Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W

Screw dislocations in bcc metals display non-planar cores at zero temperature which result in high lattice friction and thermally-activated strain rate behavior. In bcc W, electronic structure molecular statics calculations reveal a compact, non-degenerate core with an associated Peierls stress between 1.7 and 2.8 GPa. However, a full picture of the dynamic behavior of dislocations can only be gained by using more efficient atomistic simulations based on semiempirical interatomic potentials. In this paper we assess the suitability of five different potentials in terms of static properties relevant to screw dislocations in pure W. Moreover, we perform molecular dynamics simulations of stress-assisted glide using all five potentials to study the dynamic behavior of screw dislocations under shear stress. Dislocations are seen to display thermally-activated motion in most of the applied stress range, with a gradual transition to a viscous damping regime at high stresses. We find that one potential predicts a core transformation from compact to dissociated at finite temperature that affects the energetics of kink-pair production and impacts the mechanism of motion. We conclude that a modified embedded-atom potential achieves the best compromise in terms of static and dynamic screw dislocation properties, although at an expense of about ten-fold compared to central potentials.

A characterization of conserved quantities in non-equilibrium thermodynamics

The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems.

EVA: Endoscopic Video Analysis of the surgical scene for the assessment of MIS psychomotor skills

The present work covers the first validation efforts of the EVA Tracking System for the assessment of minimally invasive surgery (MIS) psychomotor skills. Instrument movements were recorded for 42 surgeons (4 expert, 22 residents, 16 novice medical students) and analyzed for a box trainer peg transfer task. Construct validation was established for 7/9 motion analysis parameters (MAPs). Concurrent validation was determined for 8/9 MAPs against the TrEndo Tracking System. Finally, automatic determination of surgical proficiency based on the MAPs was sought by 3 different approaches to supervised classification (LDA, SVM, ANFIS), with accuracy results of 61.9%, 83.3% and 80.9% respectively. Results not only reflect on the validation of EVA for skills? assessment, but also on the relevance of motion analysis of instruments in the determination of surgical competence.

On-line MRI sequences for the evaluation of apple internal quality.

On-line dynamic MRI, which is oriented to industrial grading lines, requires high-speed sequences with motion correction artefacts. In this study two different types of motion correction sequences have been used and have been implemented in real-time (FLASH and UFLARE). They are based on T2* and T2 respectively and their selection depends on the expected contrast effect of the disorder: while watercore enhances bright areas due to higher fluid mobility, internal breakdown potentiates low signal due to texture degradation. For watercore study, five different apple cultivars were used (Normanda-18-, Fuji-35-, Helada-36-, Verde Doncella-54-, Esperiega-75-) along two seasons (2011 and 2012). In total 218 fruits were measured under both, static conditions (20 slices per fruit) and under dynamic conditions (3 repetitions without slice selection). For internal breakdown, Braeburn cultivar has been studied (in total 106 fruits) under both static (20 slices per fruit) and dynamic conditions (3 replicates with slice selection). Metrological aspects such as repeatability of dynamic images and subsequent histogram feature stability become of major interest for further industrial application. Segregation ability among varying degrees of disorder is also analyzed.

1RM prediction: a data mining case study

In the last few years there has been a heightened interest in data treatment and analysis with the aim of discovering hidden knowledge and eliciting relationships and patterns within this data. Data mining techniques (also known as Knowledge Discovery in Databases) have been applied over a wide range of fields such as marketing, investment, fraud detection, manufacturing, telecommunications and health. In this study, well-known data mining techniques such as artificial neural networks (ANN), genetic programming (GP), forward selection linear regression (LR) and k-means clustering techniques, are proposed to the health and sports community in order to aid with resistance training prescription. Appropriate resistance training prescription is effective for developing fitness, health and for enhancing general quality of life. Resistance exercise intensity is commonly prescribed as a percent of the one repetition maximum. 1RM, dynamic muscular strength, one repetition maximum or one execution maximum, is operationally defined as the heaviest load that can be moved over a specific range of motion, one time and with correct performance. The safety of the 1RM assessment has been questioned as such an enormous effort may lead to muscular injury. Prediction equations could help to tackle the problem of predicting the 1RM from submaximal loads, in order to avoid or at least, reduce the associated risks. We built different models from data on 30 men who performed up to 5 sets to exhaustion at different percentages of the 1RM in the bench press action, until reaching their actual 1RM. Also, a comparison of different existing prediction equations is carried out. The LR model seems to outperform the ANN and GP models for the 1RM prediction in the range between 1 and 10 repetitions. At 75% of the 1RM some subjects (n = 5) could perform 13 repetitions with proper technique in the bench press action, whilst other subjects (n = 20) performed statistically significant (p < 0:05) more repetitions at 70% than at 75% of their actual 1RM in the bench press action. Rate of perceived exertion (RPE) seems not to be a good predictor for 1RM when all the sets are performed until exhaustion, as no significant differences (p < 0:05) were found in the RPE at 75%, 80% and 90% of the 1RM. Also, years of experience and weekly hours of strength training are better correlated to 1RM (p < 0:05) than body weight. O'Connor et al. 1RM prediction equation seems to arise from the data gathered and seems to be the most accurate 1RM prediction equation from those proposed in literature and used in this study. Epley's 1RM prediction equation is reproduced by means of data simulation from 1RM literature equations. Finally, future lines of research are proposed related to the problem of the 1RM prediction by means of genetic algorithms, neural networks and clustering techniques. RESUMEN En los últimos años ha habido un creciente interés en el tratamiento y análisis de datos con el propósito de descubrir relaciones, patrones y conocimiento oculto en los mismos. Las técnicas de data mining (también llamadas de \Descubrimiento de conocimiento en bases de datos\) se han aplicado consistentemente a lo gran de un gran espectro de áreas como el marketing, inversiones, detección de fraude, producción industrial, telecomunicaciones y salud. En este estudio, técnicas bien conocidas de data mining como las redes neuronales artificiales (ANN), programación genética (GP), regresión lineal con selección hacia adelante (LR) y la técnica de clustering k-means, se proponen a la comunidad del deporte y la salud con el objetivo de ayudar con la prescripción del entrenamiento de fuerza. Una apropiada prescripción de entrenamiento de fuerza es efectiva no solo para mejorar el estado de forma general, sino para mejorar la salud e incrementar la calidad de vida. La intensidad en un ejercicio de fuerza se prescribe generalmente como un porcentaje de la repetición máxima. 1RM, fuerza muscular dinámica, una repetición máxima o una ejecución máxima, se define operacionalmente como la carga máxima que puede ser movida en un rango de movimiento específico, una vez y con una técnica correcta. La seguridad de las pruebas de 1RM ha sido cuestionada debido a que el gran esfuerzo requerido para llevarlas a cabo puede derivar en serias lesiones musculares. Las ecuaciones predictivas pueden ayudar a atajar el problema de la predicción de la 1RM con cargas sub-máximas y son empleadas con el propósito de eliminar o al menos, reducir los riesgos asociados. En este estudio, se construyeron distintos modelos a partir de los datos recogidos de 30 hombres que realizaron hasta 5 series al fallo en el ejercicio press de banca a distintos porcentajes de la 1RM, hasta llegar a su 1RM real. También se muestra una comparación de algunas de las distintas ecuaciones de predicción propuestas con anterioridad. El modelo LR parece superar a los modelos ANN y GP para la predicción de la 1RM entre 1 y 10 repeticiones. Al 75% de la 1RM algunos sujetos (n = 5) pudieron realizar 13 repeticiones con una técnica apropiada en el ejercicio press de banca, mientras que otros (n = 20) realizaron significativamente (p < 0:05) más repeticiones al 70% que al 75% de su 1RM en el press de banca. El ínndice de esfuerzo percibido (RPE) parece no ser un buen predictor del 1RM cuando todas las series se realizan al fallo, puesto que no existen diferencias signifiativas (p < 0:05) en el RPE al 75%, 80% y el 90% de la 1RM. Además, los años de experiencia y las horas semanales dedicadas al entrenamiento de fuerza están más correlacionadas con la 1RM (p < 0:05) que el peso corporal. La ecuación de O'Connor et al. parece surgir de los datos recogidos y parece ser la ecuación de predicción de 1RM más precisa de aquellas propuestas en la literatura y empleadas en este estudio. La ecuación de predicción de la 1RM de Epley es reproducida mediante simulación de datos a partir de algunas ecuaciones de predicción de la 1RM propuestas con anterioridad. Finalmente, se proponen futuras líneas de investigación relacionadas con el problema de la predicción de la 1RM mediante algoritmos genéticos, redes neuronales y técnicas de clustering.

Dynamic earth pressures against a retaining wall caused by Rayleigh waves

An approximate procedure for studying harmonic soil-structure interaction problems is presented. The presence of Rayleigh waves is considered and the resulting governing equations of the dynamic soil-structure system are solved in the time domain. With this method the transient and steady states of a vibratory motion and also the nonlinear behaviour of the soil can be studied. As an example, the dynamic earth pressure against a rigid retaining wall is investigated. The loads are assumed to be harmonic Rayleigh waves with both static and dynamic surface surcharges. The dependence of the results on the excitation frequency is shown.

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.

On a mathematical model of tumor growth based on cancer stem cells

We consider a simple mathematical model of tumor growth based on cancer stem cells. The model consists of four hyperbolic equations of first order to describe the evolution of different subpopulations of cells: cancer stem cells, progenitor cells, differentiated cells and dead cells. A fifth equation is introduced to model the evolution of the moving boundary. The system includes non-local terms of integral type in the coefficients. Under some restrictions in the parameters we show that there exists a unique homogeneous steady state which is stable.

Influencia de un programa de ejercicio aeróbico en la calidad de vida de pacientes afectadas por cáncer de mama = Influence of an aerobic exercise program on breast cancer patients’ quality of life

INTRODUCCIÓN Actualmente las supervivientes de cáncer de mama viven durante más tiempo. Sin embargo, los tratamientos utilizados presentan importantes efectos secundarios que afectan y marcan su calidad de vida. Numerosos estudios han mostrado que el ejercicio es una herramienta apta, segura y efectiva reduciendo algunos de estos efectos secundarios y, en suma, mejorando la calidad de vida de estas pacientes, aspecto que presenta al ejercicio físico como una intervención integral para ellas. Por el contrario, se ha observado que las supervivientes de cáncer de mama reducen la cantidad de ejercicio que realizan después de dichos tratamientos. Por ello, el objetivo de este proyecto es examinar los efectos de un programa integral de ejercicio en la calidad de vida y la cantidad de ejercicio físico que realizan las pacientes con cáncer de mama en su tiempo, tras finalizar sus tratamientos. MATERIAL Y MÉTODOS Se diseñó un Ensayo Clínico Aleatorizado. Noventa pacientes diagnosticadas de cáncer de mama en estadios tempranos que habían terminado sus tratamientos de radioterapia y quimioterapia recientemente, fueron reclutadas por la Universidad Politécnica de Madrid, desde enero de 2013 hasta junio de 2014. Las pacientes fueron aleatorizadas tras las mediciones iniciales al grupo control (tratamientos habituales) o grupo intervención, durante tres meses. La intervención consistió en 24 clases de ejercicio combinando práctica aeróbica y de fuerza con el fin de reducir los efectos secundarios de dichos tratamientos. La calidad de vida, la cantidad de ejercicio físico realizado en tiempo de ocio, VO2max, la fuerza, la movilidad articular del hombro, la fatiga, la depresión y la ansiedad fueron medidos al inicio y después de los tres meses en todos los pacientes. RESULTADOS Un total de 89 pacientes con una media de 49.06±8.75 de edad fueron finalmente analizadas. El grupo intervención (n=44) mostraron significativamente mejores resultados en calidad de vida (p=0.0001; d=0.85), cantidad de ejercicio en tiempo de ocio (p=0.0001; d=2.77), en variables de la composición corporal, en variables físicas y en variables psicológicas comparado con el grupo control (n=45). Además, se observó una correlación significativa entre la calidad de vida y el ejercicio realizado en tiempo de ocio en el grupo intervención (r= 0.58; p=0.001), que no fue patente en el grupo control. Se observaron cambios significativos en el grupo de intervención relativos a la composición corporal, con aumento de la masa muscular (p=0.001) y reducción de la masa grasa (p=0.0001). Tanto las variables físicas como psicológicas también mostraron diferencias significativas a favor al grupo de intervención en las comparaciones entre grupos. CONCLUSIONES Según estos resultados, un programa de ejercicio físico específico es una intervención integral que mejora los hábitos y la calidad de vida de las supervivientes de cáncer de mama, lo que reduce determinados efectos secundarios de los tratamientos y aumenta la salud física y psicológica general de estas mujeres. Este tipo de intervenciones pude ser una herramienta barata y efectiva para ofrecer a los pacientes, integrada en los tratamientos habituales. ABSTRACT INTRODUCTION It is well known that breast cancer survivors are living longer. However, breast cancer treatments present serious side effects, which could affect breast cancer survivors’ (BCS) health and quality of life (QoL). Exercise has been presented as a feasible, safe and effective tool in reducing some of these side effects and to improve survivors’ QoL, acting as an integrative treatment for them, although it has been observed that BCS reduce their leisure time exercise (LTE) levels. Therefore, the aim of this study was to examine the effects of an integrative exercise program in QoL and LTE in BCS after the completion of their adjuvant treatment. MATERIAL AND METHODS A randomized controlled trial (RCT) was designed. Ninety patients diagnosed with an early stage of breast cancer and who recently finished chemotherapy and radiotherapy treatments were recruited by the Technical University of Madrid from January 2013 to June 2014. Patients were randomized after baseline assessments to the intervention group (IG) or to the control group (CG) (usual care) for three months. The Intervention consisted in 24 supervised exercise classes, combining aerobic and resistance exercises in order to reduce the most common side effects of the treatments. QoL, LTE, body composition, VO2max, strength, shoulder range of motion, fatigue, depression and self-esteem were measured in all the patients at baseline and after three months. RESULTS A total of 89 patients aged 49.06±8.75 years were finally assessed. IG (n=44) showed significant better results in QoL (p=0.0001; d=0.85), LTE (p=0.0001; d=2.77), in body composition, in the physical variable and in psychological outcomes, compared with the CG (n=45). In addition, a correlation between QoL and LTE (r= 0.58; p=0.001) was found in the IG, while CG did not show this correlation. Significant changes in body composition were observed in the group comparisons, especially in lean mass (p=0.001) and body fat mass (p= 0.0001). Positive changes were also observed in the physical and psychological variables in comparisons between groups. CONCLUSIONS These results suggest that this exercise program may be an integrative intervention, which is able to improve QoL and LTE levels in breast cancer survivors, reducing breast cancer side effects of treatments and improving their physical and psychological general health. Exercise may be an effective and inexpensive strategy to be included in patients integrative care.

Objective metrics for functional evaluation of upper limb during the ADL of drinking: application in SCI

Three-dimensional kinematic analysis provides quantitative assessment of upper limb motion and is used as an outcome measure to evaluate movement disorders. The aim of the present study is to present a set of kinematic metrics for quantifying characteristics of movement performance and the functional status of the subject during the execution of the activity of daily living (ADL) of drinking from a glass. Then, the objective is to apply these metrics in healthy people and a population with cervical spinal cord injury (SCI), and to analyze the metrics ability to discriminate between healthy and pathologic people. 19 people participated in the study: 7 subjects with metameric level C6 tetraplegia, 4 subjects with metameric level C7 tetraplegia and 8 healthy subjects. The movement was recorded with a photogrammetry system. The ADL of drinking was divided into a series of clearly identifiable phases to facilitate analysis. Metrics describing the time of the reaching phase, the range of motion of the joints analyzed, and characteristics of movement performance such as the efficiency, accuracy and smoothness of the distal segment and inter-joint coordination were obtained. The performance of the drinking task was more variable in people with SCI compared to the control group in relation to the metrics measured. Reaching time was longer in SCI groups. The proposed metrics showed capability to discriminate between healthy and pathologic people. Relative deficits in efficiency were larger in SCI people than in controls. These metrics can provide useful information in a clinical setting about the quality of the movement performed by healthy and SCI people during functional activities.

Influence of gravity on heavy particle statistics in turbulent channel and pipe flow at matched Kàrmàn number

In this work, we use large eddy simulations (LES) and Lagrangian tracking to study the influence of gravity on particle statistics in a fully developed turbulent upward/downward flow in a vertical channel and pipe at matched Kàrmàn number. Only drag and gravity are considered in the equation of motion for solid particles, which are assumed to have no influence on the flow field. Particle interactions with the wall are fully elastic. Our findings obtained from the particle statistics confirm that: (i) the gravity seems to modify both the quantitative and qualitative behavior of the particle distribution and statistics of the particle velocity in wall normal direction; (ii) however, only the quantitative behavior of velocity particle in streamwise direction and the root mean square of velocity components is modified; (iii) the statistics of fluid and particles coincide very well near the wall in channel and pipe flow with equal Kàrmàn number; (iv) pipe curvature seems to have quantitative and qualitative influence on the particle velocity and on the particle concentration in wall normal direction.

Comparison of linear and non-linear 2D+T registration methods for DE-MRI cardiac perfusion studies

A series of motion compensation algorithms is run on the challenge data including methods that optimize only a linear transformation, or a non-linear transformation, or both – first a linear and then a non-linear transformation. Methods that optimize a linear transformation run an initial segmentation of the area of interest around the left myocardium by means of an independent component analysis (ICA) (ICA-*). Methods that optimize non-linear transformations may run directly on the full images, or after linear registration. Non-linear motion compensation approaches applied include one method that only registers pairs of images in temporal succession (SERIAL), one method that registers all image to one common reference (AllToOne), one method that was designed to exploit quasi-periodicity in free breathing acquired image data and was adapted to also be usable to image data acquired with initial breath-hold (QUASI-P), a method that uses ICA to identify the motion and eliminate it (ICA-SP), and a method that relies on the estimation of a pseudo ground truth (PG) to guide the motion compensation.

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.

Simulación eficiente de mecanismos flexibles mediante formulaciones topológicas

El objetivo de esta Tesis es presentar un método eficiente para la evaluación de sistemas multi-cuerpo con elementos flexibles con pequeñas deformaciones, basado en métodos topológicos para la simulación de sistemas tan complejos como los que se utilizan en la práctica y en tiempo real o próximo al real. Se ha puesto un especial énfasis en la resolución eficiente de aquellos aspectos que conllevan mayor coste computacional, tales como la evaluación de las ecuaciones dinámicas y el cálculo de los términos de inercia. Las ecuaciones dinámicas se establecen en función de las variables independientes del sistema, y la integración de las mismas se realiza mediante formulaciones implícitas de index-3. Esta Tesis se articula en seis Capítulos. En el Capítulo 1 se realiza una revisión bibliográfica de la simulación de sistemas flexibles y los métodos más relevantes de integración de las ecuaciones diferenciales del movimiento. Asimismo, se presentan los objetivos de esta Tesis. En el Capítulo 2 se presenta un método semi-recursivo para la evaluación de las ecuaciones de los sistemas multi-cuerpo con elementos flexibles basado en formulaciones topológicas y síntesis modal. Esta Tesis determina la posición de cada punto del cuerpo flexible en función de un sistema de referencia flotante que se mueve con dicho cuerpo y de las amplitudes de ciertos modos de deformación calculados a partir de un mallado obtenido mediante el Método de Elementos Finitos. Se presta especial atención en las condiciones de contorno que se han de tener en cuenta a la hora de establecer las variables que definen la deformación del cuerpo flexible. El Capítulo 3 se centra en la evaluación de los términos de inercia de los sistemas flexibles que generalmente conllevan un alto coste computacional. Se presenta un método que permite el cálculo de dichos términos basado en el uso de 24 matrices constantes que pueden ser calculadas previamente al proceso de integración. Estas matrices permiten evaluar la matriz de masas y el vector de fuerzas de inercia dependientes de la velocidad sin que sea necesario evaluar la posición deformada de todos los puntos del cuerpo flexible. Se realiza un análisis pormenorizado de dichas matrices con el objetivo de optimizar su cálculo estableciendo aproximaciones que permitan reducir el número de dichos términos y optimizar aún más su evaluación. Se analizan dos posibles simplificaciones: la primera utiliza una discretización no-consistente basada en elementos finitos en los que se definen únicamente los desplazamientos axiales de los nodos; en la segunda propuesta se hace uso de una matriz de masas concentradas (Lumped Mass). Basándose en la formulación presentada, el Capítulo 4 aborda la integración eficiente de las ecuaciones dinámicas. Se presenta un método iterativo para la integración con fórmulas de index-3 basado en la proyección de las ecuaciones dinámicas según las variables independientes del sistema multi-cuerpo. El cálculo del residuo del sistema de ecuaciones no lineales que se ha de resolver de modo iterativo se realiza mediante un proceso recursivo muy eficiente que aprovecha la estructura topológica del sistema. Se analizan tres formas de evaluar la matriz tangente del citado sistema no lineal: evaluación aproximada, numérica y recursiva. El método de integración presentado permite el uso de distintas fórmulas. En esta Tesis se analizan la Regla Trapezoidal, la fórmula BDF de segundo orden y un método híbrido TR-BDF2. Para este último caso se presenta un algoritmo de paso variable. En el Capítulo 5 plantea la implementación del método propuesto en un programa general de simulación de mecanismos que permita la resolución de cualquier sistema multi-cuerpo definiéndolo mediante un fichero de datos. La implementación de este programa se ha realizado tanto en C++ como en Java. Se muestran los resultados de las formulaciones presentadas en esta Tesis mediante la simulación de cuatro ejemplos de distinta complejidad. Mediante análisis concretos se comparan la formulación presentada con otras existentes. También se analiza el efecto del lenguaje de programación utilizado en la implementación y los efectos de las posibles simplificaciones planteadas. Por último, el Capítulo 6 resume las principales conclusiones alcanzadas en la Tesis y las futuras líneas de investigación que con ella se abren. ABSTRACT This Thesis presents an efficient method for solving the forward dynamics of a multi-body sys-tem formed by rigid and flexible bodies with small strains for real-time simulation of real-life models. It is based on topological formulations. The presented work focuses on the efficient solution of the most time-consuming tasks of the simulation process, such as the numerical integration of the motion differential equations and in particular the evaluation of the inertia terms corresponding to the flexible bodies. The dynamic equations are formulated in terms of independent variables of the muti-body system, and they are integrated by means of implicit index-3 formulae. The Thesis is arranged in six chapters. Chapter 1 presents a review of the most relevant and recent contributions related to the modelization of flexible multi-body systems and the integration of the corresponding dynamic equations. The main objectives of the Thesis are also presented in detail. Chapter 2 presents a semi-recursive method for solving the equations of a multi-body system with flexible bodies based on topological formulations and modal synthesis. This Thesis uses the floating frame approach and the modal amplitudes to define the position of any point at the flexible body. These modal deformed shapes are obtained by means of the Finite Element Method. Particular attention has been taken to the boundary conditions used to define the deformation of the flexible bodies. Chapter 3 focuses on the evaluation of the inertia terms, which is usually a very time-consuming task. A new method based on the use of 24 constant matrices is presented. These matrices are evaluated during the set-up step, before the integration process. They allow the calculation of the inertia terms in terms of the position and orientation of the local coordinate system and the deformation variables, and there is no need to evaluate the position and velocities of all the nodes of the FEM mesh. A deep analysis of the inertia terms is performed in order to optimize the evaluation process, reducing both the terms used and the number of arithmetic operations. Two possible simplifications are presented: the first one uses a non-consistent approach in order to define the inertia terms respect to the Cartesian coordinates of the FEM mesh, rejecting those corresponding to the angular rotations; the second approach makes use of lumped mass matrices. Based on the previously presented formulation, Chapter 4 is focused on the numerical integration of the motion differential equations. A new predictor-corrector method based on index-3 formulae and on the use of multi-body independent variables is presented. The evaluation of the dynamic equations in a new time step needs the solution of a set on nonlinear equations by a Newton-Raphson iterative process. The computation of the corresponding residual vector is performed efficiently by taking advantage of the system’s topological structure. Three methods to compute the tangent matrix are presented: an approximated evaluation that considers only the most relevant terms, a numerical approach based on finite differences and a recursive method that uses the topological structure. The method presented for integrating the dynamic equations can use a variety of integration formulae. This Thesis analyses the use of the trapezoidal rule, the 2nd order BDF formula and the hybrid TR-BDF2 method. A variable-time step strategy is presented for the last one. Chapter 5 describes the implementation of the proposed method in a general purpose pro-gram for solving any multibody defined by a data file. This program is implemented both in C++ and Java. Four examples are used to check the validity of the formulation and to compare this method with other methods commonly used to solve the dynamic equations of multi-body systems containing flexible bodies. The efficiency of the programming methodology used and the effect of the possible simplifications proposed are also analyzed. Chapter 6 summarizes the main Conclusions obtained in this Thesis and the new lines of research that have been opened.

Analytical study of the thermal behaviour and stability of a small satellite

In this work the thermal analysis of a small satellite orbiting around the Earth has been approached by direct integration of the heat balance equations of a two-node reduced model, obtaining a linearized second order ODE problem, similar in form to the classical case of the forced vibration of a damped system. As the thermal loads (solar radiation, albedo, etc.) are harmonic, the problem is solved by means of Fourier analysis methods. Research on that field can be directly applied to the analysis of thermal problems and the results obtained are satisfactory. Working on the frequency domain streamlines the analysis, simplifies the study and facilitates the experimental testing. The transfer functions are obtained for the two-node case but the study can be extended to an n-node model.