Two-dimensional mesh optimization in the finite element method

The solution to the problem of finding the optimum mesh design in the finite element method with the restriction of a given number of degrees of freedom, is an interesting problem, particularly in the applications method. At present, the usual procedures introduce new degrees of freedom (remeshing) in a given mesh in order to obtain a more adequate one, from the point of view of the calculation results (errors uniformity). However, from the solution of the optimum mesh problem with a specific number of degrees of freedom some useful recommendations and criteria for the mesh construction may be drawn. For 1-D problems, namely for the simple truss and beam elements, analytical solutions have been found and they are given in this paper. For the more complex 2-D problems (plane stress and plane strain) numerical methods to obtain the optimum mesh, based on optimization procedures have to be used. The objective function, used in the minimization process, has been the total potential energy. Some examples are presented. Finally some conclusions and hints about the possible new developments of these techniques are also given

Mallas isostáticas bidimensionales en elementos finitos

Se plantea el problema de conseguir un método que, partiendo de una malla inicial en elementos finitos, genere una malla próxima a la óptima, conservando el mismo número de grados de libertad y, por consiguiente, sin penalizar los tiempos de análisis por ordenador. La bondad de una malla se mide por un funcional determinado (Energía Potencial Total, Error Cuadrático Medio, etc.) La Técnica de gradiente descendente, aplicada al funcional de Energía Potencial Total (1) permite, a partir de una inicial dada, obtener una malla mejorada. No obstante, este método requiere un esfuerzo de computación muy grande. Como consecuencia de la aplicación del método del gradiente descendente a numerosos casos, se ha observado que la geometría que adopta la malla mejorada, se aproxima a la de una malla tal que sus nudos se sitúen sobre las líneas isostáticas (envolventes de las tensiones principales) y generen elementos regulares (de lados iguales) o cuasirregulares. La conclusión más importante es, precisamente, que a partir de una malla inicial, razonablemente regular, se puede realizar un único análisis y definir las isostáticas correspondientes a este modelo. Ajustando una malla, con el mismo número de nudos que la inicial, a las líneas isostáticas con nudos situados de forma regular, se obtiene otra que está próxima a la óptima. A la malla así obtenida, se la denomina isostática isométrica. Esta conclusión se ha probado que es válida para los diferentes funcionales que se utilizan para evaluar la bondad de la malla en elementos finitos

Optimización de mallas bidimensionales en elementos finitos

La solución al problema de encontrar la malla óptima en Elementos Finitos (EF), con un determinado número de grados de libertad, presenta un indudable interés en la aplicación del método. En la actualidad, el problema se plantea en términos de un proceso que permite obtener una mejor malla de elementos finitos a partir de una inicial. La nueva malla se diseña matemáticamente (remallado) de forma que el error del método sea lo más uniforme posible en todo el dominio de cálculo. Sin embargo, esta técnica de indudable interés y aplicación, al aumentar el número de grados de libertad (gdl) de la aproximación, no permite deducir de un modo directo el problema de la malla óptima condicionada a un número fijo de gdl. Con la solución de este problema se podrán deducir algunos criterios y recomendaciones para el diseño de una malla de elementos finitos, que exigirá, en general, en un proceso de remallado, modificaciones menores. Para problemas unidimensionales (barras y pilares simples), se pueden encontrar soluciones analíticas. Para problemas 2-D más complicados (tensión y deformación plana), se han utilizado métodos numéricos para obtener la malla óptima. Existen varios criterios de optimización, aquí se utiliza el del mínimo de la energía potencial total (EPT). Algunos ejemplos ilustrativos del método de optimización se presentan, indicándose algunas conclusiones

Integrated methodology for assessing the effects of geomorphological river restoration on fish habitat and riparian vegetation

Changes in the geomorphology of rivers have serious repercussions, causing losses in the dynamics and naturalness of their forms, going in many cases, from a type of meandering channel, with constant erosion and sedimentation processes, to a channelized narrow river with rigid and stable margins, where the only possibility of movement occurs in the vertical, causing the only changes in channel geometry occur in the river bed. On the other hand, these changes seriously affect the naturalness of the banks, preventing the development of riparian vegetation and reducing the cross connectivity of the riparian corridor. Common canalizations and disconnections of meanders increase the slope, and therefore speed, resulting in processes of regressive erosion, effect increased as a result of the narrowing of the channel and the concentration of flows. This process of incision may turn the flood plain to be "hung", being completely disconnected from the water table, with important consequences for vegetation. As an example of the effects of these changes, it has been chosen the case of the Arga River The Arga river has been channelized and rectified, as it passes along the meander RamalHondo and Soto Gil (Funes, Navarra). The effects on fish habitat and riparian vegetation by remeandering the Arga River are presented. and Ttwo very contrasting situationsrestoration hypothesis, in terms of geomorphology concerns, have been established to assess the effects these changes have on the habitat of one of the major fish species in the area (Luciobabus graellsii) and on the riparian vegetation. To accomplish this goal, it has been necessary to used the a digital elevation model provided by LIDAR flight, bathymetric data, flow data, as inputs, and a hydraulic simulation model 2D (Infoworks RS). The results obtained not only helped to evaluate the effects of the past alterations of geomorphologic characteristics, but also to predict fish and vegetation habitat responses to this type of changes

A quasi-elastic aquifer deformational behavior: Madrid aquifer case study

The purpose of this paper is to analyze the quasi-elastic deformational behavior that has been induced by groundwater withdrawal of the Tertiary detrital aquifer of Madrid (Spain). The spatial and temporal evolution of ground surface displacement was estimated by processing two datasets of radar satellite images (SAR) using Persistent Scatterer Interferometry (PSI). The first SAR dataset was acquired between April 1992 and November 2000 by ERS-1 and ERS-2 satellites, and the second one by the ENVISAT satellite between August 2002 and September 2010. The spatial distribution of PSI measurements reveals that the magnitude of the displacement increases gradually towards the center of the well field area, where approximately 80 mm of maximum cumulated displacement is registered. The correlation analysis made between displacement and piezometric time series provides a correlation coefficient greater than 85% for all the wells. The elastic and inelastic components of measured displacements were separated, observing that the elastic component is, on average, more than 4 times the inelastic component for the studied period. Moreover, the hysteresis loops on the stress–strain plots indicate that the response is in the elastic range. These results demonstrate the quasi-elastic behavior of the aquifer. During the aquifer recovery phase ground surface uplift almost recovers from the subsidence experienced during the preceding extraction phase. Taking into account this unique aquifer system, a one dimensional elastic model was calibrated in the period 1997–2000. Subsequently, the model was used to predict the ground surface movements during the period 1992–2010. Modeled displacements were validated with PSI displacement measurements, exhibiting an error of 13% on average, related with the inelastic component of deformation occurring as a long-term trend in low permeability fine-grained units. This result further demonstrates the quasi-elastic deformational behavior of this unique aquifer system.This work was developed during Pablo Ezquerro research stay within the Geohazards InSAR laboratory and Modeling group of the Instituto Geológico y Minero de España in the framework of DORIS project (Ground Deformation Risk Scenarios: an Advanced Assessment Service) funded by the EC-GMES-FP7 initiative (Grant Agreement nº 242212). This work has been also supported by the Spanish Ministry of Science and Research (MICINN) under project TEC2011-28201-C02-02 and EU FEDER. Additional funding was obtained from Spanish Research Program through the project ESP2013-47780-C2-2-R

Multivariate optimization of the KharascheSosnovsky allylic oxidation of olefins

The multivariate optimization method known as simplex is applied to the KharascheSosnovsky allylic oxidation of double bonds. By applying this method, the amounts of three variables (copper source, oxidant, and additive) are optimized at the same time. Under the conditions thus obtained the reaction takes place in a considerable shorter time, being the alkene the limiting reagent. These conditions are applied to some monoterpenes and sesquiterpenes leading regioselectively to the corresponding benzoate esters, opening a route to the employment of this reaction in the synthesis of more complex molecules

Effects of Extending Milk Replacer Feeding during the Fattening Period on the Behaviour and Welfare of Lambs: A Preliminary Study

There is a lack of information on the behavioural and welfare effects of sustaining artificial milk feeding in fattening lambs. Therefore, the present work aimed to study the effects of prolonged artificial milk feeding during fattening with a high concentrate diet on the behaviour of lambs. The behaviour of 16 non castrated male lambs of the Manchega sheep breed (eight lambs were in the group that were fed daily a bottle of milk, and the other eight were in the weaned group) was recorded with four fixed cameras just before bottle feeding (~8:30 a.m.) of the unweaned group till four hours later, every day for 7 weeks. The solid diet (pelleted concentrate plus cereal straw) and housing conditions were the same in both groups. Solid feeds were offered ad libitum. There were no differences between groups in time spent eating nor in drinking, playing, scratching and oral activity behaviours (p > 0.05), but resting episodes were longer in weaned lambs (p < 0.05). Weaned lambs presented a higher frequency of self-grooming behaviour (p < 0.05), while the unweaned group performed a higher frequency of interaction behaviour (p < 0.05). In conclusion, the behaviours of lambs that were fed daily a bottle of milk during the fattening period did not substantially differ from the weaned individuals

Aplicación de la fotogrametría con drones al control deformacional de estructuras y terreno

This work studies the viability of the use of drones for deformational control of terrain and structures, analyzing for each case the resolution, precision and validation with other techniques. The Structure From Motion photogrammetric technique is presented in detail, allowing the production of accurate orthophotographs and 3D models without knowing previously positions and angles of incidence. The use of precise control points (Ground Control Points) as well as drones with integrated Real Time Kinetic “RTK” system, are relevant factors for obtaining high precision results. The case study of the monitoring of a large structure is presented, in this case an arch-gravity dam. The initial results show a precision in deformations of ± 2 mm. This paper confirms that drone photogrammetry is applicable to the deformational control of concrete dams, opening the possibilities to the monitoring of other large structures and infrastructures.En este trabajo se estudia la viabilidad del empleo de drones para el control de deformaciones del terreno y las estructuras, analizando para cada caso, la resolución, precisión y validación con otras técnicas. Se presenta con detalle la técnica fotogramétrica Structure From Motion, empleada para elaborar ortofotografías y modelos 3D precisos sin necesidad de conocer previamente las posiciones y ángulos de incidencia. El uso de puntos de control precisos, así como drones con sistema integrado RTK, son factores relevantes para la obtención de resultados con alta precisión. Se presenta el caso de estudio de la monitorización de una gran estructura, en este caso una presa arco-gravedad. Los resultados obtenidos presentan una precisión en deformaciones de ±2 mm para la estructura. Esto confirma que la fotogrametría dron es aplicable al control deformacional de presas de hormigón, abriendo las posibilidades a la monitorización de otras grandes estructuras e infraestructuras

SfM Photogrammetric Techniques Applied in the Building Archaeology Works of the Old Cloister of the Monastery of San Francisco from the 16th Century (Cazalla de la Sierra, Seville)

The cloister from the old monastery of San Francisco (Cazalla de la Sierra, Seville) has 12 been suffering a series of remodelling and transformations from its original construction, in the 16th 13 century, to the current day. Thus, a study of building archaeology needed to be accomplished by 14 using photogrammetric techniques by SfM (Structure from Motion) and laser scanning or TLS (Ter- 15 restrial Laser Scanning) that ensure a geometric exactitude and high resolution of the facings sur- 16 veying. For that, over 500 images were taken for the 4 existing facings (about 78 lineal metres) from 17 which a photogrammetric model was obtained of over 50 million polygons; as well as a cloud of 18 over 40 million points from the laser scanning. It can be concluded that by using the techniques of 19 SfM, the task of documenting, analysing and studying the facings of the historical buildings in order 20 to establish its evolutional process, gains, not only in precision and exactitude, but also opens the 21 possibility to go further by obtaining products that are capable in the labour of conservation, resto- 22 ration and protection of the historical heritage, as well as the generation of 3D virtualizations, 23 planned for the diffusion

Handling Low-Density LiDAR Data: Calculating the Heights of Civil Constructions and the Accuracy Expected

During the last years, in many developed countries, administrations and private companies have devoted considerable amounts of money to obtain mapping data using airborne LiDAR. For many civil activities, we can take advantage of it, since those data are available with no cost. Some important questions arise: Are those data good enough to be used for determining the heights of the civil constructions with the accuracy we need in some civil work? What accuracy can we expect when using low-density LiDAR data (0.5 pts/m2)? In order to answer those questions, we have developed a specific methodology based on establishing a set of control points on the top of several constructions and calculating the elevation of each one using postprocessing GPS. Those results have been taken as correct values and the comparison between those values and the elevations obtained, assigning values to the control points by the interpolation of the LiDAR dataset, has been carried out. This paper shows the results obtained using low-density airborne LiDAR data and the accuracy obtained. Results have shown that LiDAR can be accurate enough (10–25 cm) to determine the height of civil constructions and apply those data in many civil engineering activities