking information of multiple simultaneous moving objects from the observations reported by a set of calibrated cameras with semi-overlapping fields of view. The second extension is global, as is aimed at providing local observations performed within the field of view of one camera with a global context relating them to a much larger scene; to this end, an automatic camera positioning system relying only on observed object trajectories and a scene map is designed. The two lines of research in this thesis are addressed using Bayesian estimation as a general unifying framework. Its suitability for these two applications is justified by the flexibility and versatility of that stochastic framework, which allows the combination of multiple sources of information about the parameters to estimate in a natural and elegant way, addressing at the same time the uncertainty associated to those sources through the inclusion of models designed to this end. In addition, it opens multiple possibilities for the creation of different numerical methods for achieving satisfactory and efficient practical solutions to each addressed application. The proposed multi-camera 3D tracking method is specifically designed to work on schematic descriptions of the observations performed by each camera of the system: this choice allows the use of unspecific off-the-shelf 2D detection and/or tracking subsystems running independently at each sensor, and makes the proposal suitable for real surveillance networks with moderate computational and transmission capabilities. The robust combination of such noisy, incomplete and possibly unreliable schematic descriptors relies on a Bayesian association method, based on geometry and color, whose results allow the tracking of the targets in the scene with a particle filter. The main features exhibited by the proposal are, first, a remarkable accuracy in terms of target 3D positioning, and second, a great recovery ability after tracking losses due to insufficient input data. The proposed system for visual-based camera self-positioning uses the observations of moving objects and a schematic map of the passable areas of the environment to infer the absolute sensor position. To this end, a new Bayesian framework combining trajectory observations and map-induced dynamic models for moving objects is designed, which represents an approach to camera positioning never addressed before in the literature. This task is divided into two different sub-tasks, setting ambiguity analysis and approximate position estimation, on the one hand, and position refining, on the other, since they require the design of specific sampling algorithms to correctly exploit the discriminative features of the developed framework. This system, designed for camera positioning and demonstrated in urban traffic environments, can also be applied to different environments and sensors of other modalities after certain required adaptations.

Análisis mediante cálculo numérico (CFD) del comportamiento de anemómetros de cazoletas = CFD analysis of cup anemometers performance

El presente trabajo consiste en la simulación del flujo aerodinámico alrededor de cazoletas de anemómetros. Para ello se ha utilizado un código numérico o software comercial de análisis numérico de fluidos o CFD (Computational Fluid Dynamics). Este trabajo es un aporte más en la línea de investigación acerca del comportamiento de los anemómetros de cazoletas, que viene llevándose a cabo en el Instituto Universitario de Microgravedad “Ignacio Da Riva” (IDR/UPM). La primera parte de este proyecto consistió en la realización de simulaciones de tipo estacionarias (esto es, con la cazoleta bajo un cierto ángulo de incidencia con respecto al viento pero sin movimiento de rotación). De esta forma se analiza de forma independiente y asilada la cazoleta en cada una de las diferentes posiciones a lo largo de un giro de 360 grados. Así pues, a varios modelos de cazoleta se les fue variando su posición en incrementos de 10 grados desde de la posición angular inicial q = 0º hasta q = 180º, ya que las cazoletas presentan un comportamiento simétrico. La segunda parte de este proyecto se destinó a la realización de otra serie de simulaciones de tipo no estacionarias. Este tipo de simulaciones se realizaron concretamente a sólo un modelo de cazoleta (cónica no porosa). Estas últimas simulaciones, en concreto nueve, se realizaron variando la velocidad angular de la cazoleta respecto a la velocidad del viento.

A comparative analysis between FEM and Boundary Methods in bending of Plates

Two different methods of analysis of plate bending, FEM and BM are discussed in this paper. The plate behaviour is assumed to be represented by using the linear thin plate theory where the Poisson-Kirchoff assumption holds. The BM based in a weighted mean square error technique produced good results for the problem of plate bending. The computational effort demanded in the BM is smaller than the one needed in a FEM analysis for the same level of accuracy. The general application of the FEM cannot be matched by the BM. Particularly, different types of geometry (plates of arbitrary geometry) need a similar but not identical treatment in the BM. However, this loss of generality is counterbalanced by the computational efficiency gained in the BM in the solution achievement

Analysis of plate bending by means of high order finite hyperelements

The possibilities and limitations of high order hyperelements in plate bending analysis are discussed. Explicit shape functions for some types of triangular elements are given. These elements are applied to simple cases to assess their computational efficiency.

Wind tunnel analysis of the flow topology over complex topographies

El principal objetivo de este trabajo es aportar conocimiento para contestar la pregunta: ¿hasta que punto los ensayos en túnel aerodinámico pueden contribuir a determinar las características que afectan la respuesta dinámica de los aerogeneradores operando en terreno complejo?. Esta pregunta no es nueva, de hecho, el debate en la comunidad científica comenzó en el primer tercio del siglo pasado y aún está intensamente vivo. El método generalmente aceptado para enfrentar el mencionado problema consiste en analizar un caso de estudio determinado en el cual se aplican tanto ensayos a escala real como análisis computacionales y ensayos en túnel aerodinámico. Esto no es ni fácil ni barato. Esta es la razón por la cual desde el experimento de Askervein en 1988, los modelizadores del flujo atmosférico tuvieron que esperar hasta 2007 a que el experimento de Bolund fuese puesto en marcha con un despliegue de medios técnicos equivalentes (teniendo en cuenta la evolución de las tecnologías de sensores y computación). El problema contempla tantos aspectos que ambas experiencias fueron restringidas a condiciones de atmósfera neutra con efectos de Coriolis despreciables con objeto de reducir la complejidad. Este es el contexto en el que se ha desarrollado la presente tesis doctoral. La topología del flujo sobre la isla de Bolund ha sido estudiada mediante la reproducción del experimento de Bolund en los túneles aerodinámicos A9 y ACLA16 del IDR. Dos modelos de la isla de Bolund fueron fabricados a dos escalas, 1:230 y 1:115. El flujo de entrada en el túnel aerodinámico simulando la capa límite sin perturbar correspondía a régimen de transición (transitionally rough regime) y fue usado como situación de referencia. El modelo a escala 1:230 fue ensayado en el túnel A9 para determinar la presión sobre su superficie. La distribución del coeficiente de presión sobre la isla proporcionó una visualización y estimación de una región de desprendimiento sobre el pequeño acantilado situado al frente de la misma. Las medidas de presión instantánea con suficiente grado de resolución temporal pusieron de manifiesto la no estacionariedad en la región de desprendimiento. El modelo a escala 1:115 fue ensayado utilizando hilo caliente de tres componentes y un sistema de velocimetría por imágenes de partículas de dos componentes. El flujo fue caracterizado por el ratio de aceleración, el incremento normalizado de energía cinética turbulenta y los ángulos de inclinación y desviación horizontal. Los resultados a lo largo de la dirección 270°y alturas de 2 m y 5 m presentaron una gran similitud con los resultados a escala real del experimento de Bolund. Los perfiles verticales en las localizaciones de las torres meteorológicas mostraron un acuerdo significativo con los resultados a escala real. El análisis de los esfuerzos de Reynolds y el análisis espectral en las localizaciones de los mástiles meteorológicos presentaron niveles de acuerdo variados en ciertas posiciones, mientras que en otras presentaron claras diferencias. El mapeo horizontal del flujo, para una dirección de viento de 270°, permitió caracterizar el comportamiento de la burbuja intermitente de recirculación sobre el pequeño acantilado existente al frente de la isla así como de la región de relajación y de la capa de cortadura en la región corriente abajo de Bolund. Se realizaron medidas de velocidad con alta resolución espacial en planos perpendiculares a la dirección del flujo sin perturbar. Estas medidas permitieron detectar y caracterizar una estructura de flujo similar a un torbellino longitudinal con regiones con altos gradientes de velocidad y alta intensidad de turbulencia. Esta estructura de flujo es, sin duda, un reto para los modelos computacionales y puede considerarse un factor de riesgo para la operación de los aerogeneradores. Se obtuvieron y analizaron distribuciones espaciales de los esfuerzos de Reynolds mediante 3CHW y PIV. Este tipo de parámetros no constituyen parte de los resultados habituales en los ensayos en túnel sobre topografías y son muy útiles para los modelizadores que utilizan simulación de grades torbellinos (LES). Se proporciona una interpretación de los resultados obtenidos en el túnel aerodinámico en términos de utilidad para los diseñadores de parques eólicos. La evolución y variación de los parámetros del flujo a lo largo de líneas, planos y superficies han permitido identificar como estas propiedades del flujo podrían afectar la localización de los aerogeneradores y a la clasificación de emplazamientos. Los resultados presentados sugieren, bajo ciertas condiciones, la robustez de los ensayos en túnel para estudiar la topología sobre terreno complejo y su comparabilidad con otras técnicas de simulación, especialmente considerando el nivel de acuerdo del conjunto de resultados presentados con los resultados a escala real. De forma adicional, algunos de los parámetros del flujo obtenidos de las medidas en túnel son difícilmente determinables en ensayos a escala real o por medios computacionales, considerado el estado del arte. Este trabajo fue realizado como parte de las actividades subvencionadas por la Comisión Europea como dentro del proyecto FP7-PEOPLE-ITN-2008WAUDIT (Wind Resource Assessment Audit and Standardization) dentro de la FP7 Marie-Curie Initial Training Network y por el Ministerio Español de Economía y Competitividad dentro del proyecto ENE2012-36473, TURCO (Determinación en túnel aerodinámico de la distribución espacial de parámetros estadísticos de la turbulencia atmosférica sobre topografías complejas) del Plan Nacional de Investigación (Subprograma de investigación fundamental no orientada 2012). El informe se ha organizado en siete capítulos y un conjunto de anexos. En el primer capítulo se introduce el problema. En el capítulo dos se describen los medios experimentales utilizados. Seguidamente, en el capítulo tres, se analizan en detalle las condiciones de referencia del principal túnel aerodinámico utilizado en esta investigación. En el capítulo tres se presentan resultados de ensayos de presión superficial sobre un modelo de la isla. Los principales resultados del experimento de Bolund se reproducen en el capítulo cinco. En el capítulo seis se identifican diferentes estructuras del flujo sobre la isla y, finalmente, en el capitulo siete, se recogen las conclusiones y una propuesta de lineas de trabajo futuras. ABSTRACT The main objective of this work is to contribute to answer the question: to which extend can the wind tunnel testing contribute to determine the flow characteristics that affect the dynamic response of wind turbines operating in highly complex terrains?. This question is not new, indeed, the debate in the scientific community was opened in the first third of the past century and it is still intensely alive. The accepted approach to face this problem consists in analysing a given case study where full-scale tests, computational modelling and wind tunnel testing are applied to the same topography. This is neither easy nor cheap. This is is the reason why since the Askervein experience in 1988, the atmospheric flow modellers community had to wait till 2007 when the Bolund experiment was setup with a deployment of technical means equivalent (considering the evolution of the sensor and computing techniques). The problem is so manifold that both experiences were restricted to neutral conditions without Coriolis effects in order to reduce the complexity. This is the framework in which this PhD has been carried out. The flow topology over the Bolund Island has been studied by replicating the Bolund experiment in the IDR A9 and ACLA16 wind tunnels. Two mock-ups of the Bolund island were manufactured at two scales of 1:230 and 1:115. The in-flow in the empty wind tunnel simulating the incoming atmospheric boundary layer was in the transitionally rough regime and used as a reference case. The 1:230 model was tested in the A9 wind tunnel to measure surface pressure. The mapping of the pressure coefficient across the island gave a visualisation and estimation of a detachment region on the top of the escarpment in front of the island. Time resolved instantaneous pressure measurements illustrated the non-steadiness in the detachment region. The 1:115 model was tested using 3C hot-wires(HW) and 2C Particle Image Velocimetry(PIV). Measurements at met masts M3, M6, M7 and M8 and along Line 270°were taken to replicate the result of the Bolund experiment. The flow was characterised by the speed-up ratio, normalised increment of the turbulent kinetic energy, inclination angle and turning angle. Results along line 270°at heights of 2 m and 5 m compared very well with the full-scale results of the Bolund experiment. Vertical profiles at the met masts showed a significant agreement with the full-scale results. The analysis of the Reynolds stresses and the spectral analysis at the met mast locations gave a varied level of agreement at some locations while clear mismatch at others. The horizontal mapping of the flow field, for a 270°wind direction, allowed to characterise the behaviour of the intermittent recirculation bubble on top of the front escarpment followed by a relaxation region and the presence of a shear layer in the lee side of the island. Further detailed velocity measurements were taken at cross-flow planes over the island to study the flow structures on the island. A longitudinal vortex-like structure with high mean velocity gradients and high turbulent kinetic energy was characterised on the escarpment and evolving downstream. This flow structure is a challenge to the numerical models while posing a threat to wind farm designers when siting wind turbines. Spatial distribution of Reynold stresses were presented from 3C HW and PIV measurements. These values are not common results from usual wind tunnel measurements and very useful for modellers using large eddy simulation (LES). An interpretation of the wind tunnel results in terms of usefulness to wind farm designers is given. Evolution and variation of the flow parameters along measurement lines, planes and surfaces indicated how the flow field could affect wind turbine siting. Different flow properties were presented so compare the level of agreement to full-scale results and how this affected when characterising the site wind classes. The results presented suggest, under certain conditions, the robustness of the wind tunnel testing for studying flow topology over complex terrain and its capability to compare to other modelling techniques especially from the level of agreement between the different data sets presented. Additionally, some flow parameters obtained from wind tunnel measurements would have been quite difficult to be measured at full-scale or by computational means considering the state of the art. This work was carried out as a part of the activities supported by the EC as part of the FP7- PEOPLE-ITN-2008 WAUDIT project (Wind Resource Assessment Audit and Standardization) within the FP7 Marie-Curie Initial Training Network and by the Spanish Ministerio de Economía y Competitividad, within the framework of the ENE2012-36473, TURCO project (Determination of the Spatial Distribution of Statistic Parameters of Flow Turbulence over Complex Topographies in Wind Tunnel) belonging to the Spanish National Program of Research (Subprograma de investigación fundamental no orientada 2012). The report is organised in seven chapters and a collection of annexes. In chapter one, the problem is introduced. In chapter two the experimental setup is described. Following, in chapter three, the inflow conditions of the main wind tunnel used in this piece of research are analysed in detail. In chapter three, preliminary pressure tests results on a model of the island are presented. The main results from the Bolund experiment are replicated in chapter five. In chapter six, an identification of specific flow strutures over the island is presented and, finally, in chapter seven, conclusions and lines for future works related to the presented one are included.

A computer formulation for the analysis on continuous non prismatic folded plate structures of arbitrary cross-section

A computer solution to analyze nonprismatic folded plate structures is shown. Arbitrary cross-sections (simple and multiple), continuity over intermediate supports and general loading and longitudinal boundary conditions are dealt with. The folded plates are assumed to be straight and long (beam like structures) and some simplifications are introduced in order to reduce the computational effort. The formulation here presented may be very suitable to be used in the bridge deck analysis.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given