On the flexural vibration of cylinders under axial loads:Numerical and experimental study

The flexural vibration of a homogeneous isotropic linearly elastic cylinder of any aspect ratio is analysed in this paper. Natural frequencies of a cylinder under uniformly distributed axial loads acting on its bases are calculated numerically by the Ritz method with terms of power series in the coordinate directions as approximating functions. The effect of axial loads on the flexural vibration cannot be described by applying infinitesimal strain theory, therefore, geometrically nonlinear strain–displacement relations with second-order terms are considered here. The natural frequencies of free–free, clamped–clamped, and sliding–sliding cylinders subjected to axial loads are calculated using the proposed three-dimensional Ritz approach and are compared with those obtained with the finite element method and the Bernoulli–Euler theory. Different experiments with cylinders axially compressed by a hydraulic press are carried out and the experimental results for the lowest flexural frequency are compared with the numerical results. An approach based on the Ritz formulation is proposed for the flexural vibration of a cylinder between the platens of the press with constraints varying with the intensity of the compression. The results show that for low compressions the cylinder behaves similarly to a sliding–sliding cylinder, whereas for high compressions the cylinder vibrates as a clamped–clamped one.

Monte Carlo simulation on a system of hard cylinders at a very high packing fraction

Using the Monte Carlo method the behavior of a system of true hard cylinders has been studied. Values of the length-to-breadth ratio L/D and packing fraction η have been chosen similar to those of real nematic liquid crystals. Results include radial distribution function g(r), structure factor S(k), and orientational order parameter M. These results lead to the conclusion that the hard cylinder model may be a useful reference for real mesomorphic phases.

Characterization cement pastes degraded in lanoratory solutions and physiochemical parameters employed for modeling the process

Previously degradation studies carried out, over a number of different mortars by the research team, have shown that observed degradation does not exclusively depend on the solution equilibrium pH, nor the aggressive anions relative solubility. In our tests no reason was found that could allow us to explain, why same solubility anions with a lower pH are less aggressive than others. The aim of this paper is to study cement pastes behavior in aggressive environments. As observed in previous research, this cement pastes behaviors are not easily explained only taking into account only usual parameters, pH, solubility etc. Consequently the paper is about studying if solution physicochemical characteristics are more important in certain environments than specific pH values. The paper tries to obtain a degradation model, which starting from solution physicochemical parameters allows us to interpret the different behaviors shown by different composition cements. To that end, the rates of degradation of the solid phases were computed for each considered environment. Three cement have been studied: CEM I 42.5R/SR, CEM II/A-V 42.5R and CEM IV/B-(P-V) 32.5 N. The pastes have been exposed to five environments: sodium acetate/acetic acid 0.35 M, sodium sulfate solution 0.17 M, a solution representing natural water, saturated calcium hydroxide solution and laboratory environment. The attack mechanism was meant to be unidirectional, in order to achieve so; all sides of cylinders were sealed except from the attacked surface. The cylinders were taking out of the exposition environments after 2, 4, 7, 14, 30, 58 and 90 days. Both aggressive solution variations in solid phases and in different depths have been characterized. To each age and depth the calcium, magnesium and iron contents have been analyzed. Hydrated phases evolution studied, using thermal analysis, and crystalline compound changes, using X ray diffraction have been also analyzed. Sodium sulphate and water solutions stabilize an outer pH near to 8 in short time, however the stability of the most pH dependent phases is not the same. Although having similar pH and existing the possibility of forming a plaster layer near to the calcium leaching surface, this stability is greater than other sulphate solutions. Stability variations of solids formed by inverse diffusion, determine the rate of degradation.

A canonical UTD solution for electromagnetic scattering by an electrically large impedance circular cylinder illuminated by an obliquely incident plane wave

A uniform geometrical theory of diffraction (UTD) solution is developed for the canonical problem of the electromagnetic (EM) scattering by an electrically large circular cylinder with a uniform impedance boundary condition (IBC), when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transform, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the geometrical optics (GO) or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution.

The neocortical column

In the middle of the twentieth century, Rafael Lorente de Nó (1902?1990) introduced the fundamental concept of the ?elementary cortical unit of operation,? proposing that the cerebral cortex is formed of small cylinders containing vertical chains of neurons (Lorente de Nó, 1933, 1938). On the basis of this idea, the hypothesis was later developed of the columnar organization of the cerebral cortex, primarily following the physiological and anatomical studies of Vernon Mountcastle, David Hubel, Torsten Wiesel, János Szentágothai, Ted Jones, and Pasko Rakic (for a review of these early studies, see Mountcastle, 1998). The columnar organization hypothesis is currently the most widely adopted to explain the cortical processing of information, making its study of potential interest to any researcher interested in this tissue, both in a healthy and pathological state. However, it is frequently remarked that the nomenclature surrounding this hypothesis often generates problems, as the term ?Column? is used freely and promiscuously to refer to multiple, distinguishable entities, such as cellular or dendritic minicolumns or afferent macrocolumns, with respective diameters of menor que50 and 200?500 ?m. Another problem is the degree to which classical criteria may need to be modified (shared response properties, shared input, and common output) and if so, how. Moreover, similar problems arise when we consider the need to define area-specific and species-specific variations. Finally, and what is more an ultimate goal than a problem, it is still necessary to achieve a better fundamental understanding of what columns are and how they are used in cortical processes. Accordingly, it is now very important to translate recent technical advances and new findings in the neurosciences into practical applications for neuroscientists, clinicians, and for those interested in comparative anatomy and brain evolution.

Interference of parallel cylindrical Langmuir probes

Current to a cylindrical probe of arbitrary cross section is discussed. Previous results for circular cylinders at the high bias and moderate radius R of interest for electrodynamic bare tethers, for which space charge may be ignored over a large neighborhood of the probe, depend in separate ways on both R and perimeter p. These results are extended to a general convex cross section by introducing certain equivalent radius Req. For any concave cross section, results use a proper equivalent perimeter peq , in addition to Req. Finally, for the joint cross section of separate parallel probes, certain effective perimeter peff replaces peq. Rules to determine Req. peq. and peff are used to discuss collection interference among two or more parallel cylinders when brought from far away to contact

A new hard-particle model for anisotropic fluids

We report a new hard-particle model system consisting of hard cylinders, we have determined the geometrical conditions that let us know whether or not two given cylinders overlap. In addition we have carried out Monte Carlo simulations sampling the canonical ensemble on this system, the numerical results indicate that this system exhibits mesomorphic behaviour.

Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder

Con esta tesis ”Desarrollo de una Teoría Uniforme de la Difracción para el Análisis de los Campos Electromagnéticos Dispersados y Superficiales sobre un Cilindro” hemos iniciado una nueva línea de investigación que trata de responder a la siguiente pregunta: ¿cuál es la impedancia de superficie que describe una estructura de conductor eléctrico perfecto (PEC) convexa recubierta por un material no conductor? Este tipo de estudios tienen interés hoy en día porque ayudan a predecir el campo electromagnético incidente, radiado o que se propaga sobre estructuras metálicas y localmente convexas que se encuentran recubiertas de algún material dieléctrico, o sobre estructuras metálicas con pérdidas, como por ejemplo se necesita en determinadas aplicaciones aeroespaciales, marítimas o automovilísticas. Además, desde un punto de vista teórico, la caracterización de la impedancia de superficie de una estructura PEC recubierta o no por un dieléctrico es una generalización de varias soluciones que tratan ambos tipos de problemas por separado. En esta tesis se desarrolla una teoría uniforme de la difracción (UTD) para analizar el problema canónico del campo electromagnético dispersado y superficial en un cilindro circular eléctricamente grande con una condición de contorno de impedancia (IBC) para frecuencias altas. Construir una solución basada en UTD para este problema canónico es crucial en el desarrollo de un método UTD para el caso más general de una superficie arbitrariamente convexa, mediante el uso del principio de localización de los campos electromagnéticos a altas frecuencias. Esta tesis doctoral se ha llevado a cabo a través de una serie de hitos que se enumeran a continuación, enfatizando las contribuciones a las que ha dado lugar. Inicialmente se realiza una revisión en profundidad del estado del arte de los métodos asintóticos con numerosas referencias. As í, cualquier lector novel puede llegar a conocer la historia de la óptica geométrica (GO) y la teoría geométrica de la difracción (GTD), que dieron lugar al desarrollo de la UTD. Después, se investiga ampliamente la UTD y los trabajos más importantes que pueden encontrarse en la literatura. As í, este capítulo, nos coloca en la posición de afirmar que, hasta donde nosotros conocemos, nadie ha intentado antes llevar a cabo una investigación rigurosa sobre la caracterización de la impedancia de superficie de una estructura PEC recubierta por un material dieléctrico, utilizando para ello la UTD. Primero, se desarrolla una UTD para el problema canónico de la dispersión electromagnética de un cilindro circular eléctricamente grande con una IBC uniforme, cuando es iluminado por una onda plana con incidencia oblicua a frecuencias altas. La solución a este problema canónico se construye a partir de una solución exacta mediante una expansión de autofunciones de propagación radial. Entonces, ésta se convierte en una nueva expansión de autofunciones de propagación circunferencial muy apropiada para cilindros grandes, a través de la transformación de Watson. De esta forma, la expresión del campo se reduce a una integral que se evalúa asintóticamente, para altas frecuencias, de manera uniforme. El resultado se expresa según el trazado de rayos descrito en la UTD. La solución es uniforme porque tiene la importante propiedad de mantenerse continua a lo largo de la región de transición, a ambos lados de la superficie del contorno de sombra. Fuera de la región de transición la solución se reduce al campo incidente y reflejado puramente ópticos en la región iluminada del cilindro, y al campo superficial difractado en la región de sombra. Debido a la IBC el campo dispersado contiene una componente contrapolar a causa de un acoplamiento entre las ondas TEz y TMz (donde z es el eje del cilindro). Esta componente contrapolar desaparece cuando la incidencia es normal al cilindro, y también en la región iluminada cuando la incidencia es oblicua donde el campo se reduce a la solución de GO. La solución UTD presenta una muy buena exactitud cuando se compara numéricamente con una solución de referencia exacta. A continuación, se desarrolla una IBC efectiva para el cálculo del campo electromagnético dispersado en un cilindro circular PEC recubierto por un dieléctrico e iluminado por una onda plana incidiendo oblicuamente. Para ello se derivan dos impedancias de superficie en relación directa con las ondas creeping y de superficie TM y TE que se excitan en un cilindro recubierto por un material no conductor. Las impedancias de superficie TM y TE están acopladas cuando la incidencia es oblicua, y dependen de la geometría del problema y de los números de onda. Además, se ha derivado una impedancia de superficie constante, aunque con diferente valor cuando el observador se encuentra en la zona iluminada o en la zona de sombra. Después, se presenta una solución UTD para el cálculo de la dispersión de una onda plana con incidencia oblicua sobre un cilindro eléctricamente grande y convexo, mediante la generalización del problema canónico correspondiente al cilindro circular. La solución asintótica es uniforme porque se mantiene continua a lo largo de la región de transición, en las inmediaciones del contorno de sombra, y se reduce a la solución de rayos ópticos en la zona iluminada y a la contribución de las ondas de superficie dentro de la zona de sombra, lejos de la región de transición. Cuando se usa cualquier material no conductor se excita una componente contrapolar que tiende a desaparecer cuando la incidencia es normal al cilindro y en la región iluminada. Se discuten ampliamente las limitaciones de las fórmulas para la impedancia de superficie efectiva, y se compara la solución UTD con otras soluciones de referencia, donde se observa una muy buena concordancia. Y en tercer lugar, se presenta una aproximación para una impedancia de superficie efectiva para el cálculo de los campos superficiales en un cilindro circular conductor recubierto por un dieléctrico. Se discuten las principales diferencias que existen entre un cilindro PEC recubierto por un dieléctrico desde un punto de vista riguroso y un cilindro con una IBC. Mientras para un cilindro de impedancia se considera una impedancia de superficie constante o uniforme, para un cilindro conductor recubierto por un dieléctrico se derivan dos impedancias de superficie. Estas impedancias de superficie están asociadas a los modos de ondas creeping TM y TE excitadas en un cilindro, y dependen de la posición y de la orientación del observador y de la fuente. Con esto en mente, se deriva una solución UTD con IBC para los campos superficiales teniendo en cuenta las dependencias de la impedancia de superficie. La expansión asintótica se realiza, mediante la transformación de Watson, sobre la representación en serie de las funciones de Green correspondientes, evitando as í calcular las derivadas de orden superior de las integrales de tipo Fock, y dando lugar a una solución rápida y precisa. En los ejemplos numéricos realizados se observa una muy buena precisión cuando el cilindro y la separación entre el observador y la fuente son grandes. Esta solución, junto con el método de los momentos (MoM), se puede aplicar para el cálculo eficiente del acoplamiento mutuo de grandes arrays conformados de antenas de parches. Los métodos propuestos basados en UTD para el cálculo del campo electromagnético dispersado y superficial sobre un cilindro PEC recubierto de dieléctrico con una IBC efectiva suponen un primer paso hacia la generalización de una solución UTD para superficies metálicas convexas arbitrarias cubiertas por un material no conductor e iluminadas por una fuente electromagnética arbitraria. ABSTRACT With this thesis ”Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder” we have initiated a line of investigation whose goal is to answer the following question: what is the surface impedance which describes a perfect electric conductor (PEC) convex structure covered by a material coating? These studies are of current and future interest for predicting the electromagnetic (EM) fields incident, radiating or propagating on locally smooth convex parts of highly metallic structures with a material coating, or by a lossy metallic surfaces, as for example in aerospace, maritime and automotive applications. Moreover, from a theoretical point of view, the surface impedance characterization of PEC surfaces with or without a material coating represents a generalization of independent solutions for both type of problems. A uniform geometrical theory of diffraction (UTD) is developed in this thesis for analyzing the canonical problem of EM scattered and surface field by an electrically large circular cylinder with an impedance boundary condition (IBC) in the high frequency regime, by means of a surface impedance characterization. The construction of a UTD solution for this canonical problem is crucial for the development of the corresponding UTD solution for the more general case of an arbitrary smooth convex surface, via the principle of the localization of high frequency EM fields. The development of the present doctoral thesis has been carried out through a series of landmarks that are enumerated as follows, emphasizing the main contributions that this work has given rise to. Initially, a profound revision is made in the state of art of asymptotic methods where numerous references are given. Thus, any reader may know the history of geometrical optics (GO) and geometrical theory of diffraction (GTD), which led to the development of UTD. Then, the UTD is deeply investigated and the main studies which are found in the literature are shown. This chapter situates us in the position to state that, as far as we know, nobody has attempted before to perform a rigorous research about the surface impedance characterization for material-coated PEC convex structures via UTD. First, a UTD solution is developed for the canonical problem of the EM scattering by an electrically large circular cylinder with a uniform IBC, when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transformation, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the GO or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution. Then, an effective IBC is developed for the EM scattered field on a coated PEC circular cylinder illuminated by an obliquely incident plane wave. Two surface impedances are derived in a direct relation with the TM and TE surface and creeping wave modes excited on a coated cylinder. The TM and TE surface impedances are coupled at oblique incidence, and depend on the geometry of the problem and the wave numbers. Nevertheless, a constant surface impedance is found, although with a different value when the observation point lays in the lit or in the shadow region. Then, a UTD solution for the scattering of an obliquely incident plane wave on an electrically large smooth convex coated PEC cylinder is introduced, via a generalization of the canonical circular cylinder problem. The asymptotic solution is uniform because it remains continuous across the transition region, in the vicinity of the shadow boundary, and it recovers the ray optical solution in the deep lit region and the creeping wave formulation within the deep shadow region. When a coating is present a cross-polar field term is excited, which vanishes at normal incidence and in the deep lit region. The limitations of the effective surface impedance formulas are discussed, and the UTD solution is compared with some reference solutions where a very good agreement is met. And in third place, an effective surface impedance approach is introduced for determining surface fields on an electrically large coated metallic circular cylinder. Differences in analysis of rigorouslytreated coated metallic cylinders and cylinders with an IBC are discussed. While for the impedance cylinder case a single constant or uniform surface impedance is considered, for the coated metallic cylinder case two surface impedances are derived. These are associated with the TM and TE creeping wave modes excited on a cylinder and depend on observation and source positions and orientations. With this in mind, a UTD based method with IBC is derived for the surface fields by taking into account the surface impedance variation. The asymptotic expansion is performed, via the Watson transformation, over the appropriate series representation of the Green’s functions, thus avoiding higher-order derivatives of Fock-type integrals, and yielding a fast and an accurate solution. Numerical examples reveal a very good accuracy for large cylinders when the separation between the observation and the source point is large. Thus, this solution could be efficiently applied in mutual coupling analysis, along with the method of moments (MoM), of large conformal microstrip array antennas. The proposed UTD methods for scattered and surface EM field analysis on a coated PEC cylinder with an effective IBC are considered the first steps toward the generalization of a UTD solution for large arbitrarily convex smooth metallic surfaces covered by a material coating and illuminated by an arbitrary EM source.

Technology of bare tether current collection

The outstanding problem for useful applications of electrodynamic tethers is obtaining sufficient electron current from the ionospheric plasma. Bare tether collectors, in which the conducting tether itself, left uninsulated over kilometers of its length, acts as the collecting anode, promise to attain currents of 10 A or more from reasonably sized systems. Current collection by a bare tether is also relatively insensitive to drops in electron density, which are regularly encountered on each revolution of an orbit. This makes nighttime operation feasible. We show how the bare tether's high efficiency of current collection and ability to adjust to density variations follow from the orbital motion limited collection law of thin cylinders. We consider both upwardly deployed (power generation mode) and downwardly deployed (reboost mode) tethers, and present results that indicate how bare tether systems would perform as their magnetic and plasma environment varies in low earth orbit.

Performance of bare-tether systems under varying magnetic and plasma conditions

Electrodynamic tethered systems, in which an exposed portion of the conducting tether itself collects electrons from the ionosphere, promise to attain currents of 10 A or more in low Earth orbit. For the first time, another desirable feature of such bare-tether systems is reported and analyzed in detail: Collection by a bare tether is relatively insensitive to variations in electron density that are regularly encountered on each revolution of an orbit. This self-adjusting property of bare-tether systems occurs because the electron-collecting area on the tether is not fixed, but extends along its positively biased portion, and because the current varies as collecting length to a power greater than unity. How this adjustment to density variations follows from the basic collection law of thin cylinders is shown. The effect of variations in the motionally induced tether voltage is also analyzed. Both power and thruster modes are considered. The performance of bare-tether systems to tethered systems is compared using passive spherical collectors of fixed area, taking into consideration recent experimental results. Calculations taking into account motional voltage and plasma density around a realistic orbit for bare-tether systems suitable for space station applications are also presented.

Biosensing comparison between different geometries based on vertical submicron-structrures made of SU-8 resist

Previous work of the research group [1-4] demonstrated the viability of using periodic lattices of micro and nanopillars, called Bio-photonic sensing Cells (BICELLs), as an optical biosensor vertically characterized by visible spectrometry. Also we have studied theoretically [5] the performance of the BICELLs by 2D and 3D simulation in orde r to optimize the biosensing response. In this work we present the fabrication and biosensing comparison of different geometrical parameters on periodic lattices of pillars in order to discuss theoretical conclusions with these results. In this way, we have explored the biosensing response of other patter ns such as crosses, stars, cylinders, concentrical cylinders (Figure 1). Also we introduced a novel method to test the BICELLs in a cost-effective way by using an ultra-thin film of SU-8 spin-coated onto the patterns to reproduce the effect of a biofilm attached to the biosensor surface. Finally we have tested the biosensing response of the different geometries by the well-known Bovine Serum Albumin (BSA) immunoassay and compared with the theoretical simulation.

Prototype emitter for use in subsurface drip irrigation: Manufacturing, hydraulic evaluation and experimental analyses

The current research aims to analyse theoretically and evaluate a self-manufactured simple design for subsurface drip irrigation (SDI) emitter to avoid root and soil intrusion. It was composed of three concentric cylindrical elements: an elastic silicone membrane; a polyethylene tube with two holes drilled on its wall for water discharge; and a vinyl polychloride protector system to wrap the other elements. The discharge of the emitter depends on the change in the membrane diameter when it is deformed by the water pressure. The study of the operation of this emitter is a new approach that considers mechanical and hydraulic principles. Thus, the estimation on the membrane deformation was based on classical mechanical stress theories in composite cylinders. The hydraulic principles considered the solid deformation due to force based on water pressure and the general Darcy–Weisbach head-loss equation. Twenty emitter units, with the selected design, were handcrafted in a lathe and were used in this study. The measured pressure/discharge relationship for the emitters showed good agreement with that calculated by the theoretical approach. The variation coefficient of the handcrafted emitters was high compared to commercial emitters. Results from field evaluations showed variable values for the relative flow variation, water emission uniformity and relative flow rate coefficients, but no emitter was obstructed. Therefore, the current emitter design could be suitable for SDI following further studies to develop a final prototype.

Limit load instabilities in structural elements

Este trabajo analiza distintas inestabilidades en estructuras formadas por distintos materiales. En particular, se capturan y se modelan las inestabilidades usando el método de Riks. Inicialmente, se analiza la bifurcación en depósitos cilíndricos formados por material anisótropo sometidos a carga axial y presión interna. El análisis de bifurcación y post-bifurcación asociados con cilindros de pared gruesa se formula para un material incompresible reforzado con dos fibras que son mecánicamente equivalentes y están dispuestas simétricamente. Consideramos dos casos en la naturaleza de la anisotropía: (i) Fibras refuerzo que tienen una influencia particular sobre la respuesta a cortante del material y (ii) Fibras refuerzo que influyen sólo si la fibra cambia de longitud con la deformación. Se analiza la propagación de las inestabilidades. En concreto, se diferencia en el abultamiento (bulging) entre la propagación axial y la propagación radial de la inestabilidad. Distintos modelos sufren una u otra propagación. Por último, distintas inestabilidades asociadas al mecanismo de ablandamiento del material (material softening) en contraposición al de endurecimiento (hardening) en una estructura (viga) de a: hormigón y b: hormigón reforzado son modeladas utilizando una metodología paralela a la desarrollada en el análisis de inestabilidades en tubos sometidos a presión interna. This present work deals with the instability of structures made of various materials. It captures and models different types of instabilities using numerical analysis. Firstly, we consider bifurcation for anisotropic cylindrical shells subject to axial loading and internal pressure. Analysis of bifurcation and post bifurcation of inflated hyperelastic thick-walled cylinder is formulated using a numerical procedure based on the modified Riks method for an incompressible material with two preferred directions which are mechanically equivalent and are symmetrically disposed. Secondly, bulging/necking motion in doubly fiber-reinforced incompressible nonlinearly elastic cylindrical shells is captured and we consider two cases for the nature of the anisotropy: (i) reinforcing models that have a particular influence on the shear response of the material and (ii) reinforcing models that depend only on the stretch in the fiber direction. The different instability motions are considered. Axial propagation of the bulging instability mode in thin-walled cylinders under inflation is analyzed. We present the analytical solution for this particular motion as well as for radial expansion during bulging evolution. For illustration, cylinders that are made of either isotropic incompressible non-linearly elastic materials or doubly fiber reinforced incompressible non-linearly elastic materials are considered. Finally, strain-softening constitutive models are considered to analyze two concrete structures: a reinforced concrete beam and an unreinforced notch beam. The bifurcation point is captured using the Riks method used previously to analyze bifurcation of a pressurized cylinder.

Selected topics in the Hydrodynamics of floating offshore wind turbines: heave damping and second order surge motions

La Energía eléctrica producida mediante tecnología eólica flotante es uno de los recursos más prometedores para reducir la dependencia de energía proveniente de combustibles fósiles. Esta tecnología es de especial interés en países como España, donde la plataforma continental es estrecha y existen pocas áreas para el desarrollo de estructuras fijas. Entre los diferentes conceptos flotantes, esta tesis se ha ocupado de la tipología semisumergible. Estas plataformas pueden experimentar movimientos resonantes en largada y arfada. En largada, dado que el periodo de resonancia es largo estos puede ser inducidos por efectos de segundo orden de deriva lenta que pueden tener una influencia muy significativa en las cargas en los fondeos. En arfada las fuerzas de primer orden pueden inducir grandes movimientos y por tanto la correcta determinación del amortiguamiento es esencial para la analizar la operatividad de la plataforma. Esta tesis ha investigado estos dos efectos, para ello se ha usado como caso base el diseño de una plataforma desarrollada en el proyecto Europeo Hiprwind. La plataforma se compone de 3 columnas cilíndricas unidas mediante montantes estructurales horizontales y diagonales, Los cilindros proporcionan flotabilidad y momentos adrizante. A la base de cada columna se le ha añadido un gran “Heave Plate” o placa de cierre. El diseño es similar a otros diseños previos (Windfloat). Se ha fabricado un modelo a escala de una de las columnas para el estudio detallado del amortiguamiento mediante oscilaciones forzadas. Las dimensiones del modelo (1m diámetro en la placa de cierre) lo hacen, de los conocidos por el candidato, el mayor para el que se han publicado datos. El diseño del cilindro se ha realizado de tal manera que permite la fijación de placas de cierre planas o con refuerzo, ambos modelos se han fabricado y analizado. El modelo con refuerzos es una reproducción exacta del diseño a escala real incluyendo detalles distintivos del mismo, siendo el más importante la placa vertical perimetral. Los ensayos de oscilaciones forzadas se han realizado para un rango de frecuencias, tanto para el disco plano como el reforzado. Se han medido las fuerzas durante los ensayos y se han calculado los coeficientes de amortiguamiento y de masa añadida. Estos coeficientes son necesarios para el cálculo del fondeo mediante simulaciones en el dominio del tiempo. Los coeficientes calculados se han comparado con la literatura existente, con cálculos potenciales y por ultimo con cálculos CFD. Para disponer de información relevante para el diseño estructural de la plataforma se han medido y analizado experimentalmente las presiones en la parte superior e inferior de cada placa de cierre. Para la correcta estimación numérica de las fuerzas de deriva lenta en la plataforma se ha realizado una campaña experimental que incluye ensayos con modelo cautivo de la plataforma completa en olas bicromaticas. Pese a que estos experimentos no reproducen un escenario de oleaje realista, los mismos permiten una verificación del modelo numérico mediante la comparación de fuerzas medidas en el modelo físico y el numérico. Como resultados de esta tesis podemos enumerar las siguientes conclusiones. 1. El amortiguamiento y la masa añadida muestran una pequeña dependencia con la frecuencia pero una gran dependencia con la amplitud del movimiento. siendo coherente con investigaciones existentes. 2. Las medidas con la placa de cierre reforzada con cierre vertical en el borde, muestra un amortiguamiento significativamente menor comparada con la placa plana. Esto implica que para ensayos de canal es necesario incluir estos detalles en el modelo. 3. La masa añadida no muestra grandes variaciones comparando placa plana y placa con refuerzos. 4. Un coeficiente de amortiguamiento del 6% del crítico se puede considerar conservador para el cálculo en el dominio de la frecuencia. Este amortiguamiento es equivalente a un coeficiente de “drag” de 4 en elementos de Morison cuadráticos en las placas de cierre usadas en simulaciones en el dominio del tiempo. 5. Se han encontrado discrepancias en algunos valores de masa añadida y amortiguamiento de la placa plana al comparar con datos publicados. Se han propuesto algunas explicaciones basadas en las diferencias en la relación de espesores, en la distancia a la superficie libre y también relacionadas con efectos de escala. 6. La presión en la placa con refuerzos son similares a las de la placa plana, excepto en la zona del borde donde la placa con refuerzo vertical induce una gran diferencias de presiones entre la cara superior e inferior. 7. La máxima diferencia de presión escala coherentemente con la fuerza equivalente a la aceleración de la masa añadida distribuida sobre la placa. 8. Las masas añadidas calculadas con el código potencial (WADAM) no son suficientemente precisas, Este software no contempla el modelado de placas de pequeño espesor con dipolos, la poca precisión de los resultados aumenta la importancia de este tipo de elementos al realizar simulaciones con códigos potenciales para este tipo de plataformas que incluyen elementos de poco espesor. 9. Respecto al código CFD (Ansys CFX) la precisión de los cálculos es razonable para la placa plana, esta precisión disminuye para la placa con refuerzo vertical en el borde, como era de esperar dado la mayor complejidad del flujo. 10. Respecto al segundo orden, los resultados, en general, muestran que, aunque la tendencia en las fuerzas de segundo orden se captura bien con los códigos numéricos, se observan algunas reducciones en comparación con los datos experimentales. Las diferencias entre simulaciones y datos experimentales son mayores al usar la aproximación de Newman, que usa únicamente resultados de primer orden para el cálculo de las fuerzas de deriva media. 11. Es importante remarcar que las tendencias observadas en los resultados con modelo fijo cambiarn cuando el modelo este libre, el impacto que los errores en las estimaciones de fuerzas segundo orden tienen en el sistema de fondeo dependen de las condiciones ambientales que imponen las cargas ultimas en dichas líneas. En cualquier caso los resultados que se han obtenido en esta investigación confirman que es necesaria y deseable una detallada investigación de los métodos usados en la estimación de las fuerzas no lineales en las turbinas flotantes para que pueda servir de guía en futuros diseños de estos sistemas. Finalmente, el candidato espera que esta investigación pueda beneficiar a la industria eólica offshore en mejorar el diseño hidrodinámico del concepto semisumergible. ABSTRACT Electrical power obtained from floating offshore wind turbines is one of the promising resources which can reduce the fossil fuel energy consumption and cover worldwide energy demands. The concept is the most competitive in countries, such as Spain, where the continental shelf is narrow and does not provide space for fixed structures. Among the different floating structures concepts, this thesis has dealt with the semisubmersible one. Platforms of this kind may experience resonant motions both in surge and heave directions. In surge, since the platform natural period is long, such resonance can be excited with second order slow drift forces and may have substantial influence on mooring loads. In heave, first order forces can induce significant motion, whose damping is a crucial factor for the platform downtime. These two topics have been investigated in this thesis. To this aim, a design developed during HiPRWind EU project, has been selected as reference case study. The platform is composed of three cylindrical legs, linked together by a set of structural braces. The cylinders provide buoyancy and restoring forces and moments. Large circular heave plates have been attached to their bases. The design is similar to other documented in literature (e.g. Windfloat), which implies outcomes could have a general value. A large scale model of one of the legs has been built in order to study heave damping through forced oscillations. The final dimensions of the specimen (one meter diameter discs) make it, to the candidate’s knowledge, the largest for which data has been published. The model design allows for the fitting of either a plain solid heave plate or a flapped reinforced one; both have been built. The latter is a model scale reproduction of the prototype heave plate and includes some distinctive features, the most important being the inclusion of a vertical flap on its perimeter. The forced oscillation tests have been conducted for a range of frequencies and amplitudes, with both the solid plain model and the vertical flap one. Forces have been measured, from which added mass and damping coefficients have been obtained. These are necessary to accurately compute time-domain simulations of mooring design. The coefficients have been compared with literature, and potential flow and CFD predictions. In order to provide information for the structural design of the platform, pressure measurements on the top and bottom side of the heave discs have been recorded and pressure differences analyzed. In addition, in order to conduct a detailed investigation on the numerical estimations of the slow-drift forces of the HiPRWind platform, an experimental campaign involving captive (fixed) model tests of a model of the whole platform in bichromatic waves has been carried out. Although not reproducing the more realistic scenario, these tests allowed a preliminary verification of the numerical model based directly on the forces measured on the structure. The following outcomes can be enumerated: 1. Damping and added mass coefficients show, on one hand, a small dependence with frequency and, on the other hand, a large dependence with the motion amplitude, which is coherent with previously published research. 2. Measurements with the prototype plate, equipped with the vertical flap, show that damping drops significantly when comparing this to the plain one. This implies that, for tank tests of the whole floater and turbine, the prototype plate, equipped with the flap, should be incorporated to the model. 3. Added mass values do not suffer large alterations when comparing the plain plate and the one equipped with a vertical flap. 4. A conservative damping coefficient equal to 6% of the critical damping can be considered adequate for the prototype heave plate for frequency domain analysis. A corresponding drag coefficient equal to 4.0 can be used in time domain simulations to define Morison elements. 5. When comparing to published data, some discrepancies in added mass and damping coefficients for the solid plain plate have been found. Explanations have been suggested, focusing mainly on differences in thickness ratio and distance to the free surface, and eventual scale effects. 6. Pressures on the plate equipped with the vertical flap are similar in magnitude to those of the plain plate, even though substantial differences are present close to the edge, where the flap induces a larger pressure difference in the reinforced case. 7. The maximum pressure difference scales coherently with the force equivalent to the acceleration of the added mass, distributed over the disc surface. 8. Added mass coefficient values predicted with the potential solver (WADAM) are not accurate enough. The used solver does not contemplate modeling thin plates with doublets. The relatively low accuracy of the results highlights the importance of these elements when performing potential flow simulations of offshore platforms which include thin plates. 9. For the full CFD solver (Ansys CFX), the accuracy of the computations is found reasonable for the plain plate. Such accuracy diminishes for the disc equipped with a vertical flap, an expected result considering the greater complexity of the flow. 10. In regards to second order effects, in general, the results showed that, although the main trend in the behavior of the second-order forces is well captured by the numerical predictions, some under prediction of the experimental values is visible. The gap between experimental and numerical results is more pronounced when Newman’s approximation is considered, making use exclusively of the mean drift forces calculated in the first-order solution. 11. It should be observed that the trends observed in the fixed model test may change when the body is free to float, and the impact that eventual errors in the estimation of the second-order forces may have on the mooring system depends on the characteristics of the sea conditions that will ultimately impose the maximum loads on the mooring lines. Nevertheless, the preliminary results obtained in this research do confirm that a more detailed investigation of the methods adopted for the estimation of the nonlinear wave forces on the FOWT would be welcome and may provide some further guidance for the design of such systems. As a final remark, the candidate hopes this research can benefit the offshore wind industry in improving the hydrodynamic design of the semi-submersible concept.

Deciduous tree reconstruction algorithm based on cylinder fitting from mobile terrestrial laser scanned point clouds

Vector reconstruction of objects from an unstructured point cloud obtained with a LiDAR-based system (light detection and ranging) is one of the most promising methods to build three dimensional models of orchards. The cylinder fitting method for woody structure reconstruction of leafless trees from point clouds obtained with a mobile terrestrial laser scanner (MTLS) has been analysed. The advantage of this method is that it performs reconstruction in a single step. The most time consuming part of the algorithm is generation of the cylinder direction, which must be recalculated at the inclusion of each point in the cylinder. The tree skeleton is obtained at the same time as the cluster of cylinders is formed. The method does not guarantee a unique convergence and the reconstruction parameter values must be carefully chosen. A balanced processing of clusters has also been defined which has proven to be very efficient in terms of processing time by following the hierarchy of branches, predecessors and successors. The algorithm was applied to simulated MTLS of virtual orchard models and to MTLS data of real orchards. The constraints applied in the method have been reviewed to ensure better convergence and simpler use of parameters. The results obtained show a correct reconstruction of the woody structure of the trees and the algorithm runs in linear logarithmic time