57 resultados para Nonlinear transmissibility


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This work is concerned with the numerical solution of the evolution equations of thermomechanical systems, in such a way that the scheme itself satisfies the laws of thermodynamics. Within this framework, we present a novel integration scheme for the dynamics of viscoelastic continuum bodies in isothermal conditions. This method intrinsically satisfies the laws of thermodynamics arising from the continuum, as well as the possible additional symmetries. The resulting solutions are physically accurate since they preserve the fundamental physical properties of the model. Furthermore, the method gives an excellent performance with respect to robustness and stability. Proof for these claims as well as numerical examples that illustrate the performance of the novel scheme are provided

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Nonlinear effects in optical fibers

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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.

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El control del estado en el que se encuentran las estructuras ha experimentado un gran auge desde hace varias décadas, debido a que los costes de rehabilitación de estructuras tales como los oleoductos, los puentes, los edificios y otras más son muy elevados. En las últimas dos décadas, se han desarrollado una gran cantidad de métodos que permiten identificar el estado real de una estructura, basándose en modelos físicos y datos de ensayos. El ensayo modal es el más común; mediante el análisis modal experimental de una estructura se pueden determinar parámetros como la frecuencia, los modos de vibración y la amortiguación y también la función de respuesta en frecuencia de la estructura. Mediante estos parámetros se pueden implementar diferentes indicadores de daño. Sin embargo, para estructuras complejas y grandes, la implementación de metodologías basadas en la función de respuesta en frecuencia requeriría realizar hipótesis sobre la fuerza utilizada para excitar la estructura. Dado que el análisis modal operacional utiliza solamente las señales de respuesta del sistema para extraer los parámetros dinámicos estructurales y, por tanto, para evaluar el estado de una estructura, el uso de la transmisibilidad sería posible. En este sentido, dentro del análisis modal operacional, la transmisibilidad ha concentrado mucha atención en el mundo científico en la última década. Aunque se han publicado muchos trabajos sobre el tema, en esta Tesis se proponen diferentes técnicas para evaluar el estado de una estructura basándose exclusivamente en la transmisibilidad. En primer lugar, se propone un indicador de daño basado en un nuevo parámetro, la coherencia de transmisibilidad; El indicador se ha valido mediante resultados numéricos y experimentales obtenidos sobre un pórtico de tres pisos. En segundo lugar, la distancia de Mahalanobis se aplica sobre la transmisibilidad como procedimiento para detectar variaciones estructurales provocadas por el daño. Este método se ha validado con éxito sobre una viga libre-libre ensayada experimentalmente. En tercer lugar, se ha implementado una red neuronal basada en medidas de transmisibilidad como metodología de predicción de daño sobre una viga simulada numéricamente. ABSTRACT Structural health monitoring has experienced a huge development from several decades ago since the cost of rehabilitation of structures such as oil pipes, bridges and tall buildings is very high. In the last two decades, a lot of methods able to identify the real stage of a structure have been developed basing on both models and experimental data. Modal testing is the most common; by carrying out the experimental modal analysis of a structure, some parameters, such as frequency, mode shapes and damping, as well as the frequency response function of the structure can be obtained. From these parameters, different damage indicators have been proposed. However, for complex and large structures, any frequency domain approach that relies on frequency response function estimation would be of difficult application since an assumption of the input excitations to the system should be carried out. Operational modal analysis uses only output signals to extract the structural dynamic parameters and, therefore, to identify the structural stage. In this sense, within operational modal analysis, transmissibility has attracted a lot of attention in the scientific field in the last decade. In this work new damage detection approaches based on transmissibility are developed. Firstly, a new theory of transmissibility coherence is developed and it is tested with a three-floor-structure both in simulation and in experimental data analysis; secondly, Mahalanobis distance is taken into use with the transmissibility, and a free-free beam is used to test the approach performance; thirdly, neural networks are used in transmissibility for structural health monitoring; a simulated beam is used to validate the proposed method.

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El control del estado en el que se encuentran las estructuras ha experimentado un gran auge desde hace varias décadas, debido a que los costes de rehabilitación de estructuras tales como los oleoductos, los puentes, los edificios y otras más son muy elevados. En las últimas dos décadas, se han desarrollado una gran cantidad de métodos que permiten identificar el estado real de una estructura, basándose en modelos físicos y datos de ensayos. El ensayo modal es el más común; mediante el análisis modal experimental de una estructura se pueden determinar parámetros como la frecuencia, los modos de vibración y la amortiguación y también la función de respuesta en frecuencia de la estructura. Mediante estos parámetros se pueden implementar diferentes indicadores de daño. Sin embargo, para estructuras complejas y grandes, la implementación de metodologías basadas en la función de respuesta en frecuencia requeriría realizar hipótesis sobre la fuerza utilizada para excitar la estructura. Dado que el análisis modal operacional utiliza solamente las señales de respuesta del sistema para extraer los parámetros dinámicos estructurales y, por tanto, para evaluar el estado de una estructura, el uso de la transmisibilidad sería posible. En este sentido, dentro del análisis modal operacional, la transmisibilidad ha concentrado mucha atención en el mundo científico en la última década. Aunque se han publicado muchos trabajos sobre el tema, en esta Tesis se proponen diferentes técnicas para evaluar el estado de una estructura basándose exclusivamente en la transmisibilidad. En primer lugar, se propone un indicador de daño basado en un nuevo parámetro, la coherencia de transmisibilidad; El indicador se ha valido mediante resultados numéricos y experimentales obtenidos sobre un pórtico de tres pisos. En segundo lugar, la distancia de Mahalanobis se aplica sobre la transmisibilidad como procedimiento para detectar variaciones estructurales provocadas por el daño. Este método se ha validado con éxito sobre una viga libre-libre ensayada experimentalmente. En tercer lugar, se ha implementado una red neuronal basada en medidas de transmisibilidad como metodología de predicción de daño sobre una viga simulada numéricamente. ABSTRACT Structural health monitoring has experienced a huge development from several decades ago since the cost of rehabilitation of structures such as oil pipes, bridges and tall buildings is very high. In the last two decades, a lot of methods able to identify the real stage of a structure have been developed basing on both models and experimental data. Modal testing is the most common; by carrying out the experimental modal analysis of a structure, some parameters, such as frequency, mode shapes and damping, as well as the frequency response function of the structure can be obtained. From these parameters, different damage indicators have been proposed. However, for complex and large structures, any frequency domain approach that relies on frequency response function estimation would be of difficult application since an assumption of the input excitations to the system should be carried out. Operational modal analysis uses only output signals to extract the structural dynamic parameters and, therefore, to identify the structural stage. In this sense, within operational modal analysis, transmissibility has attracted a lot of attention in the scientific field in the last decade. In this work new damage detection approaches based on transmissibility are developed. Firstly, a new theory of transmissibility coherence is developed and it is tested with a three-floor-structure both in simulation and in experimental data analysis; secondly, Mahalanobis distance is taken into use with the transmissibility, and a free-free beam is used to test the approach performance; thirdly, neural networks are used in transmissibility for structural health monitoring; a simulated beam is used to validate the proposed method.

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Esta tesis propone una completa formulación termo-mecánica para la simulación no-lineal de mecanismos flexibles basada en métodos libres de malla. El enfoque se basa en tres pilares principales: la formulación de Lagrangiano total para medios continuos, la discretización de Bubnov-Galerkin, y las funciones de forma libres de malla. Los métodos sin malla se caracterizan por la definición de un conjunto de funciones de forma en dominios solapados, junto con una malla de integración de las ecuaciones discretas de balance. Dos tipos de funciones de forma se han seleccionado como representación de las familias interpolantes (Funciones de Base Radial) y aproximantes (Mínimos Cuadrados Móviles). Su formulación se ha adaptado haciendo sus parámetros compatibles, y su ausencia de conectividad predefinida se ha aprovechado para interconectar múltiples dominios de manera automática, permitiendo el uso de mallas de fondo no conformes. Se propone una formulación generalizada de restricciones, juntas y contactos, válida para sólidos rígidos y flexibles, siendo estos últimos discretizados mediante elementos finitos (MEF) o libres de malla. La mayor ventaja de este enfoque reside en que independiza completamente el dominio con respecto de las uniones y acciones externas a cada sólido, permitiendo su definición incluso fuera del contorno. Al mismo tiempo, también se minimiza el número de ecuaciones de restricción necesarias para la definición de uniones realistas. Las diversas validaciones, ejemplos y comparaciones detalladas muestran como el enfoque propuesto es genérico y extensible a un gran número de sistemas. En concreto, las comparaciones con el MEF indican una importante reducción del error para igual número de nodos, tanto en simulaciones mecánicas, como térmicas y termo-mecánicas acopladas. A igualdad de error, la eficiencia numérica de los métodos libres de malla es mayor que la del MEF cuanto más grosera es la discretización. Finalmente, la formulación se aplica a un problema de diseño real sobre el mantenimiento de estructuras masivas en el interior de un reactor de fusión, demostrando su viabilidad en análisis de problemas reales, y a su vez mostrando su potencial para su uso en simulación en tiempo real de sistemas no-lineales. A new complete formulation is proposed for the simulation of nonlinear dynamic of multibody systems with thermo-mechanical behaviour. The approach is founded in three main pillars: total Lagrangian formulation, Bubnov-Galerkin discretization, and meshfree shape functions. Meshfree methods are characterized by the definition of a set of shape functions in overlapping domains, and a background grid for integration of the Galerkin discrete equations. Two different types of shape functions have been chosen as representatives of interpolation (Radial Basis Functions), and approximation (Moving Least Squares) families. Their formulation has been adapted to use compatible parameters, and their lack of predefined connectivity is used to interconnect different domains seamlessly, allowing the use of non-conforming meshes. A generalized formulation for constraints, joints, and contacts is proposed, which is valid for rigid and flexible solids, being the later discretized using either finite elements (FEM) or meshfree methods. The greatest advantage of this approach is that makes the domain completely independent of the external links and actions, allowing to even define them outside of the boundary. At the same time, the number of constraint equations needed for defining realistic joints is minimized. Validation, examples, and benchmarks are provided for the proposed formulation, demonstrating that the approach is generic and extensible to further problems. Comparisons with FEM show a much lower error for the same number of nodes, both for mechanical and thermal analyses. The numerical efficiency is also better when coarse discretizations are used. A final demonstration to a real problem for handling massive structures inside of a fusion reactor is presented. It demonstrates that the application of meshfree methods is feasible and can provide an advantage towards the definition of nonlinear real-time simulation models.

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We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.

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A new effect producing self-focusing of light in a nematic MBBA film is reported. This effect produces a static diffraction pattern composed of circular rings which is different from the ones arising from self-focusing previously reported. The influence of the cell thickness, the optical intensity, and the wavelength is studied. Once the nematic is distorted by a láser beam, the effect produced in other light beam passing through the modified región is independent of its polarization. This isotropic behavior shows that a molecular reorientation has not been produced. The origin of this effect seems to be the same of that of the effect which produces a randomly oscillating diffraction pattern previously reported by our group. Some possible causes such as thermal indexing, convective instabilities and self-induced transparency are discussed.

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Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

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The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

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El uso de aritmética de punto fijo es una opción de diseño muy extendida en sistemas con fuertes restricciones de área, consumo o rendimiento. Para producir implementaciones donde los costes se minimicen sin impactar negativamente en la precisión de los resultados debemos llevar a cabo una asignación cuidadosa de anchuras de palabra. Encontrar la combinación óptima de anchuras de palabra en coma fija para un sistema dado es un problema combinatorio NP-hard al que los diseñadores dedican entre el 25 y el 50 % del ciclo de diseño. Las plataformas hardware reconfigurables, como son las FPGAs, también se benefician de las ventajas que ofrece la aritmética de coma fija, ya que éstas compensan las frecuencias de reloj más bajas y el uso más ineficiente del hardware que hacen estas plataformas respecto a los ASICs. A medida que las FPGAs se popularizan para su uso en computación científica los diseños aumentan de tamaño y complejidad hasta llegar al punto en que no pueden ser manejados eficientemente por las técnicas actuales de modelado de señal y ruido de cuantificación y de optimización de anchura de palabra. En esta Tesis Doctoral exploramos distintos aspectos del problema de la cuantificación y presentamos nuevas metodologías para cada uno de ellos: Las técnicas basadas en extensiones de intervalos han permitido obtener modelos de propagación de señal y ruido de cuantificación muy precisos en sistemas con operaciones no lineales. Nosotros llevamos esta aproximación un paso más allá introduciendo elementos de Multi-Element Generalized Polynomial Chaos (ME-gPC) y combinándolos con una técnica moderna basada en Modified Affine Arithmetic (MAA) estadístico para así modelar sistemas que contienen estructuras de control de flujo. Nuestra metodología genera los distintos caminos de ejecución automáticamente, determina las regiones del dominio de entrada que ejercitarán cada uno de ellos y extrae los momentos estadísticos del sistema a partir de dichas soluciones parciales. Utilizamos esta técnica para estimar tanto el rango dinámico como el ruido de redondeo en sistemas con las ya mencionadas estructuras de control de flujo y mostramos la precisión de nuestra aproximación, que en determinados casos de uso con operadores no lineales llega a tener tan solo una desviación del 0.04% con respecto a los valores de referencia obtenidos mediante simulación. Un inconveniente conocido de las técnicas basadas en extensiones de intervalos es la explosión combinacional de términos a medida que el tamaño de los sistemas a estudiar crece, lo cual conlleva problemas de escalabilidad. Para afrontar este problema presen tamos una técnica de inyección de ruidos agrupados que hace grupos con las señales del sistema, introduce las fuentes de ruido para cada uno de los grupos por separado y finalmente combina los resultados de cada uno de ellos. De esta forma, el número de fuentes de ruido queda controlado en cada momento y, debido a ello, la explosión combinatoria se minimiza. También presentamos un algoritmo de particionado multi-vía destinado a minimizar la desviación de los resultados a causa de la pérdida de correlación entre términos de ruido con el objetivo de mantener los resultados tan precisos como sea posible. La presente Tesis Doctoral también aborda el desarrollo de metodologías de optimización de anchura de palabra basadas en simulaciones de Monte-Cario que se ejecuten en tiempos razonables. Para ello presentamos dos nuevas técnicas que exploran la reducción del tiempo de ejecución desde distintos ángulos: En primer lugar, el método interpolativo aplica un interpolador sencillo pero preciso para estimar la sensibilidad de cada señal, y que es usado después durante la etapa de optimización. En segundo lugar, el método incremental gira en torno al hecho de que, aunque es estrictamente necesario mantener un intervalo de confianza dado para los resultados finales de nuestra búsqueda, podemos emplear niveles de confianza más relajados, lo cual deriva en un menor número de pruebas por simulación, en las etapas iniciales de la búsqueda, cuando todavía estamos lejos de las soluciones optimizadas. Mediante estas dos aproximaciones demostramos que podemos acelerar el tiempo de ejecución de los algoritmos clásicos de búsqueda voraz en factores de hasta x240 para problemas de tamaño pequeño/mediano. Finalmente, este libro presenta HOPLITE, una infraestructura de cuantificación automatizada, flexible y modular que incluye la implementación de las técnicas anteriores y se proporciona de forma pública. Su objetivo es ofrecer a desabolladores e investigadores un entorno común para prototipar y verificar nuevas metodologías de cuantificación de forma sencilla. Describimos el flujo de trabajo, justificamos las decisiones de diseño tomadas, explicamos su API pública y hacemos una demostración paso a paso de su funcionamiento. Además mostramos, a través de un ejemplo sencillo, la forma en que conectar nuevas extensiones a la herramienta con las interfaces ya existentes para poder así expandir y mejorar las capacidades de HOPLITE. ABSTRACT Using fixed-point arithmetic is one of the most common design choices for systems where area, power or throughput are heavily constrained. In order to produce implementations where the cost is minimized without negatively impacting the accuracy of the results, a careful assignment of word-lengths is required. The problem of finding the optimal combination of fixed-point word-lengths for a given system is a combinatorial NP-hard problem to which developers devote between 25 and 50% of the design-cycle time. Reconfigurable hardware platforms such as FPGAs also benefit of the advantages of fixed-point arithmetic, as it compensates for the slower clock frequencies and less efficient area utilization of the hardware platform with respect to ASICs. As FPGAs become commonly used for scientific computation, designs constantly grow larger and more complex, up to the point where they cannot be handled efficiently by current signal and quantization noise modelling and word-length optimization methodologies. In this Ph.D. Thesis we explore different aspects of the quantization problem and we present new methodologies for each of them: The techniques based on extensions of intervals have allowed to obtain accurate models of the signal and quantization noise propagation in systems with non-linear operations. We take this approach a step further by introducing elements of MultiElement Generalized Polynomial Chaos (ME-gPC) and combining them with an stateof- the-art Statistical Modified Affine Arithmetic (MAA) based methodology in order to model systems that contain control-flow structures. Our methodology produces the different execution paths automatically, determines the regions of the input domain that will exercise them, and extracts the system statistical moments from the partial results. We use this technique to estimate both the dynamic range and the round-off noise in systems with the aforementioned control-flow structures. We show the good accuracy of our approach, which in some case studies with non-linear operators shows a 0.04 % deviation respect to the simulation-based reference values. A known drawback of the techniques based on extensions of intervals is the combinatorial explosion of terms as the size of the targeted systems grows, which leads to scalability problems. To address this issue we present a clustered noise injection technique that groups the signals in the system, introduces the noise terms in each group independently and then combines the results at the end. In this way, the number of noise sources in the system at a given time is controlled and, because of this, the combinato rial explosion is minimized. We also present a multi-way partitioning algorithm aimed at minimizing the deviation of the results due to the loss of correlation between noise terms, in order to keep the results as accurate as possible. This Ph.D. Thesis also covers the development of methodologies for word-length optimization based on Monte-Carlo simulations in reasonable times. We do so by presenting two novel techniques that explore the reduction of the execution times approaching the problem in two different ways: First, the interpolative method applies a simple but precise interpolator to estimate the sensitivity of each signal, which is later used to guide the optimization effort. Second, the incremental method revolves on the fact that, although we strictly need to guarantee a certain confidence level in the simulations for the final results of the optimization process, we can do it with more relaxed levels, which in turn implies using a considerably smaller amount of samples, in the initial stages of the process, when we are still far from the optimized solution. Through these two approaches we demonstrate that the execution time of classical greedy techniques can be accelerated by factors of up to ×240 for small/medium sized problems. Finally, this book introduces HOPLITE, an automated, flexible and modular framework for quantization that includes the implementation of the previous techniques and is provided for public access. The aim is to offer a common ground for developers and researches for prototyping and verifying new techniques for system modelling and word-length optimization easily. We describe its work flow, justifying the taken design decisions, explain its public API and we do a step-by-step demonstration of its execution. We also show, through an example, the way new extensions to the flow should be connected to the existing interfaces in order to expand and improve the capabilities of HOPLITE.

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MLS-based identification of nonlinear systems is largely affected by deviations in the excitation signal amenable to the combined effect of DC-offset and an arbitrary gain. These induce orthogonality loss in the MLS filter bank output, thus invalidating the underlying identification construction. In this paper we present a correction algorithm to derive the corrected Volterra kernels from the biased estimations provided by the standard MLS-based procedure.