Using the Natural Period of a Structure as an Indicator of the Significance of Second-Order Effects

This study investigates the feasibility of predicting the momentamplification in beam-column elements of steel moment-resisting frames using the structure's natural period. Unlike previous methods, which perform moment-amplification on a story-by-story basis, this study develops and tests two models that aim to predict a global amplification factor indicative of the largest relevant instance of local moment amplification in the structure. To thisend, a variety of two-dimensional frames is investigated using first and secondorder finite element analysis. The observed moment amplification is then compared with the predicted amplification based on the structure's natural period, which is calculated by first-order finite element analysis. As a benchmark, design moment amplification factors are calculated for each story using the story stiffness approach, and serve to demonstrate the relativeconservatism and accuracy of the proposed models with respect to current practice in design. The study finds that the observed moment amplification factors may vastly exceed expectations when internal member stresses are initially very small. Where the internal stresses are small relative to the member capacities, thesecases are inconsequential for design. To qualify the significance of the observed amplification factors, two parameters are used: the second-order moment normalized to the plastic moment capacity, and the combined flexural and axial stress interaction equations developed by AISC

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

A second order in time modified Lagrange-Galerkin finite element method for the incompressible Navier-Stokes equations

We introduce a second order in time modified Lagrange--Galerkin (MLG) method for the time dependent incompressible Navier--Stokes equations. The main ingredient of the new method is the scheme proposed to calculate in a more efficient manner the Galerkin projection of the functions transported along the characteristic curves of the transport operator. We present error estimates for velocity and pressure in the framework of mixed finite elements when either the mini-element or the $P2/P1$ Taylor--Hood element are used.

InfIuence of wave induced second-order forces in semisubmersible fowt mooring design

The main focus of this paper is on hydrodynamic modelling of a semisubmersible platform (which can support a 1.5MW wind turbine and is composed by three buoyant columns connected by bracings) with especial emphasis on the estimation of the wave drift components and their effects on the design of the mooring system. Indeed, with natural periods of drift around 60 seconds, accurate computation of the low-frequency second-order components is not a straightforward task. As methods usually adopted when dealing with the slow-drifts of deep-water moored systems, such as Newman?s approximation, have their errors increased by the relatively low resonant periods, and as the effects of depth cannot be ignored, the wave diffraction analysis must be based on full Quadratic Transfer Functions (QTF) computations. A discussion on the numerical aspects of performing such computations is presented, making use of the second-order module available with the seakeeping software WAMIT®. Finally, the paper also provides a preliminary verification of the accuracy of the numerical predictions based on the results obtained in a series of model tests with the structure fixed in bichromatic waves.

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.

How should the sustainability of the location of dry ports be measured? A proposed methodology using Bayesian networks and multi-criteria decision analysis

The global economic structure, with its decentralized production and the consequent increase in freight traffic all over the world, creates considerable problems and challenges for the freight transport sector. This situation has led shipping to become the most suitable and cheapest way to transport goods. Thus, ports are configured as nodes with critical importance in the logistics supply chain as a link between two transport systems, sea and land. Increase in activity at seaports is producing three undesirable effects: increasing road congestion, lack of open space in port installations and a significant environmental impact on seaports. These adverse effects can be mitigated by moving part of the activity inland. Implementation of dry ports is a possible solution and would also provide an opportunity to strengthen intermodal solutions as part of an integrated and more sustainable transport chain, acting as a link between road and railway networks. In this sense, implementation of dry ports allows the separation of the links of the transport chain, thus facilitating the shortest possible routes for the lowest capacity and most polluting means of transport. Thus, the decision of where to locate a dry port demands a thorough analysis of the whole logistics supply chain, with the objective of transferring the largest volume of goods possible from road to more energy efficient means of transport, like rail or short-sea shipping, that are less harmful to the environment. However, the decision of where to locate a dry port must also ensure the sustainability of the site. Thus, the main goal of this article is to research the variables influencing the sustainability of dry port location and how this sustainability can be evaluated. With this objective, in this paper we present a methodology for assessing the sustainability of locations by the use of Multi-Criteria Decision Analysis (MCDA) and Bayesian Networks (BNs). MCDA is used as a way to establish a scoring, whilst BNs were chosen to eliminate arbitrariness in setting the weightings using a technique that allows us to prioritize each variable according to the relationships established in the set of variables. In order to determine the relationships between all the variables involved in the decision, giving us the importance of each factor and variable, we built a K2 BN algorithm. To obtain the scores of each variable, we used a complete cartography analysed by ArcGIS. Recognising that setting the most appropriate location to place a dry port is a geographical multidisciplinary problem, with significant economic, social and environmental implications, we consider 41 variables (grouped into 17 factors) which respond to this need. As a case of study, the sustainability of all of the 10 existing dry ports in Spain has been evaluated. In this set of logistics platforms, we found that the most important variables for achieving sustainability are those related to environmental protection, so the sustainability of the locations requires a great respect for the natural environment and the urban environment in which they are framed.

Multicriteria decision analysis applied to cover crop species andcultivars selection

Cover crop selection should be oriented to the achievement of specific agrosystem benefits. The covercrop, catch crop, green manure and fodder uses were identified as possible targets for selection. Theobjective was to apply multi-criteria decision analysis to evaluate different species (Hordeum vulgareL., Secale cereale L., ×Triticosecale Whim, Sinapis alba L., Vicia sativa L.) and cultivars according to theirsuitability to be used as cover crops in each of the uses. A field trial with 20 cultivars of the five specieswas conducted in Central Spain during two seasons (October?April). Measurements of ground cover, cropbiomass, N uptake, N derived from the atmosphere, C/N, dietary fiber content and residue quality werecollected. Aggregation of these variables through utility functions allowed ranking species and cultivarsfor each usage. Grasses were the most suitable for the cover crop, catch crop and fodder uses, while thevetches were the best as green manures. The mustard attained high ranks as cover and catch crop the firstseason, but the second decayed due to low performance in cold winters. Mustard and vetches obtainedworse rankings than grasses as fodder. Hispanic was the most suitable barley cultivar as cover and catchcrop, and Albacete as fodder. The triticale Titania attained the highest rank as cover and catch crop andfodder. Vetches Aitana and BGE014897 showed good aptitudes as green manures and catch crops. Thisanalysis allowed comparison among species and cultivars and might provide relevant information forcover crops selection and management.

Second-order elliptic PDE with discontinuous boundary data

We shall consider the weak formulation of a linear elliptic model problem with discontinuous Dirichlet boundary conditions. Since such problems are typically not well-defined in the standard H^1-H^1 setting, we will introduce a suitable saddle point formulation in terms of weighted Sobolev spaces. Furthermore, we will discuss the numerical solution of such problems. Specifically, we employ an hp-discontinuous Galerkin method and derive an L^2-norm a posteriori error estimate. Numerical experiments demonstrate the effectiveness of the proposed error indicator in both the h- and hp-version setting. Indeed, in the latter case exponential convergence of the error is attained as the mesh is adaptively refined.

Foundational, First-Order, and Second-Order Classification Theory

Both basic and applied research on the construction, implementation, maintenance, and evaluation of classification schemes is called classification theory. If we employ Ritzer’s metatheoretical method of analysis on the over one-hundred year-old body of literature, we can see categories of theory emerge. This paper looks at one particular part of knowledge organization work, namely classification theory, and asks 1) what are the contours of this intellectual space, and, 2) what have we produced in the theoretical reflection on con- structing, implementing, and evaluating classification schemes? The preliminary findings from this work are that classification theory can be separated into three kinds: foundational classification theory, first-order classification theory, and second-order classification theory, each with its own concerns and objects of study.

Developing a research method to test a new first-order decision making model for the procurement of public sector major infrastructure

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and simultaneously delivering Value for Money (VfM). The paper begins with an update on a key development in a new early/first-order procurement decision making model that deploys production cost/benefit theory and theories concerning transaction costs from the New Institutional Economics, in order to identify a procurement mode that is likely to deliver the best ratio of production costs and transaction costs to production benefits, and therefore deliver superior VfM relative to alternative procurement modes. In doing so, the new procurement model is also able to address the uncertainty concerning the relative merits of Public-Private Partnerships (PPP) and non-PPP procurement approaches. The main aim of the paper is to develop competition as a dependent variable/proxy for VfM and a hypothesis (overarching proposition), as well as developing a research method to test the new procurement model. Competition reflects both production costs and benefits (absolute level of competition) and transaction costs (level of realised competition) and is a key proxy for VfM. Using competition as a proxy for VfM, the overarching proposition is given as: When the actual procurement mode matches the predicted (theoretical) procurement mode (informed by the new procurement model), then actual competition is expected to match potential competition (based on actual capacity). To collect data to test this proposition, the research method that is developed in this paper combines a survey and case study approach. More specifically, data collection instruments for the surveys to collect data on actual procurement, actual competition and potential competition are outlined. Finally, plans for analysing this survey data are briefly mentioned, along with noting the planned use of analytical pattern matching in deploying the new procurement model and in order to develop the predicted (theoretical) procurement mode.