Estimación de la peligrosidad sísmica mediante protocolos de juicios de expertos

Este trabajo estudia la aportación que los métodos de agregación de juicios de expertos pueden realizar en el cálculo de la peligrosidad sísmica de emplazamientos. Se han realizado cálculos en dos emplazamientos de la Península Ibérica: Mugardos (La Coruña) y Cofrentes (Valencia) que están sometidos a regímenes tectónicos distintos y que, además, alojan instalaciones industriales de gran responsabilidad. Las zonas de estudio, de 320 Km de radio, son independientes. Se ha aplicado un planteamiento probabilista a la estimación de la tasa anual de superación de valores de la aceleración horizontal de pico y se ha utilizado el Método de Montecarlo para incorporar a los resultados la incertidumbre presente en los datos relativos a la definición de cada fuente sismogenética y de su sismicidad. Los cálculos se han operado mediante un programa de ordenador, desarrollado para este trabajo, que utiliza la metodología propuesta por el Senior Seismic Hazard Analysis Commitee (1997) para la NRC. La primera conclusión de los resultados ha sido que la Atenuación es la fuente principal de incertidumbre en las estimaciones de peligrosidad en ambos casos. Dada la dificultad de completar los datos históricos disponibles de esta variable se ha estudiado el comportamiento de cuatro métodos matemáticos de agregación de juicios de expertos a la hora de estimar una ley de atenuación en un emplazamiento. Los datos de partida se han obtenido del Catálogo de Isosistas del IGN. Los sismos utilizados como variables raíz se han elegido con el criterio de cubrir uniformemente la serie histórica disponible y los valores de magnitud observados. Se ha asignado un panel de expertos particular a cada uno de los dos emplazamientos y se han aplicado a sus juicios los métodos de Cooke, equipesos, Apostolakis_Mosleh y Morris. Sus propuestas se han comparado con los datos reales para juzgar su eficacia y su facilidad de operación. A partir de los resultados se ha concluido que el método de Cooke ha mostrado el comportamiento más eficiente y robusto para ambos emplazamientos. Este método, además, ha permitido identificar, razonadamente, a aquellos expertos que no deberían haberse introducido en un panel. The present work analyses the possible contribution of the mathematical methods of aggregation in the assessment of Seismic Hazzard. Two sites, in the Iberian Peninsula, have been considered: Mugardos ( La Coruña) and Cofrentes (Valencia).Both of them are subjected to different tectonic regimes an both accommodate high value industrial plants. Their areas of concern, with radius of 320 Km, are not overlapping. A probabilistic approach has been applied in the assessment the annual probability of exceedence of the horizontal peak acceleration. The Montecarlo Method has allowed to transfer the uncertainty in the models and parameters to the final results. A computer program has been developed for this purpose. The methodology proposed by the Senior Seismic Analysis Committee (1997) for the NRC has been considered. Attenuation in Ground motion has been proved to be the main source of uncertainty in seismic hazard for both sites. Taking into account the difficulties to complete existing historical data in this subject the performance of four mathematical methods of aggregation has been studied. Original data have been obtained from the catalogs of the Spanish National Institute of Geography. The seismic events considered were chosen to cover evenly the historical records and the observed values of magnitude. A panel of experts have been applied to each site and four aggregation methods have been developed : equal weights, Cooke, Apostolakis-Mosleh and Morris The four proposals have been compaired with the actual data to judge their performance and ease of application. The results have shown that the Method of Cooke have proved the most efficient and robust for both sites. This method, besides, allow the reasoned identification of those experts who should be rejected from the panel

Hierarchical boundary elements

In this paper we show the possibility of applying adaptive procedures as an alternative to the well-known philosophy of standard Boundary Elements. The three characteristic steps of adaptive procedures, i.e. hierarchical shape functions families, indicator criteria, and a posteriori estimation, can be defined in order to govern an automatic refinement and stopping of the solution process. A computer program to treat potential problems, called QUEIMADA, has been developed to show the capabilities of the new idea.

A contribution to the optimal numbering of tree structures

This paper develops an automatic procedure for the optimal numbering of members and nodes in tree structures. With it the stiffness matrix is optimally conditioned either if a direct solution algorithm or a frontal one is used to solve the system of equations. In spite of its effectiveness, the procedure is strikingly simple and so is the computer program shown below.

Elaboración de un nuevo modelo económico para la contribución al desarrollo sostenible de países del África subsahariana: implementación en Guinea Bissau

El escaso crecimiento de los países del África subsahariana, lleva a la necesidad de plantear un tipo de modelo económico que se adapte a sus especiales características y que en definitiva, conduzca a las sociedades que viven en estos países a un aumento de su calidad de vida, mediante mejoras en todos los campos sociales tales como: la enseñanza, la salud y la nutrición, que puedan ayudar a transformar las perspectivas del crecimiento económico, especialmente en los países objeto de estudio, que se caracterizan por presentar bajos ingresos y escaso desarrollo humano. Se puede concluir, por tanto, diciendo que en definitiva, el fin es el desarrollo humano y que el crecimiento económico es un medio. El propósito del crecimiento económico debe ser enriquecer la vida de la gente. Los adelantos a corto plazo en materia de desarrollo humano son posibles, merced a un mayor crecimiento económico que a su vez no debe desligarse del respeto por el medioambiente y el entorno. Para conseguir estos objetivos, se plantea en la presente tesis un modelo económico, elaborado siguiendo las directrices de la Dinámica de Sistemas, mediante el uso del programa informático VENSIM. El modelo planteado se basa en la producción de energía eléctrica, que sería capaz de abastecer a una población y generar unos excedentes que podrían ser vendidos y las ganancias reinvertidas para impulsar el crecimiento económico de la población a la que abastece. ABSTRACT Low growth in sub-Saharan Africa, leading to the need to establish a type of economic model that suits their special characteristics and ultimately lead to societies that live in these countries to increase human capacity through improvements in all social fields such as education, health and nutrition that can help transform the prospects for economic growth, especially in the countries under study, which are characterized by low income and low human development. It can be concluded, therefore, saying that ultimately, the end is human development and economic growth is a means. The purpose of economic growth should be to enrich the lives of people. The short-term advances in human development are possible, thanks to higher economic growth which in turn should not be separated from respect for the environment and intone. To achieve these objectives, we propose in this thesis an economic model, developed under the guidance of dynamic systems, using the computer program VENSIM. The proposed model is based on the production of electricity, which would be able to supply a population and generate a surplus that could be sold and the proceeds reinvested to boost economic growth in the population it serves.

Numerical models for coastal zone management

The basic equations for modelling two-dimensional hydrodynamics and transport in estuaries and coastal regions have been developed. By using the finite element method, it is possible to transform the model into a discretized counterpart. The model has been applied in order to study the dispersion of an effluent within the Bay of Santander. The results obtained by means of a computer program are discussed.

Analysis of the railway track as a spatially periodic structure

This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structural analysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, i.e. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (DFT) in order to reduce a large system of q(2N + 1) linear stiffness equilibrium equations to a set of 2N + 1 uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q = 2, the vertical displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartín [1], i.e. the continuous beam railway track response. The comparison between the proposed method and other methods of analysis of railway tracks, such as Lorente de Nó and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N. In addition, identical results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Small but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article also presents a detailed sensitivity analysis of the vertical displacement of the sleepers. Although standard matrix methods of structural analysis can handle this railway model, one of the objectives of this article is to show the efficiency of DFT method with respect to standard matrix structural analysis. A comparative analysis between standard matrix structural analysis and the proposed method (DFT), in terms of computational time, input, output and also software programming, will be carried out. Finally, a URL link to a MatLab computer program list, based on the proposed method, is given

A nonlinear analysis of laying a floating pipeline on the seabed

In this article, a model for the determination of displacements, strains, and stresses of a submarine pipeline during its construction is presented. Typically, polyethylene outfall pipelines are the ones treated by this model. The process is carried out from an initial floating situation to the final laying position on the seabed. The following control variables are considered in the laying process: the axial load in the pipe, the flooded inner length, and the distance of the control barge from the coast. External loads such as self-weight, dead loads, and forces due to currents and small waves are also taken into account.This paper describes both the conceptual framework for the proposed model and its practical application in a real engineering situation. The authors also consider how the model might be used as a tool to study how sensitive the behavior of the pipeline is to small changes in the values of the control variables. A detailed description of the actions is considered, especially the ones related to the marine environment such as buoyancy, current, and sea waves. The structural behavior of the pipeline is simulated in the framework of a geometrically nonlinear dynamic analysis. The pipeline is assumed to be a two-dimensional Navier_Bernoulli beam. In the nonlinear analysis an updated Lagrangian formulation is used, and special care is taken regarding the numerical aspects of sea bed contact, follower forces due to external water pressures, and dynamic actions. The paper concludes by describing the implementation of the proposed techniques, using the ANSYS computer program with a number of subroutines developed by the authors. This implementation permits simulation of the two-dimensional structural pipe behavior of the whole construction process. A sensitivity analysis of the bending moments, axial forces, and stresses for different values of the control variables is carried out. Using the techniques described, the engineer may optimize the construction steps in the pipe laying process

Dynamic analysis of translational shells

In this paper a dynamic analysis of transnational shells is presented. The general linear shell theory is used in conjunction with additional shallow and curved plate approximations. In order to apply some type of extended Levy solution, the shell is assumed to be limited by a rectangular plan form, with two opposite edges simply supported (gable boundary conditions). First, the shells free vibrations are studied in the usual way, obtaining for each Fourier term the natural frequencies as solutions of a transcendental equation. However, solving these equations arises enormous computational difficulties. This paper deals specifically with this problem, trying to reduce its dimension by a discretization procedure. In the shell dynamic characteristics, namely the mass. The shell mass is lumped along a family of coordinate lines. Therefore, the natural frequencies for each harmonic term can be found from the solution of a typical matrix eigenvalues problem and standard numerical techniques can be applied. The shell response to forced vibrations, particularly to earthquake excitation, can be determined by using conventional procedure either in the time or in the frequency domain. Finally, extending the above procedure, any system of translational shells under dynamic loading can be studied. Then, by using matrix methods, a general computer program is written and applied to some illustrative examples. Numerical results has been obtained in two cases: circular cylindrical shell and box girder bridge.

Geometría de presas bóveda

Se presenta en este artículo un programa para cálculo mediante ordenador, de utilización frecuente en el Departamento de Estudios Experimentales de Presas del Labo¬ratorio Central. Este programa se refiere a presas bóvedas asimétricas de tres centros y determina: a) el replanteo geométrico de las mismas para su construcción en modelo reducido. b) la posición -punto de aplicación y dirección- de las cargas puntuales equivalentes a las acciones de peso propio y presión hidrostática, que se introducen en el modelo median¬te gatos hidráulicos. c) la directriz de la presa, dato necesario para un posible cálculo estático posterior. This paper presents a computer program currently used in the Department of Experimental Studies of Dams in the Laboratorio Central. This program concerns asymmetric arch dams of three centers and it determines: a) The geometrical definition of the arch dams for the scaled model construction. b) The position, acting point and direction of the punctual loads equivalent to the actions of self-weight and water pressure, which are applied to the model by means of hydraulic jacks. c) The middle surface of the dam, which later would be introduced for a stress analy¬sis of the dam itself

Certificación energética mediante la herramienta CE3X y rehabilitación energética de una vivienda unifamiliar

El siguiente proyecto lleva a cabo un estudio sobre la eficiencia energética en una vivienda unifamiliar basándose en la legislación actual europea y española. Para empezar se obtendrá la calificación energética del inmueble mediante el programa informático de la opción simplificada CE3X. A continuación se proporcionará un estudio con las medidas de mejora más adecuadas para mejorar la eficiencia energética de la vivienda, las medidas que se llevarán a cabo serán: la mejora de la envolvente térmica, mejorando el aislamiento de la fachada y la sustitución de ventanas, la instalación de una caldera de biomasa y la instalación de un sistema de colectores solares para cubrir la demanda de calefacción y ACS. Para finalizar se realiza un presupuesto de las medidas de mejoras propuestas, así como un análisis económico y una planificación y programación temporal. ABSTRACT The object of this Project is to carry out a study on the energy efficiency of a single family home in accordance with the present European and Spanish legislation. The first step is to obtain the home energy efficiency by means of a CE3X computer program. The second step is a study with the most appropriate improvement measures is provided in order to improve the home energy efficiency. The measures to be carried out will be as follows: improving the heat insulation, as well as, the facade heat insulation and replacing the windows, installing a biomass heating system and a solar collector in order to satisfy the heating and domestic hot water (DHW) demands. Finally a budget with the proposed improvement measures is made as well as a financial analysis and a time planning and programming of the project.

Emotion transplantation through adaptation in HMM-based speech synthesis

This paper proposes an emotion transplantation method capable of modifying a synthetic speech model through the use of CSMAPLR adaptation in order to incorporate emotional information learned from a different speaker model while maintaining the identity of the original speaker as much as possible. The proposed method relies on learning both emotional and speaker identity information by means of their adaptation function from an average voice model, and combining them into a single cascade transform capable of imbuing the desired emotion into the target speaker. This method is then applied to the task of transplanting four emotions (anger, happiness, sadness and surprise) into 3 male speakers and 3 female speakers and evaluated in a number of perceptual tests. The results of the evaluations show how the perceived naturalness for emotional text significantly favors the use of the proposed transplanted emotional speech synthesis when compared to traditional neutral speech synthesis, evidenced by a big increase in the perceived emotional strength of the synthesized utterances at a slight cost in speech quality. A final evaluation with a robotic laboratory assistant application shows how by using emotional speech we can significantly increase the students’ satisfaction with the dialog system, proving how the proposed emotion transplantation system provides benefits in real applications.

Aprendizaje integrado en arquitectura con modelos virtuales : implementación de metodología BIM en la docencia universitaria

Los procesos de diseño y construcción en Arquitectura han mostrado un desarrollo de optimización históricamente muy deficiente cuando se compara con las restantes actividades típicamente industriales. La aspiración constante a una industrialización efectiva, tanto en aras de alcanzar mayores cotas de calidad así como de ahorro de recursos, recibe hoy una oportunidad inmejorable desde el ámbito informático: el Building Information Modelling o BIM. Lo que en un inicio puede parecer meramente un determinado tipo de programa informático, en realidad supone un concepto de “proceso” que subvierte muchas rutinas hoy habituales en el desarrollo de proyectos y construcciones arquitectónicas. La inclusión y desarrollo de datos ligados al proyecto, desde su inicio hasta el fin de su ciclo de vida, conlleva la oportunidad de crear una realidad virtual dinámica y actualizable, que por añadidura posibilita su ensayo y optimización en todos sus aspectos: antes y durante su ejecución, así como vida útil. A ello se suma la oportunidad de transmitir eficientemente los datos completos de proyecto, sin apenas pérdidas o reelaboración, a la cadena de fabricación, lo que facilita el paso a una industrialización verdaderamente significativa en edificación. Ante una llamada mundial a la optimización de recursos y el interés indudable de aumentar beneficios económicos por medio de la reducción del factor de incertidumbre de los procesos, BIM supone un opción de mejora indudable, y así ha sido reconocido a través de la inminente implantación obligatoria por parte de los gobiernos (p. ej. Gran Bretaña en 2016 y España en 2018). La modificación de procesos y roles profesionales que conlleva la incorporación de BIM resulta muy significativa y marcará el ejercicio profesional de los futuros graduados en las disciplinas de Arquitectura, Ingeniería y Construcción (AEC por sus siglas en inglés). La universidad debe responder ágilmente a estas nuevas necesidades incorporando esta metodología en la enseñanza reglada y aportando una visión sinérgica que permita extraer los beneficios formativos subyacentes en el propio marco BIM. En este sentido BIM, al aglutinar el conjunto de datos sobre un único modelo virtual, ofrece un potencial singularmente interesante. La realidad tridimensional del modelo, desarrollada y actualizada continuamente, ofrece al estudiante una gestión radicalmente distinta de la representación gráfica, en la que las vistas parciales de secciones y plantas, tan complejas de asimilar en los inicios de la formación universitaria, resultan en una mera petición a posteriori, para ser extraída según necesidad del modelo virtual. El diseño se realiza siempre sobre el propio modelo único, independientemente de la vista de trabajo elegida en cada momento, permaneciendo los datos y sus relaciones constructivas siempre actualizados y plenamente coherentes. Esta descripción condensada de características de BIM preconfiguran gran parte de las beneficios formativos que ofrecen los procesos BIM, en especial, en referencia al desarrollo del diseño integrado y la gestión de la información (incluyendo TIC). Destacan a su vez las facilidades en comprensión visual de elementos arquitectónicos, sistemas técnicos, sus relaciones intrínsecas así como procesos constructivos. A ello se une el desarrollo experimental que la plataforma BIM ofrece a través de sus software colaborativos: la simulación del comportamiento estructural, energético, económico, entre otros muchos, del modelo virtual en base a los datos inherentes del proyecto. En la presente tesis se describe un estudio de conjunto para explicitar tanto las cualidades como posibles reservas en el uso de procesos BIM, en el marco de una disciplina concreta: la docencia de la Arquitectura. Para ello se ha realizado una revisión bibliográfica general sobre BIM y específica sobre docencia en Arquitectura, así como analizado las experiencias de distintos grupos de interés en el marco concreto de la enseñanza de la en Arquitectura en la Universidad Europea de Madrid. El análisis de beneficios o reservas respecto al uso de BIM se ha enfocado a través de la encuesta a estudiantes y la entrevista a profesionales AEC relacionados o no con BIM. Las conclusiones del estudio permiten sintetizar una implantación de metodología BIM que para mayor claridad y facilidad de comunicación y manejo, se ha volcado en un Marco de Implantación eminentemente gráfico. En él se orienta sobre las acciones docentes para el desarrollo de competencias concretas, valiéndose de la flexibilidad conceptual de los Planes de Estudio en el contexto del Espacio Europeo de Educación Superior (Declaración de Bolonia) para incorporar con naturalidad la nueva herramienta docente al servicio de los objetivos formativo legalmente establecidos. El enfoque global del Marco de Implementación propuesto facilita la planificación de acciones formativas con perspectiva de conjunto: combinar los formatos puntuales o vehiculares BIM, establecer sinergias transversales y armonizar recursos, de modo que la metodología pueda beneficiar tanto la asimilación de conocimientos y habilidades establecidas para el título, como el propio flujo de aprendizaje o learn flow BIM. Del mismo modo reserva, incluso visualmente, aquellas áreas de conocimiento en las que, al menos en la planificación actual, la inclusión de procesos BIM no se considera ventajosa respecto a otras metodologías, o incluso inadecuadas para los objetivos docentes establecidos. Y es esta última categorización la que caracteriza el conjunto de conclusiones de esta investigación, centrada en: 1. la incuestionable necesidad de formar en conceptos y procesos BIM desde etapas muy iniciales de la formación universitaria en Arquitectura, 2. los beneficios formativos adicionales que aporta BIM en el desarrollo de competencias muy diversas contempladas en el currículum académico y 3. la especificidad del rol profesional del arquitecto que exigirá una implantación cuidadosa y ponderada de BIM que respete las metodologías de desarrollo creativo tradicionalmente efectivas, y aporte valor en una reorientación simbiótica con el diseño paramétrico y fabricación digital que permita un diseño finalmente generativo. ABSTRACT The traditional architectural design and construction procedures have proven to be deficient where process optimization is concerned, particularly when compared to other common industrial activities. The ever‐growing strife to achieve effective industrialization, both in favor of reaching greater quality levels as well as sustainable management of resources, has a better chance today than ever through a mean out of the realm of information technology, the Building Information Modelling o BIM. What may initially seem to be merely another computer program, in reality turns out to be a “process” concept that subverts many of today’s routines in architectural design and construction. Including and working with project data from the very beginning to the end of its full life cycle allows for creating a dynamic and updatable virtual reality, enabling data testing and optimizing throughout: before and during execution, all the way to the end of its lifespan. In addition, there is an opportunity to transmit complete project data efficiently, with hardly any loss or redeveloping of the manufacture chain required, which facilitates attaining a truly significant industrialization within the construction industry. In the presence of a world‐wide call for optimizing resources, along with an undeniable interest in increasing economic benefits through reducing uncertainty factors in its processes, BIM undoubtedly offers a chance for improvement as acknowledged by its imminent and mandatory implementation on the part of governments (for example United Kingdom in 2016 and Spain in 2018). The changes involved in professional roles and procedures upon incorporating BIM are highly significant and will set the course for future graduates of Architecture, Engineering and Construction disciplines (AEC) within their professions. Higher Education must respond to such needs with swiftness by incorporating this methodology into their educational standards and providing a synergetic vision that focuses on the underlying educational benefits inherent in the BIM framework. In this respect, BIM, in gathering data set under one single virtual model, offers a uniquely interesting potential. The three‐dimensional reality of the model, under continuous development and updating, provides students with a radically different graphic environment, in which partial views of elevation, section or plan that tend characteristically to be difficult to assimilate at the beginning of their studies, become mere post hoc requests to be ordered when needed directly out the virtual model. The design is always carried out on the sole model itself, independently of the working view chosen at any particular moment, with all data and data relations within construction permanently updated and fully coherent. This condensed description of the features of BIM begin to shape an important part of the educational benefits posed by BIM processes, particularly in reference to integrated design development and information management (including ITC). At the same time, it highlights the ease with which visual understanding is achieved regarding architectural elements, technology systems, their intrinsic relationships, and construction processes. In addition to this, there is the experimental development the BIM platform grants through its collaborative software: simulation of structural, energetic, and economic behavior, among others, of the virtual model according to the data inherent to the project. This doctoral dissertation presents a broad study including a wide array of research methods and issues in order to specify both the virtues and possible reservations in the use of BIM processes within the framework of a specific discipline: teaching Architecture. To do so, a literature review on BIM has been carried out, specifically concerning teaching in the discipline of Architecture, as well as an analysis of the experience of different groups of interest delimited to Universidad Europea de Madrid. The analysis of the benefits and/or limitations of using BIM has been approached through student surveys and interviews with professionals from the AEC sector, associated or not, with BIM. Various diverse educational experiences are described and academic management for experimental implementation has been analyzed. The conclusions of this study offer a synthesis for a Framework of Implementation of BIM methodology, which in order to reach greater clarity, communication ease and user‐friendliness, have been posed in an eminently graphic manner. The proposed framework proffers guidance on teaching methods conducive to the development of specific skills, taking advantage of the conceptual flexibility of the European Higher Education Area guidelines based on competencies, which naturally facilitate for the incorporation of this new teaching tool to achieve the educational objectives established by law. The global approach of the Implementation Framework put forth in this study facilitates the planning of educational actions within a common perspective: combining exceptional or vehicular BIM formats, establishing cross‐disciplinary synergies, and sharing resources, so as to purport a methodology that contributes to the assimilation of knowledge and pre‐defined competencies within the degree program, and to the flow of learning itself. At the same time, it reserves, even visually, those areas of knowledge in which the use of BIM processes is not considered necessarily an advantage over other methodologies, or even inadequate for the learning outcomes established, at least where current planning is concerned. It is this last category which characterizes the research conclusions as a whole, centering on: 1. The unquestionable need for teaching BIM concepts and processes in Architecture very early on, in the initial stages of higher education; 2. The additional educational benefits that BIM offers in a varied array of competency development within the academic curriculum; and 3. The specific nature of the professional role of the Architect, which demands a careful and balanced implementation of BIM that respects the traditional teaching methodologies that have proven effective and creative, and adds value by a symbiotic reorientation merged with parametric design and digital manufacturing so to enable for a finally generative design.

DETERMINAÇÃO DAS FORMAS DO ARCO DENTÁRIO INFERIOR NA OCLUSÃO NORMAL NATURAL

Com a finalidade de determinar as formas do arco dentário inferior de maior incidência na oclusão normal natural, utilizou-se um método matemático associado ao emprego de uma função polinomial, o qual foi aplicado a 63 modelos de arcadas inferiores selecionados a partir de 6118 adolescentes. Todos os indivíduos eram portadores de dentição permanente, incluindo os segundos molares, e oclusão normal natural. Em cada dente foi fixada uma esfera de vidro, que teve a função de simular o acessório do aparelho ortodôntico, sendo utilizada na medição das distâncias entre o centro da imagem dessas esferas aos eixos x e y. Após a digitalização dos modelos de gesso, as imagens foram plotadas em um programa de computador, a fim de se obterem a função polinomial de sexto grau e o gráfico dessa função para os 126 segmentos de curva, originados das secções das imagens em lado direito e esquerdo. A seguir organizaram-se esses segmentos, de acordo com as características da curvatura anterior dos arcos dentários, em oito grupos diferentes de formas, que receberam as denominações de Forma A, Forma B, Forma C, Forma D, Forma E, Forma F, Forma G, Forma H. Cada grupo foi, então, dividido em três subgrupos, conforme os tamanhos pequeno, médio e grande. Os resultados indicaram 23 formas representativas do arco dentário inferior e uma forma média para a oclusão normal natural.

DETERMINAÇÃO DAS FORMAS DO ARCO DENTÁRIO INFERIOR NA OCLUSÃO NORMAL NATURAL

Com a finalidade de determinar as formas do arco dentário inferior de maior incidência na oclusão normal natural, utilizou-se um método matemático associado ao emprego de uma função polinomial, o qual foi aplicado a 63 modelos de arcadas inferiores selecionados a partir de 6118 adolescentes. Todos os indivíduos eram portadores de dentição permanente, incluindo os segundos molares, e oclusão normal natural. Em cada dente foi fixada uma esfera de vidro, que teve a função de simular o acessório do aparelho ortodôntico, sendo utilizada na medição das distâncias entre o centro da imagem dessas esferas aos eixos x e y. Após a digitalização dos modelos de gesso, as imagens foram plotadas em um programa de computador, a fim de se obterem a função polinomial de sexto grau e o gráfico dessa função para os 126 segmentos de curva, originados das secções das imagens em lado direito e esquerdo. A seguir organizaram-se esses segmentos, de acordo com as características da curvatura anterior dos arcos dentários, em oito grupos diferentes de formas, que receberam as denominações de Forma A, Forma B, Forma C, Forma D, Forma E, Forma F, Forma G, Forma H. Cada grupo foi, então, dividido em três subgrupos, conforme os tamanhos pequeno, médio e grande. Os resultados indicaram 23 formas representativas do arco dentário inferior e uma forma média para a oclusão normal natural.

AVALIAÇÃO DAS ALTERAÇÕES DO SORRISO EM INDIVÍDUOS SUBMETIDOS À EXPANSÃO RÁPIDA DA MAXILA

O objetivo deste estudo foi avaliar as possíveis alterações das características horizontais, verticais, de simetria e do arco do sorriso de pacientes com atresia maxilar submetidos à expansão rápida da maxila. A amostra consistiu de 81 fotografias extra-bucais do sorriso máximo de 27 pacientes com idade média de 10 anos e 3 meses. Foram realizadas fotografias do sorriso máximo nos períodos: inicial (antes da instalação do aparelho expansor); 3 meses após a fixação do parafuso expansor; 6 meses após a fixação do parafuso expansor. Para a calibragem e análise das fotografias foi utilizado o programa CEFX 2001 CDT. Os pontos fotométricos e as medidas a serem analisadas foram escolhidos após revisão da literatura do sorriso realizada. Para avaliar as alterações no sorriso durante as fases, foi utilizada a análise de variância ANOVA, com nível de significância de 5%. A expansão rápida da maxila promoveu aumento estatisticamente significante da dimensão transversal do sorriso; aumento da quantidade de exposição dos incisivos centrais e laterais superiores; manutenção da simetria entre os lados direito e esquerdo e da falta de paralelismo entre a curvatura das bordas dos incisivos superiores com a curvatura do lábio inferior (arco do sorriso).(AU)