Improvements for B.E.M. implementation in micros

This paper presents a computer program developed to run in a micro I.B.M.-P.C. wich incorporates some features in order to optimize the number of operations needed to compute the solution of plane potential problems governed by Laplace's equation by using the Boundary Integral Equation Method (B.I.E.M.). Also incorporated is a routine to plot isolines inside the domain under study.

On the design of spherical gradient index lenses

Classical spherical gradient index (GRIN) lenses (such as Maxwell Fish Eye lens, Eaton lens, Luneburg lens, etc.) design procedure using the Abel integral equation is reviewed and reorganized. Each lens is fully defined by a function called the angle of flight which describes the ray deflection through the lens. The radial refractive index distribution is obtained by applying a linear integral transformation to the angle of flight. The interest of this formulation is in the linearity of the integral transformation which allows us to derive new solutions from linear combinations of known lenses. Beside the review of the classical GRIN designs, we present a numerical method for GRIN lenses defined by the Abel integral equation with fixed limits, which is an ill-posed problem.

Numerical treatment of thick shells with holes

A Boundary Integral Equation Method (B.I.E.M.)formulation is presented. After a general situation of the method among other usual numerical ones, the possibilities of discretization are developed. As this is done only in the boundary the treatment of tridimensional problems is greatly simplified in comparison with other methods. Some results on a simple shell with holes are finally presented.

B.I.E.M. in solid mechanics

In solid mechanics the weak formulation produces an integral equation ready for a discretization and with less restrictive requiremets than the standard field equations. Fundamentally the weak formulation is a expresion of a green formula. An alternative is to choose another green formula materializing a reciprocity relationship between the basis unknowns and an auxiliary family of functions. The degree of smoothness requiered to practice the discretization is then translated to the auxiliar functions. The subsequent discretization (constant, linear etc.)produces a set of equations on the boundary of the domain. For linear 3-D problems the BIEM appears then as a powerful alternative to FEM, because of the reduction to 2-D thanks to the features previously described.

Los métodos proyectivos en la mecánica de los medios contínuos

El Método de las Ecuaciones Integrales es una potente alternativa a los Métodos de Dominio tales como el Método de los Elementos Finitos. La idea ensencial es la combinación de la clásica relación de la reciprocidad con la filosofía de la discretización del F.E.M. La aplicación a algunos problemas reales ha demostrado que en ciertos casos el B.I.E.M. es preferiole al F.E.M. y ello es especialmente así cuando los problemas a tratar son tridimensionales y con geometría complicada. En esta ocasión se analizan comparativamente algunos aspectos matemáticos del procedimiento = Boundary integral equation method (B.I.E.M.)is a powerful alternative to the domain methods, as the well know Finite Element Method (F .E.M.) The esential idea, are the combination of the classical reciprocity re!ations with the discretization phylosophy of F.E.M. The reduction in dimension of the domain to be discretized, the easy treatment of infinite domains and the high accuracy of the results are the main adventages of B.I.E.M. Between the drawacks the nonsymetry and non sparseness of the matrices to be treated are worth remembering. Application to several real problems has shown that in certain cases B.I.E.M. is better than F.E.M. and this is specially true when tridimensional problems of complicated geometries have to be treated. Active research is in progress of its extensión to non linear and time dependent problems.

B.I.E.M. y estudio de singularidades en problemas de potencial

El objeto del presente artículo es el estudio de singularidades en problemas de Potencial mediante el uso del Método de las Ecuaciones Integrales sobre el contorno del dominio en estudio. Frente a soluciones basadas en la mejora de la discretización, análisis asintótico o introducción de funciones de forma que representen mejor la evolución de la función, una nueva hipótesis es presentada: el término responsable de la singularidad es incluido en la integral sobre el contorno de la función auxiliar. Los resultados obtenidos mejoran los de soluciones anteriores simplificando también el tiempo de cálculo = The subject of this paper is the modelling of singularities in potential problems, using the Boundary Integral Equation Method. As a logical alternative to classical methods (discretization refinement, asymptotic analysis, high order interpolatory functions) a new hypothesis is presented: the singularity responsible term is included in the interpolatory shape function. As shown by several exemples results are splendid and computer time radically shortened.

Guía de introducción al Método de los Elementos de Contorno

Entre la impresionante floración de procedimientos de cálculo, provocada por la aplicación intensiva del ordenador, el llamado Método de los Elementos de Contorno (Boundary Element Method o Boundary Integral Equation Method) parece afianzarse como una alternativa útil al omnipresente Método de los Elementos Finitos que ya ha sido incorporado, como una herramienta de trabajo más, al cotidiano quehacer de la ingeniería. En España, tras unos intentos precursores que se señalan en el texto, la actividad más acusada en su desarrollo y mejora se ha centrado alrededor del Departamento que dirige uno de los autores. Después de la tesis doctoral de J. Domínguez en 1977 que introdujo en España la técnica del llamado "método directo", se han producido numerosas aportaciones en forma de artículos o tesis de investigación que han permitido alcanzar un nivel de conocimientos notable. En esta obrita se pretende transmitir parte de la experiencia adquirida, siquiera sea a nivel elemental y en un campo limitado de aplicación. La filosofía es semejante a la del pequeño libro de Hinton y Owen "A simple guide to finite elements" (Pineridge Press, 1980) que tanta aceptación ha tenido entre los principiantes. El libro se articula alrededor de un sólo tema, la solución del problema de Laplace, y se limitan los desarrollos matemáticos al mínimo imprescindible para el fácil seguimiento de áquel. Tras unos capítulos iniciales de motivación y centrado se desarrolla la técnica para problemas planos, tridimensionales y axisimétricos, limitando los razonamientos a los elementos más sencillos de variación constante o lineal. Finalmente, se incluye un capítulo descriptivo donde se avizoran temas que pueden provocar un futuro interés del estudioso. Para completar la información se ha añadido un apéndice en el que se recoge un pequeño programa para microordenador, con el objetivo de que se contemple la sencillez de programación para el caso plano. El programa es mejorable en muchos aspectos pero creemos que, con ello, mantiene un nivel de legibilidad adecuado para que el lector ensaye sobre él las modificaciones que se indican en los ejercicios al final del capítulo y justamente la provocación de ese aprendizaje es nuestro objetivo final.

Medidas experimentales de la complejidad computacional de un código autoadaptativo HP para problemas abiertos acelerado mediante ACA

The aim of the novel experimental measures presented in this paper is to show the improvement achieved in the computation time for a 2D self-adaptive hp finite element method (FEM) software accelerated through the Adaptive Cross Approximation (ACA) method. This algebraic method (ACA) was presented in an previous paper in the hp context for the analysis of open region problems, where the robust behaviour, good accuracy and high compression levels of ACA were demonstrated. The truncation of the infinite domain is settled through an iterative computation of the Integral Equation (IE) over a ficticious boundary, which, regardless its accuracy and efficiency, turns out to be the bottelneck of the code. It will be shown that in this context ACA reduces drastically the computational effort of the problem.

Nitrogen fixation by native Bradyrhizobia in symbiosis with Lupinus mariae-josephae requires a T3SS encoding a NopE-like effector

Several bradyrhizobial isolates from L. mariae-josephae root nodules [1] contain a type III secretion system (T3SS) within a cluster of about 30 genes. Among those genes, ttsI codes for the transcriptional activator of the system. Mutation of ttsI resulted in the formation of white, non-fixing nodules with the natural legume host, L. mariae-josephae. The T3SS cluster also contains a gene coding for a NopE-like protein. NopE proteins have been demonstrated to be effectors in the Bradyrhizobium-soybean symbiosis [2] and belong to a small group of poorly characterized proteins from plant-associated bacteria that contain one or two autocleavage motifs known as DUF1521 (Schirrmeister et al. 2011). The amino acid sequence of a NopE-like protein in the L. mariae-josephae strain LmjC contains just one autocatalytic motif. This is unlike NopE1 and NopE2 proteins secreted by the T3SS of B. japonicum, that contain two motifs [3]. The autocleavage of LmjC NopE protein was analyzed after expression in E. coli and purification. Two protein fragments of the predicted sizes appeared in the presence of Ca2+, Cu2+, Cd2+, Zn2+ and Mn2+ cations. In contrast, autocleavage did not take place in the presence of Ni2+, Co2+ or Mg2+. Site-directed mutagenesis of the DUF1521 motif in LmjC NopE abolished self-cleavage in vitro. Symbiotic competence of a NopE- mutant with the L. mariae-josephae host was not affected. Possible roles of NopE are discussed.

Native bradyrhizobia isolated from Lupinus mariae-josephae possess an essential T3SS for symbiosis

Analysis of the genome sequence of bradyrhizobia strains isolated from root nodules of Lupinus mariae-josephae revealed the presence of a type III secretion system (T3SS). Mutagenesis of ttsI gene that codes for the transcriptional activator (TtsI) resulted in the formation of white, non-fixing nodules in L. mariae-josephae. The T3SS cluster includes a gene coding for a NopE-like protein with an autocleavage motif. The NopE protein is an effector in the Bradyrhizobium-soybean symbiosis (Wenzel et al., 2010). The autocatalytic properties of the purified NopE-like protein have been studied.

Comparison of the seismic behaviour between three building tests, all based on a two storey model house

Integral Masonry System consisting of intersecting steel trusses alo ng each of the three dimensional directions of space on walls and slabs using any masonry material, had yet been backed up by the previous adobe test for seismic areas. This paper presents the comparison this last test and the adaptation of the IMS using h ollow brick. A prototype based on a two storey model house (6mx6mx6m) has being also built in two different scales in order to maximize the load and size of the shake table: the first one half size the whole building (3mx3mx3m) and the second, a quarter of the real size (3mx3mx6m). Both tests have suffered some mild to moderate damages while supporting the higher seismic action subjected by the shake table, without even fissuring the first test and with very few damages the second one. The thickness of the hollow brick wall and the diameter of the tree - dimensional truss reinforcement were scaled to the real size test in order to ascertain its great structural behaviour in relation to the previous structural model calculations. The aim of this study is to sum marize the results of the research collaboration between the ETSAM - UPM and the PUCP in whose laboratory these tests were carried out.

Desarrollo de un sistema de almacenamiento térmico para la central termosolar Astexol 2

En este proyecto se elabora la ingeniería básica de un sistema de almacenamiento térmico para la central termosolar Astexol 2 (Badajoz, España). Para ello, primeramente se decidió que el sistema térmico de almacenamiento a diseñar fuera indirecto de dos tanques con sales fundidas. Una vez seleccionado el tipo de almacenamiento adecuado, se seleccionó la capacidad de almacenamiento óptima, en base a unos objetivos establecidos para la instalación del TES en Astexol 2. Finalmente, se procedió con el diseño de los equipos principales y con la realización de los planos de implantación y de los PFD’s (diagramas de flujo) y P&ID’s (diagramas de instrumentación y control) del sistema de almacenamiento. ABSTRACT This project includes the basic engineering of a thermal storage system for the concentrating solar power plant Astexol 2 (Badajoz, Spain). First of all, it was decided that the type of thermal storage system to design had to be an indirect two-tank molten salt thermal storage system. Once the proper type of storage system was chosen, the optimum storage capacity was selected, according to the main aims designated for the thermal storage system installation in Astexol 2.Finally, the design of the main equipment of the thermal storage system was done, together with the elaboration of the associated plot plans, PFD’s (Process Flow Diagrams) and P&ID’s (Process and Instrumentation Diagrams).

Application of PZT and FBG impedance sensors for structural health monitoring of reinforced concrete beams strengthened with FRP composite materials

Esta Tesis tiene como objetivo principal el desarrollo de métodos de identificación del daño que sean robustos y fiables, enfocados a sistemas estructurales experimentales, fundamentalmente a las estructuras de hormigón armado reforzadas externamente con bandas fibras de polímeros reforzados (FRP). El modo de fallo de este tipo de sistema estructural es crítico, pues generalmente es debido a un despegue repentino y frágil de la banda del refuerzo FRP originado en grietas intermedias causadas por la flexión. La detección de este despegue en su fase inicial es fundamental para prevenir fallos futuros, que pueden ser catastróficos. Inicialmente, se lleva a cabo una revisión del método de la Impedancia Electro-Mecánica (EMI), de cara a exponer sus capacidades para la detección de daño. Una vez la tecnología apropiada es seleccionada, lo que incluye un analizador de impedancias así como novedosos sensores PZT para monitorización inteligente, se ha diseñado un procedimiento automático basado en los registros de impedancias de distintas estructuras de laboratorio. Basándonos en el hecho de que las mediciones de impedancias son posibles gracias a una colocación adecuada de una red de sensores PZT, la estimación de la presencia de daño se realiza analizando los resultados de distintos indicadores de daño obtenidos de la literatura. Para que este proceso sea automático y que no sean necesarios conocimientos previos sobre el método EMI para realizar un experimento, se ha diseñado e implementado un Interfaz Gráfico de Usuario, transformando la medición de impedancias en un proceso fácil e intuitivo. Se evalúa entonces el daño a través de los correspondientes índices de daño, intentando estimar no sólo su severidad, sino también su localización aproximada. El desarrollo de estos experimentos en cualquier estructura genera grandes cantidades de datos que han de ser procesados, y algunas veces los índices de daño no son suficientes para una evaluación completa de la integridad de una estructura. En la mayoría de los casos se pueden encontrar patrones de daño en los datos, pero no se tiene información a priori del estado de la estructura. En este punto, se ha hecho una importante investigación en técnicas de reconocimiento de patrones particularmente en aprendizaje no supervisado, encontrando aplicaciones interesantes en el campo de la medicina. De ahí surge una idea creativa e innovadora: detectar y seguir la evolución del daño en distintas estructuras como si se tratase de un cáncer propagándose por el cuerpo humano. En ese sentido, las lecturas de impedancias se emplean como información intrínseca de la salud de la propia estructura, de forma que se pueden aplicar las mismas técnicas que las empleadas en la investigación del cáncer. En este caso, se ha aplicado un algoritmo de clasificación jerárquica dado que ilustra además la clasificación de los datos de forma gráfica, incluyendo información cualitativa y cuantitativa sobre el daño. Se ha investigado la efectividad de este procedimiento a través de tres estructuras de laboratorio, como son una viga de aluminio, una unión atornillada de aluminio y un bloque de hormigón reforzado con FRP. La primera ayuda a mostrar la efectividad del método en sencillos escenarios de daño simple y múltiple, de forma que las conclusiones extraídas se aplican sobre los otros dos, diseñados para simular condiciones de despegue en distintas estructuras. Demostrada la efectividad del método de clasificación jerárquica de lecturas de impedancias, se aplica el procedimiento sobre las estructuras de hormigón armado reforzadas con bandas de FRP objeto de esta tesis, detectando y clasificando cada estado de daño. Finalmente, y como alternativa al anterior procedimiento, se propone un método para la monitorización continua de la interfase FRP-Hormigón, a través de una red de sensores FBG permanentemente instalados en dicha interfase. De esta forma, se obtienen medidas de deformación de la interfase en condiciones de carga continua, para ser implementadas en un modelo de optimización multiobjetivo, cuya solución se haya por medio de una expansión multiobjetivo del método Particle Swarm Optimization (PSO). La fiabilidad de este último método de detección se investiga a través de sendos ejemplos tanto numéricos como experimentales. ABSTRACT This thesis aims to develop robust and reliable damage identification methods focused on experimental structural systems, in particular Reinforced Concrete (RC) structures externally strengthened with Fiber Reinforced Polymers (FRP) strips. The failure mode of this type of structural system is critical, since it is usually due to sudden and brittle debonding of the FRP reinforcement originating from intermediate flexural cracks. Detection of the debonding in its initial stage is essential thus to prevent future failure, which might be catastrophic. Initially, a revision of the Electro-Mechanical Impedance (EMI) method is carried out, in order to expose its capabilities for local damage detection. Once the appropriate technology is selected, which includes impedance analyzer as well as novel PZT sensors for smart monitoring, an automated procedure has been design based on the impedance signatures of several lab-scale structures. On the basis that capturing impedance measurements is possible thanks to an adequately deployed PZT sensor network, the estimation of damage presence is done by analyzing the results of different damage indices obtained from the literature. In order to make this process automatic so that it is not necessary a priori knowledge of the EMI method to carry out an experimental test, a Graphical User Interface has been designed, turning the impedance measurements into an easy and intuitive procedure. Damage is then assessed through the analysis of the corresponding damage indices, trying to estimate not only the damage severity, but also its approximate location. The development of these tests on any kind of structure generates large amounts of data to be processed, and sometimes the information provided by damage indices is not enough to achieve a complete analysis of the structural health condition. In most of the cases, some damage patterns can be found in the data, but none a priori knowledge of the health condition is given for any structure. At this point, an important research on pattern recognition techniques has been carried out, particularly on unsupervised learning techniques, finding interesting applications in the medicine field. From this investigation, a creative and innovative idea arose: to detect and track the evolution of damage in different structures, as if it were a cancer propagating through a human body. In that sense, the impedance signatures are used to give intrinsic information of the health condition of the structure, so that the same clustering algorithms applied in the cancer research can be applied to the problem addressed in this dissertation. Hierarchical clustering is then applied since it also provides a graphical display of the clustered data, including quantitative and qualitative information about damage. The performance of this approach is firstly investigated using three lab-scale structures, such as a simple aluminium beam, a bolt-jointed aluminium beam and an FRP-strengthened concrete specimen. The first one shows the performance of the method on simple single and multiple damage scenarios, so that the first conclusions can be extracted and applied to the other two experimental tests, which are designed to simulate a debonding condition on different structures. Once the performance of the impedance-based hierarchical clustering method is proven to be successful, it is then applied to the structural system studied in this dissertation, the RC structures externally strengthened with FRP strips, where the debonding failure in the interface between the FRP and the concrete is successfully detected and classified, proving thus the feasibility of this method. Finally, as an alternative to the previous approach, a continuous monitoring procedure of the FRP-Concrete interface is proposed, based on an FBGsensors Network permanently deployed within that interface. In this way, strain measurements can be obtained under controlled loading conditions, and then they are used in order to implement a multi-objective model updating method solved by a multi-objective expansion of the Particle Swarm Optimization (PSO) method. The feasibility of this last proposal is investigated and successfully proven on both numerical and experimental RC beams strengthened with FRP.

Contribución al análisis eficiente y a la mejora de prestaciones de antenas reflectarray

El diseño de una antena reflectarray bajo la aproximación de periodicidad local requiere la determinación de la matriz de scattering de estructuras multicapa con metalizaciones periódicas para un gran número de geometrías diferentes. Por lo tanto, a la hora de diseñar antenas reflectarray en tiempos de CPU razonables, se necesitan herramientas númericas rápidas y precisas para el análisis de las estructuras periódicas multicapa. En esta tesis se aplica la versión Galerkin del Método de los Momentos (MDM) en el dominio espectral al análisis de las estructuras periódicas multicapa necesarias para el diseño de antenas reflectarray basadas en parches apilados o en dipolos paralelos coplanares. Desgraciadamente, la aplicación de este método numérico involucra el cálculo de series dobles infinitas, y mientras que algunas series convergen muy rápidamente, otras lo hacen muy lentamente. Para aliviar este problema, en esta tesis se propone un novedoso MDM espectral-espacial para el análisis de las estructuras periódicas multicapa, en el cual las series rápidamente convergente se calculan en el dominio espectral, y las series lentamente convergentes se calculan en el dominio espacial mediante una versión mejorada de la formulación de ecuaciones integrales de potenciales mixtos (EIPM) del MDM. Esta versión mejorada se basa en la interpolación eficiente de las funciones de Green multicapa periódicas, y en el cálculo eficiente de las integrales singulares que conducen a los elementos de la matriz del MDM. El novedoso método híbrido espectral-espacial y el tradicional MDM en el dominio espectral se han comparado en el caso de los elementos reflectarray basado en parches apilados. Las simulaciones numéricas han demostrado que el tiempo de CPU requerido por el MDM híbrido es alrededor de unas 60 veces más rápido que el requerido por el tradicional MDM en el dominio espectral para una precisión de dos cifras significativas. El uso combinado de elementos reflectarray con parches apilados y técnicas de optimización de banda ancha ha hecho posible diseñar antenas reflectarray de transmisiónrecepción (Tx-Rx) y polarización dual para aplicaciones de espacio con requisitos muy restrictivos. Desgraciadamente, el nivel de aislamiento entre las polarizaciones ortogonales en antenas DBS (típicamente 30 dB) es demasiado exigente para ser conseguido con las antenas basadas en parches apilados. Además, el uso de elementos reflectarray con parches apilados conlleva procesos de fabricación complejos y costosos. En esta tesis se investigan varias configuraciones de elementos reflectarray basadas en conjuntos de dipolos paralelos con el fin de superar los inconvenientes que presenta el elemento basado en parches apilados. Primeramente, se propone un elemento consistente en dos conjuntos apilados ortogonales de tres dipolos paralelos para aplicaciones de polarización dual. Se ha diseñado, fabricado y medido una antena basada en este elemento, y los resultados obtenidos para la antena indican que tiene unas altas prestaciones en términos de ancho de banda, pérdidas, eficiencia y discriminación contrapolar, además de requerir un proceso de fabricación mucho más sencillo que el de las antenas basadas en tres parches apilados. Desgraciadamente, el elemento basado en dos conjuntos ortogonales de tres dipolos paralelos no proporciona suficientes grados de libertad para diseñar antenas reflectarray de transmisión-recepción (Tx-Rx) de polarización dual para aplicaciones de espacio por medio de técnicas de optimización de banda ancha. Por este motivo, en la tesis se propone un nuevo elemento reflectarray que proporciona los grados de libertad suficientes para cada polarización. El nuevo elemento consiste en dos conjuntos ortogonales de cuatro dipolos paralelos. Cada conjunto contiene tres dipolos coplanares y un dipolo apilado. Para poder acomodar los dos conjuntos de dipolos en una sola celda de la antena reflectarray, el conjunto de dipolos de una polarización está desplazado medio período con respecto al conjunto de dipolos de la otra polarización. Este hecho permite usar solamente dos niveles de metalización para cada elemento de la antena, lo cual simplifica el proceso de fabricación como en el caso del elemento basados en dos conjuntos de tres dipolos paralelos coplanares. Una antena de doble polarización y doble banda (Tx-Rx) basada en el nuevo elemento ha sido diseñada, fabricada y medida. La antena muestra muy buenas presentaciones en las dos bandas de frecuencia con muy bajos niveles de polarización cruzada. Simulaciones numéricas presentadas en la tesis muestran que estos bajos de niveles de polarización cruzada se pueden reducir todavía más si se llevan a cabo pequeñas rotaciones de los dos conjuntos de dipolos asociados a cada polarización. ABSTRACT The design of a reflectarray antenna under the local periodicity assumption requires the determination of the scattering matrix of a multilayered structure with periodic metallizations for quite a large number of different geometries. Therefore, in order to design reflectarray antennas within reasonable CPU times, fast and accurate numerical tools for the analysis of the periodic multilayered structures are required. In this thesis the Galerkin’s version of the Method of Moments (MoM) in the spectral domain is applied to the analysis of the periodic multilayered structures involved in the design of reflectarray antennas made of either stacked patches or coplanar parallel dipoles. Unfortunately, this numerical approach involves the computation of double infinite summations, and whereas some of these summations converge very fast, some others converge very slowly. In order to alleviate this problem, in the thesis a novel hybrid MoM spectral-spatial domain approach is proposed for the analysis of the periodic multilayered structures. In the novel approach, whereas the fast convergent summations are computed in the spectral domain, the slowly convergent summations are computed by means of an enhanced Mixed Potential Integral Equation (MPIE) formulation of the MoM in the spatial domain. This enhanced formulation is based on the efficient interpolation of the multilayered periodic Green’s functions, and on the efficient computation of the singular integrals leading to the MoM matrix entries. The novel hybrid spectral-spatial MoM code and the standard spectral domain MoM code have both been compared in the case of reflectarray elements based on multilayered stacked patches. Numerical simulations have shown that the CPU time required by the hybrid MoM is around 60 times smaller than that required by the standard spectral MoM for an accuracy of two significant figures. The combined use of reflectarray elements based on stacked patches and wideband optimization techniques has made it possible to design dual polarization transmit-receive (Tx-Rx) reflectarrays for space applications with stringent requirements. Unfortunately, the required level of isolation between orthogonal polarizations in DBS antennas (typically 30 dB) is hard to achieve with the configuration of stacked patches. Moreover, the use of reflectarrays based on stacked patches leads to a complex and expensive manufacturing process. In this thesis, we investigate several configurations of reflectarray elements based on sets of parallel dipoles that try to overcome the drawbacks introduced by the element based on stacked patches. First, an element based on two stacked orthogonal sets of three coplanar parallel dipoles is proposed for dual polarization applications. An antenna made of this element has been designed, manufactured and measured, and the results obtained show that the antenna presents a high performance in terms of bandwidth, losses, efficiency and cross-polarization discrimination, while the manufacturing process is cheaper and simpler than that of the antennas made of stacked patches. Unfortunately, the element based on two sets of three coplanar parallel dipoles does not provide enough degrees of freedom to design dual-polarization transmit-receive (Tx-Rx) reflectarray antennas for space applications by means of wideband optimization techniques. For this reason, in the thesis a new reflectarray element is proposed which does provide enough degrees of freedom for each polarization. This new element consists of two orthogonal sets of four parallel dipoles, each set containing three coplanar dipoles and one stacked dipole. In order to accommodate the two sets of dipoles in each reflectarray cell, the set of dipoles for one polarization is shifted half a period from the set of dipoles for the other polarization. This also makes it possible to use only two levels of metallization for the reflectarray element, which simplifies the manufacturing process as in the case of the reflectarray element based on two sets of three parallel dipoles. A dual polarization dual-band (Tx-Rx) reflectarray antenna based on the new element has been designed, manufactured and measured. The antenna shows a very good performance in both Tx and Rx frequency bands with very low levels of cross-polarization. Numerical simulations carried out in the thesis have shown that the low levels of cross-polarization can be even made smaller by means of small rotations of the two sets of dipoles associated to each polarization.

Co-simulation Methodologies for Hybrid and Electric Vehicle Dynamics

In recent decades, full electric and hybrid electric vehicles have emerged as an alternative to conventional cars due to a range of factors, including environmental and economic aspects. These vehicles are the result of considerable efforts to seek ways of reducing the use of fossil fuel for vehicle propulsion. Sophisticated technologies such as hybrid and electric powertrains require careful study and optimization. Mathematical models play a key role at this point. Currently, many advanced mathematical analysis tools, as well as computer applications have been built for vehicle simulation purposes. Given the great interest of hybrid and electric powertrains, along with the increasing importance of reliable computer-based models, the author decided to integrate both aspects in the research purpose of this work. Furthermore, this is one of the first final degree projects held at the ETSII (Higher Technical School of Industrial Engineers) that covers the study of hybrid and electric propulsion systems. The present project is based on MBS3D 2.0, a specialized software for the dynamic simulation of multibody systems developed at the UPM Institute of Automobile Research (INSIA). Automobiles are a clear example of complex multibody systems, which are present in nearly every field of engineering. The work presented here benefits from the availability of MBS3D software. This program has proven to be a very efficient tool, with a highly developed underlying mathematical formulation. On this basis, the focus of this project is the extension of MBS3D features in order to be able to perform dynamic simulations of hybrid and electric vehicle models. This requires the joint simulation of the mechanical model of the vehicle, together with the model of the hybrid or electric powertrain. These sub-models belong to completely different physical domains. In fact the powertrain consists of energy storage systems, electrical machines and power electronics, connected to purely mechanical components (wheels, suspension, transmission, clutch…). The challenge today is to create a global vehicle model that is valid for computer simulation. Therefore, the main goal of this project is to apply co-simulation methodologies to a comprehensive model of an electric vehicle, where sub-models from different areas of engineering are coupled. The created electric vehicle (EV) model consists of a separately excited DC electric motor, a Li-ion battery pack, a DC/DC chopper converter and a multibody vehicle model. Co-simulation techniques allow car designers to simulate complex vehicle architectures and behaviors, which are usually difficult to implement in a real environment due to safety and/or economic reasons. In addition, multi-domain computational models help to detect the effects of different driving patterns and parameters and improve the models in a fast and effective way. Automotive designers can greatly benefit from a multidisciplinary approach of new hybrid and electric vehicles. In this case, the global electric vehicle model includes an electrical subsystem and a mechanical subsystem. The electrical subsystem consists of three basic components: electric motor, battery pack and power converter. A modular representation is used for building the dynamic model of the vehicle drivetrain. This means that every component of the drivetrain (submodule) is modeled separately and has its own general dynamic model, with clearly defined inputs and outputs. Then, all the particular submodules are assembled according to the drivetrain configuration and, in this way, the power flow across the components is completely determined. Dynamic models of electrical components are often based on equivalent circuits, where Kirchhoff’s voltage and current laws are applied to draw the algebraic and differential equations. Here, Randles circuit is used for dynamic modeling of the battery and the electric motor is modeled through the analysis of the equivalent circuit of a separately excited DC motor, where the power converter is included. The mechanical subsystem is defined by MBS3D equations. These equations consider the position, velocity and acceleration of all the bodies comprising the vehicle multibody system. MBS3D 2.0 is entirely written in MATLAB and the structure of the program has been thoroughly studied and understood by the author. MBS3D software is adapted according to the requirements of the applied co-simulation method. Some of the core functions are modified, such as integrator and graphics, and several auxiliary functions are added in order to compute the mathematical model of the electrical components. By coupling and co-simulating both subsystems, it is possible to evaluate the dynamic interaction among all the components of the drivetrain. ‘Tight-coupling’ method is used to cosimulate the sub-models. This approach integrates all subsystems simultaneously and the results of the integration are exchanged by function-call. This means that the integration is done jointly for the mechanical and the electrical subsystem, under a single integrator and then, the speed of integration is determined by the slower subsystem. Simulations are then used to show the performance of the developed EV model. However, this project focuses more on the validation of the computational and mathematical tool for electric and hybrid vehicle simulation. For this purpose, a detailed study and comparison of different integrators within the MATLAB environment is done. Consequently, the main efforts are directed towards the implementation of co-simulation techniques in MBS3D software. In this regard, it is not intended to create an extremely precise EV model in terms of real vehicle performance, although an acceptable level of accuracy is achieved. The gap between the EV model and the real system is filled, in a way, by introducing the gas and brake pedals input, which reflects the actual driver behavior. This input is included directly in the differential equations of the model, and determines the amount of current provided to the electric motor. For a separately excited DC motor, the rotor current is proportional to the traction torque delivered to the car wheels. Therefore, as it occurs in the case of real vehicle models, the propulsion torque in the mathematical model is controlled through acceleration and brake pedal commands. The designed transmission system also includes a reduction gear that adapts the torque coming for the motor drive and transfers it. The main contribution of this project is, therefore, the implementation of a new calculation path for the wheel torques, based on performance characteristics and outputs of the electric powertrain model. Originally, the wheel traction and braking torques were input to MBS3D through a vector directly computed by the user in a MATLAB script. Now, they are calculated as a function of the motor current which, in turn, depends on the current provided by the battery pack across the DC/DC chopper converter. The motor and battery currents and voltages are the solutions of the electrical ODE (Ordinary Differential Equation) system coupled to the multibody system. Simultaneously, the outputs of MBS3D model are the position, velocity and acceleration of the vehicle at all times. The motor shaft speed is computed from the output vehicle speed considering the wheel radius, the gear reduction ratio and the transmission efficiency. This motor shaft speed, somehow available from MBS3D model, is then introduced in the differential equations corresponding to the electrical subsystem. In this way, MBS3D and the electrical powertrain model are interconnected and both subsystems exchange values resulting as expected with tight-coupling approach.When programming mathematical models of complex systems, code optimization is a key step in the process. A way to improve the overall performance of the integration, making use of C/C++ as an alternative programming language, is described and implemented. Although this entails a higher computational burden, it leads to important advantages regarding cosimulation speed and stability. In order to do this, it is necessary to integrate MATLAB with another integrated development environment (IDE), where C/C++ code can be generated and executed. In this project, C/C++ files are programmed in Microsoft Visual Studio and the interface between both IDEs is created by building C/C++ MEX file functions. These programs contain functions or subroutines that can be dynamically linked and executed from MATLAB. This process achieves reductions in simulation time up to two orders of magnitude. The tests performed with different integrators, also reveal the stiff character of the differential equations corresponding to the electrical subsystem, and allow the improvement of the cosimulation process. When varying the parameters of the integration and/or the initial conditions of the problem, the solutions of the system of equations show better dynamic response and stability, depending on the integrator used. Several integrators, with variable and non-variable step-size, and for stiff and non-stiff problems are applied to the coupled ODE system. Then, the results are analyzed, compared and discussed. From all the above, the project can be divided into four main parts: 1. Creation of the equation-based electric vehicle model; 2. Programming, simulation and adjustment of the electric vehicle model; 3. Application of co-simulation methodologies to MBS3D and the electric powertrain subsystem; and 4. Code optimization and study of different integrators. Additionally, in order to deeply understand the context of the project, the first chapters include an introduction to basic vehicle dynamics, current classification of hybrid and electric vehicles and an explanation of the involved technologies such as brake energy regeneration, electric and non-electric propulsion systems for EVs and HEVs (hybrid electric vehicles) and their control strategies. Later, the problem of dynamic modeling of hybrid and electric vehicles is discussed. The integrated development environment and the simulation tool are also briefly described. The core chapters include an explanation of the major co-simulation methodologies and how they have been programmed and applied to the electric powertrain model together with the multibody system dynamic model. Finally, the last chapters summarize the main results and conclusions of the project and propose further research topics. In conclusion, co-simulation methodologies are applicable within the integrated development environments MATLAB and Visual Studio, and the simulation tool MBS3D 2.0, where equation-based models of multidisciplinary subsystems, consisting of mechanical and electrical components, are coupled and integrated in a very efficient way.