Fallo mecánico debido a grietas en Niobato de Litio bajo irradiación, simulación mediante elementos finitos

Ion-induced nano-track in LiNbO3. Motivation. From macro to nanoscale. Finite element method for nano-structured materials. Simulations of X-cut and Z-cut in LiNbO3. Experiments versus Simulations. Conclusions

Impedance of foundations using the Boundary Integral Equation Method

Dynamic soil-structure interaction has been for a long time one of the most fascinating areas for the engineering profession. The building of large alternating machines and their effects on surrounding structures as well as on their own functional behavior, provided the initial impetus; a large amount of experimental research was done,and the results of the Russian and German groups were especially worthwhile. Analytical results by Reissner and Sehkter were reexamined by Quinlan, Sung, et. al., and finally Veletsos presented the first set of reliable results. Since then, the modeling of the homogeneous, elastic halfspace as a equivalent set of springs and dashpots has become an everyday tool in soil engineering practice, especially after the appearance of the fast Fourier transportation algorithm, which makes possible the treatment of the frequency-dependent characteristics of the equivalent elements in a unified fashion with the general method of analysis of the structure. Extensions to the viscoelastic case, as well as to embedded foundations and complicated geometries, have been presented by various authors. In general, they used the finite element method with the well known problems of geometric truncations and the subsequent use of absorbing boundaries. The properties of boundary integral equation methods are, in our opinion, specially well suited to this problem, and several of the previous results have confirmed our opinion. In what follows we present the general features related to steady-state elastodynamics and a series of results showing the splendid results that the BIEM provided. Especially interesting are the outputs obtained through the use of the so-called singular elements, whose description is incorporated at the end of the paper. The reduction in time spent by the computer and the small number of elements needed to simulate realistically the global properties of the halfspace make this procedure one of the most interesting applications of the BIEM.

Modelling of chloride penetration into non-saturated concrete: Case study application for real marine off shore structures

The aim of this paper is to explain the chloride concentration profiles obtained experimentally from control samples of an offshore platform after 25 years of service life. The platform is located 12 km off the coast of the Brazilian province Rio Grande do Norte, in the north-east of Brazil. The samples were extracted at different orientations and heights above mean sea level. A simple model based on Fick’s second law is considered and compared with a finite element model which takes into account transport of chloride ions by diffusion and convection. Results show that convective flows significantly affect the studied chloride penetrations. The convection velocity is obtained by fitting the finite element solution to the experimental data and seems to be directly proportional to the height above mean sea level and also seems to depend on the orientation of the face of the platform. This work shows that considering solely diffusion as transport mechanism does not allow a good prediction of the chloride profiles. Accounting for capillary suction due to moisture gradients permits a better interpretation of the material’s behaviour.

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.

Large scale multiphysics modeling of neurites

Situado en el límite entre Ingeniería, Informática y Biología, la mecánica computacional de las neuronas aparece como un nuevo campo interdisciplinar que potencialmente puede ser capaz de abordar problemas clínicos desde una perspectiva diferente. Este campo es multiescala por naturaleza, yendo desde la nanoescala (como, por ejemplo, los dímeros de tubulina) a la macroescala (como, por ejemplo, el tejido cerebral), y tiene como objetivo abordar problemas que son complejos, y algunas veces imposibles, de estudiar con medios experimentales. La modelización computacional ha sido ampliamente empleada en aplicaciones Neurocientíficas tan diversas como el crecimiento neuronal o la propagación de los potenciales de acción compuestos. Sin embargo, en la mayoría de los enfoques de modelización hechos hasta ahora, la interacción entre la célula y el medio/estímulo que la rodea ha sido muy poco explorada. A pesar de la tremenda importancia de esa relación en algunos desafíos médicos—como, por ejemplo, lesiones traumáticas en el cerebro, cáncer, la enfermedad del Alzheimer—un puente que relacione las propiedades electrofisiológicas-químicas y mecánicas desde la escala molecular al nivel celular todavía no existe. Con ese objetivo, esta investigación propone un marco computacional multiescala particularizado para dos escenarios respresentativos: el crecimiento del axón y el acomplamiento electrofisiológicomecánico de las neuritas. En el primer caso, se explora la relación entre los constituyentes moleculares del axón durante su crecimiento y sus propiedades mecánicas resultantes, mientras que en el último, un estímulo mecánico provoca deficiencias funcionales a nivel celular como consecuencia de sus alteraciones electrofisiológicas-químicas. La modelización computacional empleada en este trabajo es el método de las diferencias finitas, y es implementada en un nuevo programa llamado Neurite. Aunque el método de los elementos finitos es también explorado en parte de esta investigación, el método de las diferencias finitas tiene la flexibilidad y versatilidad necesaria para implementar mode los biológicos, así como la simplicidad matemática para extenderlos a simulaciones a gran escala con un coste computacional bajo. Centrándose primero en el efecto de las propiedades electrofisiológicas-químicas sobre las propiedades mecánicas, una versión adaptada de Neurite es desarrollada para simular la polimerización de los microtúbulos en el crecimiento del axón y proporcionar las propiedades mecánicas como función de la ocupación de los microtúbulos. Después de calibrar el modelo de crecimiento del axón frente a resultados experimentales disponibles en la literatura, las características mecánicas pueden ser evaluadas durante la simulación. Las propiedades mecánicas del axón muestran variaciones dramáticas en la punta de éste, donde el cono de crecimiento soporta las señales químicas y mecánicas. Bansándose en el conocimiento ganado con el modelo de diferencias finitas, y con el objetivo de ir de 1D a 3D, este esquema preliminar pero de una naturaleza innovadora allana el camino a futuros estudios con el método de los elementos finitos. Centrándose finalmente en el efecto de las propiedades mecánicas sobre las propiedades electrofisiológicas- químicas, Neurite es empleado para relacionar las cargas mecánicas macroscópicas con las deformaciones y velocidades de deformación a escala microscópica, y simular la propagación de la señal eléctrica en las neuritas bajo carga mecánica. Las simulaciones fueron calibradas con resultados experimentales publicados en la literatura, proporcionando, por tanto, un modelo capaz de predecir las alteraciones de las funciones electrofisiológicas neuronales bajo cargas externas dañinas, y uniendo lesiones mecánicas con las correspondientes deficiencias funcionales. Para abordar simulaciones a gran escala, aunque otras arquitecturas avanzadas basadas en muchos núcleos integrados (MICs) fueron consideradas, los solvers explícito e implícito se implementaron en unidades de procesamiento central (CPU) y unidades de procesamiento gráfico (GPUs). Estudios de escalabilidad fueron llevados acabo para ambas implementaciones mostrando resultados prometedores para casos de simulaciones extremadamente grandes con GPUs. Esta tesis abre la vía para futuros modelos mecánicos con el objetivo de unir las propiedades electrofisiológicas-químicas con las propiedades mecánicas. El objetivo general es mejorar el conocimiento de las comunidades médicas y de bioingeniería sobre la mecánica de las neuronas y las deficiencias funcionales que aparecen de los daños producidos por traumatismos mecánicos, como lesiones traumáticas en el cerebro, o enfermedades neurodegenerativas como la enfermedad del Alzheimer. ABSTRACT Sitting at the interface between Engineering, Computer Science and Biology, Computational Neuron Mechanics appears as a new interdisciplinary field potentially able to tackle clinical problems from a new perspective. This field is multiscale by nature, ranging from the nanoscale (e.g., tubulin dimers) to the macroscale (e.g., brain tissue), and aims at tackling problems that are complex, and sometime impossible, to study through experimental means. Computational modeling has been widely used in different Neuroscience applications as diverse as neuronal growth or compound action potential propagation. However, in the majority of the modeling approaches done in this field to date, the interactions between the cell and its surrounding media/stimulus have been rarely explored. Despite of the tremendous importance of such relationship in several medical challenges—e.g., traumatic brain injury (TBI), cancer, Alzheimer’s disease (AD)—a bridge between electrophysiological-chemical and mechanical properties of neurons from the molecular scale to the cell level is still lacking. To this end, this research proposes a multiscale computational framework particularized for two representative scenarios: axon growth and electrophysiological-mechanical coupling of neurites. In the former case, the relation between the molecular constituents of the axon during its growth and its resulting mechanical properties is explored, whereas in the latter, a mechanical stimulus provokes functional deficits at cell level as a consequence of its electrophysiological-chemical alterations. The computational modeling approach chosen in this work is the finite difference method (FDM), and was implemented in a new program called Neurite. Although the finite element method (FEM) is also explored as part of this research, the FDM provides the necessary flexibility and versatility to implement biological models, as well as the mathematical simplicity to extend them to large scale simulations with a low computational cost. Focusing first on the effect of electrophysiological-chemical properties on the mechanical proper ties, an adaptation of Neurite was developed to simulate microtubule polymerization in axonal growth and provide the axon mechanical properties as a function of microtubule occupancy. After calibrating the axon growth model against experimental results available in the literature, the mechanical characteristics can be tracked during the simulation. The axon mechanical properties show dramatic variations at the tip of the axon, where the growth cone supports the chemical and mechanical signaling. Based on the knowledge gained from the FDM scheme, and in order to go from 1D to 3D, this preliminary yet novel scheme paves the road for future studies with FEM. Focusing then on the effect of mechanical properties on the electrophysiological-chemical properties, Neurite was used to relate macroscopic mechanical loading to microscopic strains and strain rates, and simulate the electrical signal propagation along neurites under mechanical loading. The simulations were calibrated against experimental results published in the literature, thus providing a model able to predict the alteration of neuronal electrophysiological function under external damaging load, and linking mechanical injuries to subsequent acute functional deficits. To undertake large scale simulations, although other state-of-the-art architectures based on many integrated cores (MICs) were considered, the explicit and implicit solvers were implemented for central processing units (CPUs) and graphics processing units (GPUs). Scalability studies were done for both implementations showing promising results for extremely large scale simulations with GPUs. This thesis opens the avenue for future mechanical modeling approaches aimed at linking electrophysiological- chemical properties to mechanical properties. Its overarching goal is to enhance the bioengineering and medical communities knowledge on neuronal mechanics and functional deficits arising from damages produced by direct mechanical insults, such as TBI, or neurodegenerative evolving illness, such as AD.

Numerical model for the study of hydrodynamics on bays and estuaries

A nonlinear implicit finite element model for the solution of two-dimensional (2-D) shallow water equations, based on a Galerkin formulation of the 2-D estuaries hydrodynamic equations, has been developed. Spatial discretization has been achieved by the use of isoparametric, Lagrangian elements. To obtain the different element matrices, Simpson numerical integration has been applied. For time integration of the model, several schemes in finite differences have been used: the Cranck-Nicholson iterative method supplies a superior accuracy and allows us to work with the greatest time step Δt; however, central differences time integration produces a greater velocity of calculation. The model has been tested with different examples to check its accuracy and advantages in relation to computation and handling of matrices. Finally, an application to the Bay of Santander is also presented.

Dynamic analysis of payloads and structures with intermediate modal density

La necesidad de desarrollar técnicas para predecir la respuesta vibroacústica de estructuras espaciales lia ido ganando importancia en los últimos años. Las técnicas numéricas existentes en la actualidad son capaces de predecir de forma fiable el comportamiento vibroacústico de sistemas con altas o bajas densidades modales. Sin embargo, ambos rangos no siempre solapan lo que hace que sea necesario el desarrollo de métodos específicos para este rango, conocido como densidad modal media. Es en este rango, conocido también como media frecuencia, donde se centra la presente Tesis doctoral, debido a la carencia de métodos específicos para el cálculo de la respuesta vibroacústica. Para las estructuras estudiadas en este trabajo, los mencionados rangos de baja y alta densidad modal se corresponden, en general, con los rangos de baja y alta frecuencia, respectivamente. Los métodos numéricos que permiten obtener la respuesta vibroacústica para estos rangos de frecuencia están bien especificados. Para el rango de baja frecuencia se emplean técnicas deterministas, como el método de los Elementos Finitos, mientras que, para el rango de alta frecuencia las técnicas estadísticas son más utilizadas, como el Análisis Estadístico de la Energía. En el rango de medias frecuencias ninguno de estos métodos numéricos puede ser usado con suficiente precisión y, como consecuencia -a falta de propuestas más específicas- se han desarrollado métodos híbridos que combinan el uso de métodos de baja y alta frecuencia, intentando que cada uno supla las deficiencias del otro en este rango medio. Este trabajo propone dos soluciones diferentes para resolver el problema de la media frecuencia. El primero de ellos, denominado SHFL (del inglés Subsystem based High Frequency Limit procedure), propone un procedimiento multihíbrido en el cuál cada subestructura del sistema completo se modela empleando una técnica numérica diferente, dependiendo del rango de frecuencias de estudio. Con este propósito se introduce el concepto de límite de alta frecuencia de una subestructura, que marca el límite a partir del cual dicha subestructura tiene una densidad modal lo suficientemente alta como para ser modelada utilizando Análisis Estadístico de la Energía. Si la frecuencia de análisis es menor que el límite de alta frecuencia de la subestructura, ésta se modela utilizando Elementos Finitos. Mediante este método, el rango de media frecuencia se puede definir de una forma precisa, estando comprendido entre el menor y el mayor de los límites de alta frecuencia de las subestructuras que componen el sistema completo. Los resultados obtenidos mediante la aplicación de este método evidencian una mejora en la continuidad de la respuesta vibroacústica, mostrando una transición suave entre los rangos de baja y alta frecuencia. El segundo método propuesto se denomina HS-CMS (del inglés Hybrid Substructuring method based on Component Mode Synthesis). Este método se basa en la clasificación de la base modal de las subestructuras en conjuntos de modos globales (que afectan a todo o a varias partes del sistema) o locales (que afectan a una única subestructura), utilizando un método de Síntesis Modal de Componentes. De este modo es posible situar espacialmente los modos del sistema completo y estudiar el comportamiento del mismo desde el punto de vista de las subestructuras. De nuevo se emplea el concepto de límite de alta frecuencia de una subestructura para realizar la clasificación global/local de los modos en la misma. Mediante dicha clasificación se derivan las ecuaciones globales del movimiento, gobernadas por los modos globales, y en las que la influencia del conjunto de modos locales se introduce mediante modificaciones en las mismas (en su matriz dinámica de rigidez y en el vector de fuerzas). Las ecuaciones locales se resuelven empleando Análisis Estadístico de Energías. Sin embargo, este último será un modelo híbrido, en el cual se introduce la potencia adicional aportada por la presencia de los modos globales. El método ha sido probado para el cálculo de la respuesta de estructuras sometidas tanto a cargas estructurales como acústicas. Ambos métodos han sido probados inicialmente en estructuras sencillas para establecer las bases e hipótesis de aplicación. Posteriormente, se han aplicado a estructuras espaciales, como satélites y reflectores de antenas, mostrando buenos resultados, como se concluye de la comparación de las simulaciones y los datos experimentales medidos en ensayos, tanto estructurales como acústicos. Este trabajo abre un amplio campo de investigación a partir del cual es posible obtener metodologías precisas y eficientes para reproducir el comportamiento vibroacústico de sistemas en el rango de la media frecuencia. ABSTRACT Over the last years an increasing need of novel prediction techniques for vibroacoustic analysis of space structures has arisen. Current numerical techniques arc able to predict with enough accuracy the vibro-acoustic behaviour of systems with low and high modal densities. However, space structures are, in general, very complex and they present a range of frequencies in which a mixed behaviour exist. In such cases, the full system is composed of some sub-structures which has low modal density, while others present high modal density. This frequency range is known as the mid-frequency range and to develop methods for accurately describe the vibro-acoustic response in this frequency range is the scope of this dissertation. For the structures under study, the aforementioned low and high modal densities correspond with the low and high frequency ranges, respectively. For the low frequency range, deterministic techniques as the Finite Element Method (FEM) are used while, for the high frequency range statistical techniques, as the Statistical Energy Analysis (SEA), arc considered as more appropriate. In the mid-frequency range, where a mixed vibro-acoustic behaviour is expected, any of these numerical method can not be used with enough confidence level. As a consequence, it is usual to obtain an undetermined gap between low and high frequencies in the vibro-acoustic response function. This dissertation proposes two different solutions to the mid-frequency range problem. The first one, named as The Subsystem based High Frequency Limit (SHFL) procedure, proposes a multi-hybrid procedure in which each sub-structure of the full system is modelled with the appropriate modelling technique, depending on the frequency of study. With this purpose, the concept of high frequency limit of a sub-structure is introduced, marking out the limit above which a substructure has enough modal density to be modelled by SEA. For a certain analysis frequency, if it is lower than the high frequency limit of the sub-structure, the sub-structure is modelled through FEM and, if the frequency of analysis is higher than the high frequency limit, the sub-structure is modelled by SEA. The procedure leads to a number of hybrid models required to cover the medium frequency range, which is defined as the frequency range between the lowest substructure high frequency limit and the highest one. Using this procedure, the mid-frequency range can be define specifically so that, as a consequence, an improvement in the continuity of the vibro-acoustic response function is achieved, closing the undetermined gap between the low and high frequency ranges. The second proposed mid-frequency solution is the Hybrid Sub-structuring method based on Component Mode Synthesis (HS-CMS). The method adopts a partition scheme based on classifying the system modal basis into global and local sets of modes. This classification is performed by using a Component Mode Synthesis, in particular a Craig-Bampton transformation, in order to express the system modal base into the modal bases associated with each sub-structure. Then, each sub-structure modal base is classified into global and local set, fist ones associated with the long wavelength motion and second ones with the short wavelength motion. The high frequency limit of each sub-structure is used as frequency frontier between both sets of modes. From this classification, the equations of motion associated with global modes are derived, which include the interaction of local modes by means of corrections in the dynamic stiffness matrix and the force vector of the global problem. The local equations of motion are solved through SEA, where again interactions with global modes arc included through the inclusion of an additional input power into the SEA model. The method has been tested for the calculation of the response function of structures subjected to structural and acoustic loads. Both methods have been firstly tested in simple structures to establish their basis and main characteristics. Methods are also verified in space structures, as satellites and antenna reflectors, providing good results as it is concluded from the comparison with experimental results obtained in both, acoustic and structural load tests. This dissertation opens a wide field of research through which further studies could be performed to obtain efficient and accurate methodologies to appropriately reproduce the vibro-acoustic behaviour of complex systems in the mid-frequency range.

Numerical models for coastal zone management

The basic equations for modelling two-dimensional hydrodynamics and transport in estuaries and coastal regions have been developed. By using the finite element method, it is possible to transform the model into a discretized counterpart. The model has been applied in order to study the dispersion of an effluent within the Bay of Santander. The results obtained by means of a computer program are discussed.

Análisis mediante elementos finitos del comportamiento de losas de hormigón armado sometidas a explosiones

Se presenta en este trabajo una investigación sobre el comportamiento de losas de hormigón armado sometidas a explosiones y la simulación numérica de dicho fenómeno mediante el método de los elementos finitos. El trabajo aborda el estudio de la respuesta de dichos elementos estructurales por comparación entre los resultados obtenidos en ensayos reales a escala 1:1 y los cálculos realizados mediante modelos de ordenador. Este procedimiento permite verificar la idoneidad, o no, de estos últimos. Se expone en primer lugar el comportamiento mecánico de los modelos de material que son susceptibles de emplearse en la simulación de estructuras mediante el software empleado en la presente investigación, así como las diferentes formas de aplicar cargas explosivas en estructuras modeladas mediante el método de los Elementos Finitos, razonándose en ambos casos la elección llevada a cabo. Posteriormente, se describen los ensayos experimentales disponibles, que tuvieron lugar en las instalaciones del Laboratorio de Balística de Efectos, perteneciente al Instituto Tecnológico de la Marañosa (ITM), de Madrid, para estudiar el comportamiento de losas de hormigón armado a escala 1:1 sometidas a explosiones reales. Se ha propuesto un método de interpretación del nivel de daño en las losas mediante el martillo de Schmidt, que posteriormente permitirá comparar resultados con los modelos de ordenador realizados. Asimismo, se propone un método analítico para la determinación del tamaño óptimo de la malla en las simulaciones realizadas, basado en la distribución de la energía interna del sistema. Es conocido que el comportamiento de los modelos pueden verse fuertemente influenciados por el mallado empleado. Según el mallado sea “grosero” o “fino” el fallo puede no alcanzarse o hacerlo de forma prematura, o excesiva, respectivamente. Es más, algunos modelos de material contemplan una “regularización” del tamaño de la malla, pero en la presente investigación se evidencia que dicho procedimiento tiene un rango de validez limitado, incluso se determina un entorno óptimo de valores. Finalmente, se han elaborado los modelos numéricos con el software comercial LS-DYNA, contemplando todos los aspectos reseñados en los párrafos anteriores, procediendo a realizar una comparación de los resultados obtenidos en las simulaciones con los procedidos en los ensayos reales a escala 1:1, observando que existe una muy buena correlación entre ambas situaciones que evidencian que el procedimiento propuesto en la investigación es de todo punto adecuado para la simulación de losas de hormigón armado sometidas a explosiones. ABSTRACT This doctoral thesis presents an investigation on the behavior of reinforced concrete slabs subjected to explosions along with the numerical simulation of this phenomenon by the finite elements method. The work involves the study of the response of these structural elements by comparing the results of field tests at full scale and the calculations performed by the computer model. This procedure allows to verify the appropriateness or not of the latter. Firstly, the mechanical behavior of the material models that are likely to be used in the modelling of structures is explained. In addition, different ways of choosing explosive charges when conducting finite element methods are analyzed and discussed. Secondly, several experimental tests, which took place at the Laboratorio de Balística de Efectos at the Instituto Tecnológico de la Marañosa (ITM), in Madrid, are described in order to study the behavior of these reinforced concrete slabs. A method for the description of the slab damage level by the Schmidt hammer is proposed, which will make possible to compare the modelling results extracted from the computation experiments. Furthermore, an analytical method for determining the optimal mesh size to be used in the simulations is proposed. It is well known that the behavior of the models can be strongly influenced by the mesh size used. According to this, when modifiying the meshing density the damaged cannot be reached or do it prematurely, or excessive, respectively. Moreover, some material models include a regularization of the mesh size, but the present investigation evidenced that this procedure has a limited range of validity, even an optimal environment values are determined. The method proposed is based on the distribution of the internal energy of the system. Finally, several expecific numerical models have been performed by using LS-DYNA commercial software, considering all the aspects listed in the preceding paragraphs. Comparisons of the results extracted from the simulations and full scale experiments were carried out, noting that there exists a very good correlation between both of them. This fact demonstrates that the proposed research procedure is highly suitable for the modelling of reinforced concrete slabs subjected to blast loading.

Modelling of chloride penetration into non-saturated concrete: case study application for real marine offshore structures

The aim of this paper is to explain the chloride concentration profiles obtained experimentally from control samples of an offshore platform after 25 years of service life. The platform is located 12 km off the coast of the Brazilian province Rio Grande do Norte, in the north-east of Brazil. The samples were extracted at different orientations and heights above mean sea level. A simple model based on Fick’s second law is considered and compared with a finite element model which takes into account transport of chloride ions by diffusion and convection. Results show that convective flows significantly affect the studied chloride penetrations. The convection velocity is obtained by fitting the finite element solution to the experimental data and seems to be directly proportional to the height above mean sea level and also seems to depend on the orientation of the face of the platform. This work shows that considering solely diffusion as transport mechanism does not allow a good prediction of the chloride profiles. Accounting for capillary suction due to moisture gradients permits a better interpretation of the material’s behaviour

Influencia de la configuración geométrica de placas prefabricadas para forjados en las tensiones originadas por la transferencia del pretensado en elementos realizados con armaduras pretesas ancladas por adherencia

Las piezas pretensadas de hormigón presentan zonas muy solicitadas correspondientes a la zona de transferencia. En muchos casos se ha detectado figuración en tales zonas cuyo origen está ligado a la transferencia de la fuerza de pretensado, pudiendo llegar a causar el rechazo de la pieza. En el caso de las piezas prefabricadas con armaduras pretesas adherentes, no siempre es posible disponer armado transversal para controlar esta fisuración, ya sea por el proceso constructivo, ya sea por disponer en general de secciones transversales muy optimizadas. Recientemente se desarrolló una nueva tipología de piezas de hormigón prefabricado para forjados unidireccionales pretensadas con armadura activa pretesa y sin armadura transversal. La tipología se asimila a una sección en PI invertida, con alas de gran envergadura en comparación con el ancho de nervio, y armadura activa distribuida en las alas. Este diseño parece propenso a la aparición de fisuración en el momento de la transferencia del pretensado. Así, se han producido fallos de carácter frágil: colapso de piezas ya colocadas en obra, separándose la losa inferior de los nervios y cayendo sobre el piso. Las herramientas de análisis usuales han resultado inútiles al aplicarse a la investigación de esta patología. Para afrontar el estudio de los problemas detectados en la tipología, se ha analizado el fenómeno de las tensiones de tracción en la zona de transferencia, usualmente denominadas exfoliación y estallido, así como los métodos de análisis aplicables a elementos pretesos sin armadura transversal. En algunas ocasiones se trata del resultado de trabajos desarrollados para piezas postesadas, o para calcular cuantías de armadura transversal, adaptados a posteriori. También existen métodos desarrollados específicamente para piezas pretesas sin armadura transversal. Junto a los factores considerados en los métodos existentes se han localizado otros, no tenidos en cuenta habitualmente, pero que pueden ser determinantes en piezas no convencionales, como son: la existencia de pretensado superior e inferior, la falta de simetría de la sección transversal, el ancho variable de las piezas, una relación entre el ancho del ala y el espesor de los nervios elevada, la distribución transversal del pretensado en relación al ancho variable. Además, la mayoría de los métodos se han basado en simplificaciones bidimensionales. Para tener en cuenta la influencia de estos factores, se han modelizado piezas en las que varían tanto la geometría de la sección transversal y la cuantía de pretensado, como la ley de adherencia o la distribución de armadura activa en la sección. Estos modelos se han analizado mediante el método de elementos finitos, efectuándose u análisis elástico lineal tridimensional. En general, los métodos existentes no han predicho adecuadamente las tensiones obtenidas mediante elementos finitos. Sobre los resultados obtenidos por elementos finitos se ha desarrollado un ajuste experimental, que presentan un alto grado de correlación y de significación, así como una reducida dispersión y error relativo. En consecuencia, se propone un método de obtención de la tensión máxima de exfoliación, consistente en varias ecuaciones, que tienen en cuenta las peculiaridades de la configuración de las piezas citadas y permiten considerar cualquier ley de adherencia, manteniendo la coherencia con la longitud de transmisión. Las ecuaciones se emplean para la obtención de la tensión máxima de exfoliación en piezas de la tipología estudiada cuya armadura activa se sitúe fuera del núcleo central de la sección transversal. Respecto al estallido, se propone una modificación de los métodos existentes que, comparado con los resultados del análisis por elementos finitos, mejora el valor medio y la dispersión a valores admisibles y del lado de la seguridad. El método considera la geometría de la sección y la distribución del pretensado en la losa inferior. Finalmente, se ofrecen estrategias de diseño para piezas de la tipología o semejantes. End zones of prestressed concrete members are highly stressed. Cracking have often appeared at end zone, and its beginning is related to prestress release. Some members become rejected because of these cracks. Sometimes it is not possible having transverse reinforcement in order to control cracking, when referring to pretensioned precast members. The reason may be the construction process or highly optimized crosssections. A new typology of precast concrete members designed for one-way composite floors was recently developed. The members, without transverse reinforcement, are prestressed with pretensioned wires or strands. This typology is similar to an inverted TT slab, with a large flange related to the web thickness and prestressing reinforcement spread across the flange. This design is highly susceptible to appear cracking at prestress release. Therefore, brittle failures have been reported: fail of slabs laid in place on a construction site, resulting in the separation of the flange from the webs,, and the subsequent fall on the lower floor. Usual analytical methods have been useless to study the failure. End zone tensile stresses have been analysed to study the detected typology problems. These tensile stresses are usually called spalling and bursting (also called splitting in the U.S.). Analysis methods applicable to pretensioned members without transverse reinforcement have been analysed too. Some methods were originally developed for postensioned concrete or for obtaining the amount of transverse reinforcement. In addition, there are methods developed specifically for pretensioned members without transverse reinforcement. Some factors, frequently ignored, have been found, such as lower and upper prestress, lack of symmetry in the cross section, variable width, a high ratio between flange width and web thickness or prestressing reinforcement location related to variable width. They can play a decisive role in non-conventional members. In addition, most methods are based on 2D simplifications. Finite Element modelling has been conducted in order to consider the influence of these factors. A linear 3D approach has been used. The modelled members vary according to cross section geometry, bond behaviour, or prestressing reinforcement location. In general, the obtained tensile stresses don’t agree with existing methods. An experimental adjustment has been conducted on the obtained results, with a high correlation ratio and significance level as well as a low dispersion and relative error. Therefore, a method to obtain the maximum spalling stress is proposed. The proposal consists on some equations that consider the special features of the typology and bond behaviour. Consistency between transmission length and bond behaviour is considered too. The equations are used to calculate maximum spalling stress for the studied typology members whose prestressing reinforcement is located out of the core of the cross section. In relation to bursting, a modification of existing methods is proposed. Compared to finite element results, the proposal improves mean value and dispersion, whose ranges are considered acceptable and secure. The method takes into account cross section geometry and location of prestressing reinforcement across the lower flange. Finally, strategies to design members of this typology or similar are proposed.

Beam Spectral Element with FRP Debonding

The behaviour of the interface between the FRP and the concrete is the key factor controlling debonding failures in FRP-strengthened RC structures. This defect can cause reductions in static strength, structural integrity and the change in the dynamic behavior of the structure. The adverse effect on the dynamic behavior of the defects can be utilized as an effective means for identifying and assessing both the location and size of debonding at its earliest stages. The presence of debonding changes the structural dynamic characteristics and might be traced in modal parameters, dynamic strain and wave patterns etc. Detection of minor local defects, as those origin of a future debonding, requires working at high frequencies so that the wavelength of the excited is small and sensitive enough to detect local damage. The development of a spectral element method gives a large potential in high-frequency structural modeling. In contrast to the conventional finite element, since inertial properties are modeled exactly few elements are necessary to capture very accurate solutions at the highest frequencies in large regions. A wide variety of spectral elements have been developed for structural members over finite and semi-infinite regions. The objective of this paper is to develop a Spectral Finite Element Model to efficiently capture the behavior of intermediate debonding of a FRP strengthened RC beam during wave-based diagnostics.

Nonlinear seismic behaviour of concrete arch bridges

Arch bridge structural solution has been known for centuries, in fact the simple nature of arch that require low tension and shear strength was an advantage as the simple materials like stone and brick were the only option back in ancient centuries. By the pass of time especially after industrial revolution, the new materials were adopted in construction of arch bridges to reach longer spans. Nowadays one long span arch bridge is made of steel, concrete or combination of these two as "CFST", as the result of using these high strength materials, very long spans can be achieved. The current record for longest arch belongs to Chaotianmen bridge over Yangtze river in China with 552 meters span made of steel and the longest reinforced concrete type is Wanxian bridge which also cross the Yangtze river through a 420 meters span. Today the designer is no longer limited by span length as long as arch bridge is the most applicable solution among other approaches, i.e. cable stayed and suspended bridges are more reasonable if very long span is desired. Like any super structure, the economical and architectural aspects in construction of a bridge is extremely important, in other words, as a narrower bridge has better appearance, it also require smaller volume of material which make the design more economical. Design of such bridge, beside the high strength materials, requires precise structural analysis approaches capable of integrating the combination of material behaviour and complex geometry of structure and various types of loads which may be applied to bridge during its service life. Depend on the design strategy, analysis may only evaluates the linear elastic behaviour of structure or consider the nonlinear properties as well. Although most of structures in the past were designed to act in their elastic range, the rapid increase in computational capacity allow us to consider different sources of nonlinearities in order to achieve a more realistic evaluations where the dynamic behaviour of bridge is important especially in seismic zones where large movements may occur or structure experience P - _ effect during the earthquake. The above mentioned type of analysis is computationally expensive and very time consuming. In recent years, several methods were proposed in order to resolve this problem. Discussion of recent developments on these methods and their application on long span concrete arch bridges is the main goal of this research. Accordingly available long span concrete arch bridges have been studied to gather the critical information about their geometrical aspects and properties of their materials. Based on concluded information, several concrete arch bridges were designed for further studies. The main span of these bridges range from 100 to 400 meters. The Structural analysis methods implemented in in this study are as following: Elastic Analysis: Direct Response History Analysis (DRHA): This method solves the direct equation of motion over time history of applied acceleration or imposed load in linear elastic range. Modal Response History Analysis (MRHA): Similar to DRHA, this method is also based on time history, but the equation of motion is simplified to single degree of freedom system and calculates the response of each mode independently. Performing this analysis require less time than DRHA. Modal Response Spectrum Analysis (MRSA): As it is obvious from its name, this method calculates the peak response of structure for each mode and combine them using modal combination rules based on the introduced spectra of ground motion. This method is expected to be fastest among Elastic analysis. Inelastic Analysis: Nonlinear Response History Analysis (NL-RHA): The most accurate strategy to address significant nonlinearities in structural dynamics is undoubtedly the nonlinear response history analysis which is similar to DRHA but extended to inelastic range by updating the stiffness matrix for every iteration. This onerous task, clearly increase the computational cost especially for unsymmetrical buildings that requires to be analyzed in a full 3D model for taking the torsional effects in to consideration. Modal Pushover Analysis (MPA): The Modal Pushover Analysis is basically the MRHA but extended to inelastic stage. After all, the MRHA cannot solve the system of dynamics because the resisting force fs(u; u_ ) is unknown for inelastic stage. The solution of MPA for this obstacle is using the previously recorded fs to evaluate system of dynamics. Extended Modal Pushover Analysis (EMPA): Expanded Modal pushover is a one of very recent proposed methods which evaluates response of structure under multi-directional excitation using the modal pushover analysis strategy. In one specific mode,the original pushover neglect the contribution of the directions different than characteristic one, this is reasonable in regular symmetric building but a structure with complex shape like long span arch bridges may go through strong modal coupling. This method intend to consider modal coupling while it take same time of computation as MPA. Coupled Nonlinear Static Pushover Analysis (CNSP): The EMPA includes the contribution of non-characteristic direction to the formal MPA procedure. However the static pushovers in EMPA are performed individually for every mode, accordingly the resulted values from different modes can be combined but this is only valid in elastic phase; as soon as any element in structure starts yielding the neutral axis of that section is no longer fixed for both response during the earthquake, meaning the longitudinal deflection unavoidably affect the transverse one or vice versa. To overcome this drawback, the CNSP suggests executing pushover analysis for governing modes of each direction at the same time. This strategy is estimated to be more accurate than MPA and EMPA, moreover the calculation time is reduced because only one pushover analysis is required. Regardless of the strategy, the accuracy of structural analysis is highly dependent on modelling and numerical integration approaches used in evaluation of each method. Therefore the widely used Finite Element Method is implemented in process of all analysis performed in this research. In order to address the study, chapter 2, starts with gathered information about constructed long span arch bridges, this chapter continuous with geometrical and material definition of new models. Chapter 3 provides the detailed information about structural analysis strategies; furthermore the step by step description of procedure of all methods is available in Appendix A. The document ends with the description of results and conclusion of chapter 4.

Análisis paramétrico determinista y aleatorio de problemas dinámicos en estructuras aeroespaciales

Los fenómenos dinámicos pueden poner en peligro la integridad de estructuras aeroespaciales y los ingenieros han desarrollado diferentes estrategias para analizarlos. Uno de los grandes problemas que se plantean en la ingeniería es cómo atacar un problema dinámico estructural. En la presente tesis se plantean distintos fenómenos dinámicos y se proponen métodos para estimar o simular sus comportamientos mediante un análisis paramétrico determinista y aleatorio del problema. Se han propuesto desde problemas sencillos con pocos grados de libertad que sirven para analizar las diferentes estrategias y herramientas a utilizar, hasta fenómenos muy dinámicos que contienen comportamientos no lineales, daños y fallos. Los primeros ejemplos de investigación planteados cubren una amplia gama de los fenómenos dinámicos, como el análisis de vibraciones de elementos másicos, incluyendo impactos y contactos, y el análisis de una viga con carga armónica aplicada a la que también se le añaden parámetros aleatorios que pueden responder a un desconocimiento o incertidumbre de los mismos. Durante el desarrollo de la tesis se introducen conceptos y se aplican distintos métodos, como el método de elementos finitos (FEM) en el que se analiza su resolución tanto por esquemas implícitos como explícitos, y métodos de análisis paramétricos y estadísticos mediante la técnica de Monte Carlo. Más adelante, una vez ya planteadas las herramientas y estrategias de análisis, se estudian fenómenos más complejos, como el impacto a baja velocidad en materiales compuestos, en el que se busca evaluar la resistencia residual y, por lo tanto, la tolerancia al daño de la estructura. Se trata de un suceso que puede producirse por la caída de herramienta, granizo o restos en la pista de aterrizaje. Otro de los fenómenos analizados también se da en un aeropuerto y se trata de la colisión con un dispositivo frangible, el cual tiene que romperse bajo ciertas cargas y, sin embargo, soportar otras. Finalmente, se aplica toda la metodología planteada en simular y analizar un posible incidente en vuelo, el fenómeno de la pérdida de pala de un turbohélice. Se trata de un suceso muy particular en el que la estructura tiene que soportar unas cargas complejas y excepcionales con las que la aeronave debe ser capaz de completar con éxito el vuelo. El análisis incluye comportamientos no lineales, daños, y varios tipos de fallos, y en el que se trata de identificar los parámetros clave en la secuencia del fallo. El suceso se analiza mediante análisis estructurales deterministas más habituales y también mediante otras técnicas como el método de Monte Carlo con el que se logran estudiar distintas incertidumbres en los parámetros con variables aleatorias. Se estudian, entre otros, el tamaño de pala perdida, la velocidad y el momento en el que se produce la rotura, y la rigidez y resistencia de los apoyos del motor. Se tiene en cuenta incluso el amortiguamiento estructural del sistema. Las distintas estrategias de análisis permiten obtener unos resultados valiosos e interesantes que han sido objeto de distintas publicaciones. ABSTRACT Dynamic phenomena can endanger the integrity of aerospace structures and, consequently, engineers have developed different strategies to analyze them. One of the major engineering problems is how to deal with the structural dynamics. In this thesis, different dynamic phenomena are introduced and several methods are proposed to estimate or simulate their behaviors. The analysis is considered through parametric, deterministic and statistical methods. The suggested issues are from simple problems with few degrees of freedom, in order to develop different strategies and tools to solve them, to very dynamic phenomena containing nonlinear behaviors failures, damages. The first examples cover a wide variety of dynamic phenomena such as vibration analysis of mass elements, including impacts and contacts, and beam analysis with harmonic load applied, in which random parameters are included. These parameters can represent the unawareness or uncertainty of certain variables. During the development of the thesis several concepts are introduced and different methods are applied, such as the finite element method (FEM), which is solved through implicit and explicit schemes, and parametrical and statistical methods using the Monte Carlo analysis technique. Next, once the tools and strategies of analysis are set out more complex phenomena are studied. This is the case of a low-speed impact in composite materials, the residual strength of the structure is evaluated, and therefore, its damage tolerance. This incident may occur from a tool dropped, hail or debris throw on the runway. At an airport may also occur, and it is also analyzed, a collision between an airplane and a frangible device. The devise must brake under these loads, however, it must withstand others. Finally, all the considered methodology is applied to simulate and analyze a flight incident, the blade loss phenomenon of a turboprop. In this particular event the structure must support complex and exceptional loads and the aircraft must be able to successfully complete the flight. Nonlinear behavior, damage, and different types of failures are included in the analysis, in which the key parameters in the failure sequence are identified. The incident is analyzed by deterministic structural analysis and also by other techniques such as Monte Carlo method, in which it is possible to include different parametric uncertainties through random variables. Some of the evaluated parameters are, among others, the blade loss size, propeller rotational frequency, speed and angular position where the blade is lost, and the stiffness and strength of the engine mounts. The study does also research on the structural damping of the system. The different strategies of analysis obtain valuable and interesting results that have been already published.

Determining the elastic-plastic properties of metallic materials through instrumented indentation

En los últimos años, y asociado al desarrollo de la tecnología MEMS, la técnica de indentación instrumentada se ha convertido en un método de ensayo no destructivo ampliamente utilizado para hallar las características elástico-plásticas de recubrimientos y capas delgadas, desde la escala macroscópica a la microscópica. Sin embargo, debido al complejo mecanismo de contacto debajo de la indentación, es urgente proponer un método más simple y conveniente para obtener unos resultados comparables con otras mediciones tradicionales. En este estudio, el objetivo es mejorar el procedimiento analítico para extraer las propiedades elástico-plásticas del material mediante la técnica de indentación instrumentada. La primera parte se centra en la metodología llevada a cabo para medir las propiedades elásticas de los materiales elásticos, presentándose una nueva metodología de indentación, basada en la evolución de la rigidez de contacto y en la curva fuerza-desplazamiento del ensayo de indentación. El método propuesto permite discriminar los valores de indentación experimental que pudieran estar afectados por el redondeo de la punta del indentador. Además, esta técnica parece ser robusta y permite obtener valores fiables del modulo elástico. La segunda parte se centra en el proceso analítico para determinar la curva tensión-deformación a partir del ensayo de indentación, empleando un indentador esférico. Para poder asemejar la curva tension-deformación de indentación con la que se obtendría de un ensayo de tracción, Tabor determinó empíricamente un factor de constricción de la tensión () y un factor de constricción de la deformación (). Sin embargo, la elección del valor de y  necesitan una derivación analítica. Se describió analíticamente una nueva visión de la relación entre los factores de constricción de tensión y la deformación basado en la deducción de la ecuación de Tabor. Un modelo de elementos finitos y un diseño experimental se realizan para evaluar estos factores de constricción. A partir de los resultados obtenidos, las curvas tension-deformación extraidas de los ensayos de indentación esférica, afectadas por los correspondientes factores de constricción de tension y deformación, se ajustaron a la curva nominal tensión-deformación obtenida de ensayos de tracción convencionales. En la última parte, se estudian las propiedades del revestimiento de cermet Inconel 625-Cr3C2 que es depositado en el medio de una aleación de acero mediante un láser. Las propiedades mecánicas de la matriz de cermet son estudiadas mediante la técnica de indentación instrumentada, haciendo uso de las metodologías propuestas en el presente trabajo. In recent years, along with the development of MEMS technology, instrumented indentation, as one type of a non-destructive measurement technique, is widely used to characterize the elastic and plastic properties of metallic materials from the macro to the micro scale. However, due to the complex contact mechanisms under the indentation tip, it is necessary to propose a more convenient and simple method of instrumented indention to obtain comparable results from other conventional measurements. In this study, the aim is to improve the analytical procedure for extracting the elastic plastic properties of metallic materials by instrumented indentation. The first part focuses on the methodology for measuring the elastic properties of metallic materials. An alternative instrumented indentation methodology is presented. Based on the evolution of the contact stiffness and indentation load versus the depth of penetration, the possibility of obtaining the actual elastic modulus of an elastic-plastic bulk material through instrumented sharp indentation tests has been explored. The proposed methodology allows correcting the effect of the rounding of the indenter tip on the experimental indentation data. Additionally, this technique does not seem too sensitive to the pile-up phenomenon and allows obtaining convincing values of the elastic modulus. In the second part, an analytical procedure is proposed to determine the representative stress-strain curve from the spherical indentation. Tabor has determined the stress constraint factor (stress CF), and strain constraint factor (strain CF), empirically but the choice of a value for and is debatable and lacks analytical derivation. A new insight into the relationship between stress and strain constraint factors is analytically described based on the formulation of Tabor’s equation. Finite element model and experimental tests have been carried out to evaluate these constraint factors. From the results, representative stress-strain curves using the proposed strain constraint factor fit better with the nominal stress-strain curve than those using Tabor’s constraint factors. In the last part, the mechanical properties of an Inconel 625-Cr3C2 cermet coating which is deposited onto a medium alloy steel by laser cladding has been studied. The elastic and plastic mechanical properties of the cermet matrix are studied using depth-sensing indentation (DSI) on the micro scale.