Combining a Similar Coefficient Identification Algorithm with the Boundary Element Method

The boundary element method (BEM) has been applied successfully to many engineering problems during the last decades. Compared with domain type methods like the finite element method (FEM) or the finite difference method (FDM) the BEM can handle problems where the medium extends to infinity much easier than domain type methods as there is no need to develop special boundary conditions (quiet or absorbing boundaries) or infinite elements at the boundaries introduced to limit the domain studied. The determination of the dynamic stiffness of arbitrarily shaped footings is just one of these fields where the BEM has been the method of choice, especially in the 1980s. With the continuous development of computer technology and the available hardware equipment the size of the problems under study grew and, as the flop count for solving the resulting linear system of equations grows with the third power of the number of equations, there was a need for the development of iterative methods with better performance. In [1] the GMRES algorithm was presented which is now widely used for implementations of the collocation BEM. While the FEM results in sparsely populated coefficient matrices, the BEM leads, in general, to fully or densely populated ones, depending on the number of subregions, posing a serious memory problem even for todays computers. If the geometry of the problem permits the surface of the domain to be meshed with equally shaped elements a lot of the resulting coefficients will be calculated and stored repeatedly. The present paper shows how these unnecessary operations can be avoided reducing the calculation time as well as the storage requirement. To this end a similar coefficient identification algorithm (SCIA), has been developed and implemented in a program written in Fortran 90. The vertical dynamic stiffness of a single pile in layered soil has been chosen to test the performance of the implementation. The results obtained with the 3-d model may be compared with those obtained with an axisymmetric formulation which are considered to be the reference values as the mesh quality is much better. The entire 3D model comprises more than 35000 dofs being a soil region with 21168 dofs the biggest single region. Note that the memory necessary to store all coefficients of this single region is about 6.8 GB, an amount which is usually not available with personal computers. In the problem under study the interface zone between the two adjacent soil regions as well as the surface of the top layer may be meshed with equally sized elements. In this case the application of the SCIA leads to an important reduction in memory requirements. The maximum memory used during the calculation has been reduced to 1.2 GB. The application of the SCIA thus permits problems to be solved on personal computers which otherwise would require much more powerful hardware.

Stresses and stability of a mine paste fill

Se describe el comportamiento de los rellenos de pasta de las cámaras primarias de la mina de Aguas Teñidas y se calcula la resistencia que deben tener dichos rellenos para que no se desmoronen las paredes de los mismos que quedan expuestas al extraer las cámaras secundarias.Abstract:This article presents the study carried out at an underground mine to understand the stress distribution in the paste fills and to calculate the stability of the paste walls. The mine is operated using sublevel stopes. Three-dimensional numerical models designed with the FLAC 3D software are used to study the distribution of the vertical stresses in the paste. The numerical models have demonstrated that an arc-like effect is produced in the paste fills of the primary stopes. This effect relieves the vertical stresses and increases the stability of the exposed paste wall fill. Based on the results of the numerical models, in the 30m high secondary stopes, the arc effect starts to be evident only in paste walls with a width/height ratio lower than 0.8. 3-D calculations show that the use of Mitchell, R. J. et al. (1982) formula may be risky when estimating the fill stability in secondary stopes.

Indicators and Estimators in P-Adaptive Boundary Elements

The paper presents the possibility of implementing a p-adaptive process with the B.E.M. Although the exemples show that good results can be obtained with a limited amount of storage and with the simple ideas explained above, more research is needed in order to improve the two main problems of the method, i.e.: the criteria of where to refine and until what degree. Mathematically based reasoning is still lacking and will be useful to simplify the decission making. Nevertheless the method seems promising and, we hope, opens a path for a series of research lines of maximum interest. Although the paper has dealt only with plane potential problem the extension to plane elasticity as well as to 3-D potential problem is straight-forward.

Sudden transition to chaos in plasma wave interactions

The coherent three-wave interaction, with linear growth in the higher frequency wave and damping in the two other waves, is reconsidered; for equal dampings, the resulting three-dimensional (3-D) flow of a relative phase and just two amplitudes behaved chaotically, no matter how small the growth of the unstable wave. The general case of different dampings is studied here to test whether, and how, that hard scenario for chaos is preserved in passing from 3-D to four-dimensional flows. It is found that the wave with higher damping is partially slaved to the other damped wave; this retains a feature of the original problem an invariant surface that meets an unstable fixed point, at zero growth rate! that gave rise to the chaotic attractor and determined its structure, and suggests that the sudden transition to chaos should appear in more complex wave interactions.

A Three-Dimensional B.I.E.M. Program

The program PECET (Boundary Element Program in Three-Dimensional Elasticity) is presented in this paper. This program, written in FORTRAN V and implemen ted on a UNIVAC 1100,has more than 10,000 sentences and 96 routines and has a lot of capabilities which will be explained in more detail. The object of the program is the analysis of 3-D piecewise heterogeneous elastic domains, using a subregionalization process and 3-D parabolic isopara, metric boundary elements. The program uses special data base management which will be described below, and the modularity followed to write it gives a great flexibility to the package. The Method of Analysis includes an adaptive integration process, an original treatment of boundary conditions, a complete treatment of body forces, the utilization of a Modified Conjugate Gradient Method of solution and an original process of storage which makes it possible to save a lot of memory.

B.I.E.M. in solid mechanics

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

Método interactivo para la extrapolación de ondas sísmicas. Aplicación a la prospección geofísica (Parte 1)

En los análisis sísmicos por reflexión existe una creciente demanda de estimaciones geológicas y geométricas más precisas y sofisticadas. En último término se pretende extraer estimaciones fiables de las secciones de reflexión, estimaciones que afectan a parámetros tales como la velocidad de propagación, densidad y, por supuesto, contenido de hidrocarburos. Ello exige gran precisión en las técnicas de procesado y representación gráfica, pudiendo decirse que los métodos gráficos interactivos son clave en las tendencias futuras de prospección. Un área de investigación actual es el procesado y representación de datos representados por "horizontes". Un horizonte sísmico se define como la superficie que separa dos capas diferentes de roca. Estas interfases están asociadas a reflexiones que se pueden identificar claramente en las secciones sísmicas. Usando una pantalla gráfica adecuada estos horizontes aparecen coloreados en la sección,pudiendo tornarse puntos selectos para definirlas. Si se utilizan secciones concentradas ("stacked") es preciso determinar la posición correcta de las interfases. Es el proceso llamado "emigración". Tradicionalmente se han aplicado fórmulas de representación o transformaciones integrales para realizar este proceso. Sin embargo es suficiente hacer emigrar las curvas seleccionadas (superficies en el caso 3-D) que representan menos del 1% del total de los datos, con lo que el tiempo de CPU se reduce considerablemente. Si se desprecia la información sobre amplitudes, fases y frecuencias la teoría de rayos es el método más rápido y simple para la conversión en profundidad, poniéndose todo el énfasis en el proceso interactivo y en la representación gráfica. Puesto que en estructuras complejas, como las del Mar del Norte o las del Norte de Alemania, las funciones de velocidad nunca se conocen con precisión, es preciso repetir la emigración mediante diferentes velocidades especificadas por el usuario en forma interactiva. En este artículo se presenta la aplicación del procedimiento para horizontes de separación nula (zero-offset sections) y al final se indica la posibilidad de extensión del estudio a casos con separación constante y al análisis de velocidad.

Offshore remote sensing of the ocean by stereo vision systems

In recent years, remote sensing imaging systems for the measurement of oceanic sea states have attracted renovated attention. Imaging technology is economical, non-invasive and enables a better understanding of the space-time dynamics of ocean waves over an area rather than at selected point locations of previous monitoring methods (buoys, wave gauges, etc.). We present recent progress in space-time measurement of ocean waves using stereo vision systems on offshore platforms, which focus on sea states with wavelengths in the range of 0.01 m to 1 m. Both traditional disparity-based systems and modern elevation-based ones are presented in a variational optimization framework: the main idea is to pose the stereoscopic reconstruction problem of the surface of the ocean in a variational setting and design an energy functional whose minimizer is the desired temporal sequence of wave heights. The functional combines photometric observations as well as spatial and temporal smoothness priors. Disparity methods estimate the disparity between images as an intermediate step toward retrieving the depth of the waves with respect to the cameras, whereas elevation methods estimate the ocean surface displacements directly in 3-D space. Both techniques are used to measure ocean waves from real data collected at offshore platforms in the Black Sea (Crimean Peninsula, Ukraine) and the Northern Adriatic Sea (Venice coast, Italy). Then, the statistical and spectral properties of the resulting observed waves are analyzed. We show the advantages and disadvantages of the presented stereo vision systems and discuss future lines of research to improve their performance in critical issues such as the robustness of the camera calibration in spite of undesired variations of the camera parameters or the processing time that it takes to retrieve ocean wave measurements from the stereo videos, which are very large datasets that need to be processed efficiently to be of practical usage. Multiresolution and short-time approaches would improve efficiency and scalability of the techniques so that wave displacements are obtained in feasible times.

Parametric Generation of Planing Hulls with NURBS Surfaces

This article presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This article is focused on unstepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine, and sheer lines as well as their geometric features including position, slope, and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic, and stability implications from the design point of view. The proposed method uses two-dimensional orthogonal projections of the control curves and then produces three-dimensional (3-D) definitions using B-spline fitting of the 3-D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3-D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.

Space-time ocean wave measurement using variational stereo vision systems

Remote sensing imaging systems for the measurement of oceanic sea states have recently attracted renovated attention. Imaging technology is economical, non-invasive and enables a better understanding of the space-time dynamics of ocean waves over an area rather than at selected point locations of previous monitoring methods (buoys, wave gauges, etc.). We present recent progress in space-time measurement of ocean waves using stereo vision systems on offshore platforms. Both traditional disparity-based systems and modern elevation-based ones are presented in a variational optimization framework: the main idea is to pose the stereoscopic reconstruction problem of the surface of the ocean in a variational setting and design an energy functional whose minimizer is the desired temporal sequence of wave heights. The functional combines photometric observations as well as spatial and temporal smoothness priors. Disparity methods estimate the disparity between images as an intermediate step toward retrieving the depth of the waves with respect to the cameras, whereas elevation methods estimate the ocean surface displacements directly in 3-D space. Both techniques are used to measure ocean waves from real data collected at offshore platforms in the Black Sea (Crimean Peninsula, Ukraine) and the Northern Adriatic Sea (Venice coast, Italy). Then, the statistical and spectral properties of the resulting observed waves are analyzed. We show the advantages and disadvantages of the presented stereo vision systems and discuss the improvement of their performance in critical issues such as the robustness of the camera calibration in spite of undesired variations of the camera parameters.

Un estudio sobre la exactitud del método de los elementos finitos : aplicación a la barra recta de sección variable bajo esfuerzos axiles

El objetivo de este trabajo se centra en la formulación clásica del método de los elementos finitos y dentro de ella, únicamente en un aspecto todavía no bien estudiado: su exactitud. En opinión del autor, la complejidad de este estudio, en el estado actual de conocimientos, motiva que aquel no sea susceptible de un planteamiento general. Por esta razón, ha parecido conveniente la consideración de un caso estructural muy simple -la columna de sección variable-, correspondiente a un problema en elementos finitos - de clase C0, que, sin embargo, permite, por un lado, su extensión a situaciones estructurales análogas (problemas de torsión, membranas de revolución, bandas finitas, etc.), sin apenas modificación conceptual, y, por otra parte, aportar indicaciones sobre las posibilidades de llevar a cabo un análisis paralelo en elementos y estructuras más complejos, bien en mayor dimensión (estructuras 2-D y 3-D), bien en requerimientos de continuidad más elevada (estructuras de flexión, tipo c1 , etc.).

Problemas de homogeneización en la ingeniería. Una experimentación numérica

Se expone brevemente el problema matemático de homogeneización, en sus facetas: homogeneización en el dominio y en el contorno. Con respecto a esta última, se introducen los conceptos de talla crítica y problema límite. Los resultados obtenidos se aplican a un caso particular representado por un cilindro con condiciones de borde periódicas. Se comprueba la validez del desarrollo teórico mediante una experimentación numérica utilizando elementos finitos 3-D observándose la velocidad de convergencia que se obtiene en relación con el caso límite. Finalmente se comenta la posibilidad de utilizar la técnica de homogeneización para obtener unos criterios hacia un diseño eficiente y óptimo de los resultados de las barras corrugadas en el hormigón armado.

El pensamiento creativo de Fernando Higueras

Para acercarnos al pensamiento creativo de Fernando Higueras como arquitecto, partimos del estudio de sus constantes creativas en evolución cronológica divididas en 9 direcciones de investigación. En ellas observamos la importancia de su obra NO CONSTRUIDA, como germen de las constantes creativas de su pensamiento y parte de ella la estudiamos, analizamos y reconstruimos gráficamente en 3D. Fernando Higueras aprendía de sus obras o propuestas arquitectónicas anteriores llegando a la madurez constructiva y formal colmada de Belleza a través de la composición y combinación de dichas constantes con pasmosa naturalidad. Además es importante añadir, para llegar a la comprensión de las constantes del pensamiento creativo del arquitecto, el componente de “intuición” de todo artista, de su modo de mirar y observar las cosas como fuente de inspiración. El “modo de mirar” del arquitecto nos habla de su sensibilidad al hábitat popular y vernáculo del hombre. Gracias a Antonio Miró en el período 1963-1970, Fernando Higueras pudo dar marco real a gran parte de sus ideas constructivas. El objeto de estudio del presente trabajo es llegar a las “invariantes” del arquitecto para comprender su pensamiento creativo. Los objetivos del presente estudio han sido conocer mejor su pensamiento, su obra desde un punto de vista cronológico-evolutivo para poder llegar a entender las relaciones y conexiones creativas entre unas y otras, observar y constatar la evolución de sus constantes creativas y compositivas, de analizar gráficamente parte de su obra no construida para llegar a la mejor comprensión de dichas constantes reconstruyéndolas con los medios gráficos digitales actuales. La reconstrucción en 3D de parte de su obra no construida constata la magnitud de su pensamiento creativo. La metodología empleada parte de la recopilación de toda la información necesaria, escritos, artículos en revistas o periódicos, críticas, observaciones, planos, proyectos, memorias, fotografías de la época, maquetas, opiniones de sus contemporáneos, familiares o amigos y visita de parte de su obra construida. A partir de ahí se fijan 9 direcciones de investigación para cada constante de su pensamiento creativo. En cada dirección se analiza desde dos puntos de vista diferentes. Un primer punto de vista teórico o cronológico-evolutivo a partir de la selección de algunas de sus obras construidas y no construidas. Y otro segundo punto de vista gráfico basándose en el estudio y reconstrucción de parte de su obra no construida. En resultado, se ha estudiado la evolución de su obra viendo las conexiones y relaciones entre unas y otras llegando a la madurez de sus constantes creativas en sus obras, algunas construidas y otras no construidas. Fernando Higueras se perfecciona así mismo, intentando hacer las cosas cada vez un poco mejor, llegando a dominar sus propias constantes en total madurez y expresión formal y constructiva. La elaboración de modelos tridimensionales en 13 proyectos de su obra no construida nos refresca la capacidad de su pensamiento creativo, además de analizar en parte de ellas los gérmenes constructivos y compositivos de muchas de sus ideas o constantes creativas. Finalmente, este trabajo ha contribuido a llegar a entender a Fernando Higueras en una dimensión más amplia, desde el frescor de su obra no construida hasta la capacidad de su pensamiento creativo, de la evolución de sus constantes, del estudio de sus últimos proyectos no construidos, de su sensibilidad a todas las artes y a todo lo que engloba Belleza. Las 360 láminas de dibujos que se aportan inician el estudio y análisis de su vasta obra no construida. ABSTRACT The analysis of Fernando Higueras's creative thought as an architect begins with a study of his main creative themes and their chronological evolution, divided into nine directions of research. Here we see the importance of his UNBUILT work as the germ of the creative themes of his thought, part of which we study, analyse and reconstruct graphically in 3-D. Fernando Higueras drew on his earlier architectural works and ideas and reached an ultimate constructive and formal maturity that was infused with beauty through composition and the amazingly natural combination of these keynote themes. In order to gain a greater understanding of the key themes of the architect's creative thought it is also worth noting the element of artists' intuition, their way of seeing and observing the world as a source of inspiration. The architect's "way of seeing" reveals his sensitivity to the popular and traditional human habitat. Thanks to Antonio Miró, in the period between 1963 and 1970 Fernando Higueras was able to provide a real framework for a large part of his constructive ideas. The object of study of the present work is to determine the architect's “invariables” as a means of understanding his creative thought. The aims of the present study are to explore his thoughts in greater depth, to examine his work from the chronological-evolutionary point of view for an insight into the relationships and the creative connections between them, to observe and apprehend the evolution of his main creative themes and compositional keynotes, to analyse graphically part of his unbuilt work in order to improve our understanding of these underlying themes through their reconstruction using the latest graphic digital resources. The 3-D reconstruction of part of his unbuilt work highlights the magnitude of his creative thought. The methodology used to collect all the necessary information includes an examination of his writings and articles in journals and newspapers, criticisms, observations, plans, projects, building specifications, period photographs, models, the opinions of his contemporaries, family and friends, and visits to some of his built work. Nine directions of research were then established for each main theme of his creative thought. Each direction includes an analysis from two different points of view: the first, theoretical or chronological-evolutionary aspect, based on a selection of some of his built and unbuilt works; and a second graphic aspect based on the study and reconstruction of part of his unbuilt work. The result is a survey of the evolution of his work with a view to establishing the connections and their interrelationships, through to the ultimate maturity of his creative themes in both his built and unbuilt work. Fernando Higueras is on a constant quest for excellence, a perpetual desire to do things a little better, until a point where he gains mastery over his own recurrent themes, in the fullness of maturity and of his formal and constructive expression. The creation of three-dimensional models in 13 projects of his unbuilt work offers a new look at the capacity of his creative thought, in addition to the analysis of the evidence in some of these projects of the constructive and compositional germs of many of his ideas and themes. Finally, this work has contributed to the understanding of Fernando Higueras in a broader dimension, from the freshness of his unbuilt work through to the capacity of his creative thought, the evolution of his main themes, the study of his final unbuilt works, his sensitivity to the arts as a whole and to everything beautiful. The 360 plates of illustrations provided form the basis of the study and analysis of his extensive unbuilt work.

Numerical methods in Nonlinear Analysis of shell structures

The design of shell and spatial structures represents an important challenge even with the use of the modern computer technology.If we concentrate in the concrete shell structures many problems must be faced,such as the conceptual and structural disposition, optimal shape design, analysis, construction methods, details etc. and all these problems are interconnected among them. As an example the shape optimization requires the use of several disciplines like structural analysis, sensitivity analysis, optimization strategies and geometrical design concepts. Similar comments can be applied to other space structures such as steel trusses with single or double shape and tension structures. In relation to the analysis the Finite Element Method appears to be the most extended and versatile technique used in the practice. In the application of this method several issues arise. First the derivation of the pertinent shell theory or alternatively the degenerated 3-D solid approach should be chosen. According to the previous election the suitable FE model has to be adopted i.e. the displacement,stress or mixed formulated element. The good behavior of the shell structures under dead loads that are carried out towards the supports by mainly compressive stresses is impaired by the high imperfection sensitivity usually exhibited by these structures. This last effect is important particularly if large deformation and material nonlinearities of the shell may interact unfavorably, as can be the case for thin reinforced shells. In this respect the study of the stability of the shell represents a compulsory step in the analysis. Therefore there are currently very active fields of research such as the different descriptions of consistent nonlinear shell models given by Simo, Fox and Rifai, Mantzenmiller and Buchter and Ramm among others, the consistent formulation of efficient tangent stiffness as the one presented by Ortiz and Schweizerhof and Wringgers, with application to concrete shells exhibiting creep behavior given by Scordelis and coworkers; and finally the development of numerical techniques needed to trace the nonlinear response of the structure. The objective of this paper is concentrated in the last research aspect i.e. in the presentation of a state-of-the-art on the existing solution techniques for nonlinear analysis of structures. In this presentation the following excellent reviews on this subject will be mainly used.

Managing daily surgery schedules in a teaching hospital: a mixed-integer optimization approach

Background: This study examined the daily surgical scheduling problem in a teaching hospital. This problem relates to the use of multiple operating rooms and different types of surgeons in a typical surgical day with deterministic operation durations (preincision, incision, and postincision times). Teaching hospitals play a key role in the health-care system; however, existing models assume that the duration of surgery is independent of the surgeon's skills. This problem has not been properly addressed in other studies. We analyze the case of a Spanish public hospital, in which continuous pressures and budgeting reductions entail the more efficient use of resources. Methods: To obtain an optimal solution for this problem, we developed a mixed-integer programming model and user-friendly interface that facilitate the scheduling of planned operations for the following surgical day. We also implemented a simulation model to assist the evaluation of different dispatching policies for surgeries and surgeons. The typical aspects we took into account were the type of surgeon, potential overtime, idling time of surgeons, and the use of operating rooms. Results: It is necessary to consider the expertise of a given surgeon when formulating a schedule: such skill can decrease the probability of delays that could affect subsequent surgeries or cause cancellation of the final surgery. We obtained optimal solutions for a set of given instances, which we obtained through surgical information related to acceptable times collected from a Spanish public hospital. Conclusions: We developed a computer-aided framework with a user-friendly interface for use by a surgical manager that presents a 3-D simulation of the problem. Additionally, we obtained an efficient formulation for this complex problem. However, the spread of this kind of operation research in Spanish public health hospitals will take a long time since there is a lack of knowledge of the beneficial techniques and possibilities that operational research can offer for the health-care system.