A shape sensitivity analysis module with geometric representation by NURBs for a 2D finite element program based on Cartesian meshes independent of the geometry

[ES] El Método de los Elementos Finitos se ha convertido en una de las técnicas más potentes y más ampliamente utilizadas para encontrar soluciones aproximadas de las ecuaciones diferenciales que rigen numerosos tipos problemas ingenieriles. Los procesos de optimización de forma en componentes mecánicos requieren que la información de los gradientes (sensibilidades) de las magnitudes de interés esté calculada con suficiente precisión. En este sentido, en esta tesis de máster, ha sido desarrollado un módulo de cálculo de sensibilidades de forma con representación geométrica mediante NURBs (Non-Uniform Rational B-splines) para un programa de análisis de problemas elásticos lineales, resueltos mediante el MEF dentro de un entorno de mallados cartesianos 2-D independientes de la geometria, Cartesian Grid-FEM, con vistas a una futura implementación 3-D. En primer lugar, se ha implementado, a traves de interfaz gráfica, la posibilidad de crear entidades geométricas tipo NURB, que se han convertido en los últimos años en la tecnología gráfica más usada en el campo del diseño en ingeniería. Este tipo de curvas son muy adecuadas para el modelado de todo tipo de superficies y pueden representar exactamente secciones cónicas, es decir, circunferencias, cilindros o esferas entre otras, que no podían ser representadas con la técnica de representación geométrica hasta ahora implementada basada en el uso de splines. En segundo lugar, se ha adaptado la teoría existente en MEF estándar sobre el cálculo de sensibilidades de forma, a un entorno basado en mallas cartesianas independientes de la geometría, lo que implica, por ejemplo, la necesidad de implementación de nuevos métodos de creación del campo de velocidades, que es un paso crucial en este tipo de análisis. Los resultados obtenidos muestran que la utilización de curvas tipo NURB suponen la disminución significativa del error geométrico durante el cálculo de EF, y que el módulo de cálculo implementado es capaz de crear diversas alternativas de campo de velocidades dando muy buenos resultados en la obtención de las sensibilidades.[EN] The Finite Element Method has become one of the most powerful and widely used techniques to find approximate solutions of differential equations governing many types of engineering problems. Optimization processes of mechanical components require that the information of the gradients (sensitivity) of the magnitudes of interest is calculated with sufficient accuracy. The aim of this master thesis is to develop a module for calculation of shape sensitivities with geometric representation by NURBs (Non-Uniform Rational B-Splines) for a program created to analize linear elastic problems, solved by FEM using 2-D cartesian meshes independent of geometry, Cartesian Grid-FEM, looking at a future 3-D implementation. First, it has been implemented, through graphical interface, the ability to create NURB geometric entities, which have become in recent years in the most used geometric technology in the field of engineering design. Such curves are very suitable for modeling all types of surfaces and can accurately represent conic sections, i.e., circles, cylinders or spheres, among others, that could not be represented with the geometric representation technique so far implemented based on splines. Secondly, theory on calculation of shape sensitivities, for standard FEM, has been adapted to an environment based on cartesian meshes independent of geometry, which implies, for instance, the need to implement new methods of velocity field generation, which is a crucial step in this kind of analysis. The results show that the use of NURB curves involve significant decrease of geometrical error during FE calculation, and that the calculation module implemented is able to create several alternative velocity field giving back good results in different sensitivities analyses.[CA] El Mètode dels Elements Finits s¿ha convertit en una de les tècniques més potents i més àmpliament utilitzades per a trobar solucions aproximades de les equacions diferencials que regixen nombrosos tipus problemes en enginyeria. Els processos d¿optimització de forma en components mecànics requerixen que la informació dels gradients (sensibilitats) de les magnituds d¿interés estiga calculada amb suficient precisió. En este sentit, en esta tesi de màster, ha sigut desenrotllat un mòdul de càlcul de sensibilitats de forma amb representació geomètrica per mitjà de NURBs (Non-Uniform Rational B-splines) per a un programa d¿anàlisi de problemes elàstics lineals, resolts per mitjà del MEF dins d¿un entorn de malles cartesians 2-D independents de la geometria, Cartesian Grid-FEM, amb vista a una futura implementació 3-D. En primer lloc, s¿ha implementat, a través d¿interfície gràfica, la possibilitat de crear entitats geomètriques tipus NURB, que s¿han convertit en els últims anys en la tecnologia gràfica més usada en el camp del disseny en enginyeria. Este tipus de corbes son molt adequades per al modelatge de qualsevol tipus de superfícies i poden representar exactament seccions còniques, és a dir, circumferències, cilindres o esferes entre altres, que no podien ser representades amb la tècnica de representació geomètrica fins ara implementada basada en l¿ús de splines. En segon lloc, s¿ha adaptat la teoria existent en MEF estàndard sobre el càlcul de sensibilitats de forma, a un entorn basat en malles cartesianes independents de la geometria, la qual cosa implica, per exemple, la necessitat d¿implementació de nous mètodes de creació del camp de velocitats, que és un pas crucial en este tipus d¿anàlisi. Els resultats obtinguts mostren que la utilització de corbes tipus NURB suposen la disminució significativa de l¿error geomètric durant el càlcul d¿EF, i que el mòdul de càlcul implementat és capaç de crear diverses alternatives de camp de velocitats donant molt bons resultats en l¿obtenció de les sensibilitats.Marco Alacid, O. (2012). A shape sensitivity analysis module with geometric representation by NURBs for a 2D finite element program based on Cartesian meshes independent of the geometry. http://hdl.handle.net/10251/27254Archivo delegad

Feature-Based Models for Three-Dimensional Data Fitting.

There are numerous techniques available for fitting a surface to any supplied data set. The feature-based modeling technique takes advantage of the known, geometric shape of the data by deforming a model having this generic shape to approximate the data. The model is constructed as a rational B-spline surface with characteristic features superimposed on its definition. The first step in the fitting process is to align the model with a data set using the center of mass, principal axes and/or landmarks. Using this initial orientation, the position, rotation and scale parameters are optimized using a Newton-type optimization of a least squares cost function. Once aligned, features embedded within the model, corresponding to pertinent characteristics of the shape, are used to improve the fit of the model to the data. Finally, the control vertex weights and positions of the rational B-spline model are optimized to approximate the data to within a specified tolerance. Since the characteristic features are defined within the model a creation, important measures are easily extracted from a data set, once fit. The feature-based modeling approach is demonstrated in two-dimensions by the fitting of five facial, silhouette profiles and in three-dimensions by the fitting of eleven human foot scans. The algorithm is tested for sensitivity to data distribution and structure and the extracted measures are tested for repeatability and accuracy. Limitations within the current implementation, future work and potential applications are also provided

Parametric Spiral And Its Application As Transition Curve

Lengkung Bezier merupakan suatu perwakilan lengkungan yang paling popular digunakan di dalam applikasi Rekabentuk Berbantukan Komputer (RBK) dan Rekabentuk Geometrik Berbantukan Komputer (RGBK). The Bezier curve representation is frequently utilized in computer-aided design (CAD) and computer-aided geometric design (CAGD) applications. The curve is defined geometrically, which means that the parameters have geometric meaning; they are just points in three-dimensional space

Grid sensitivity for aerodynamic optimization and flow analysis

After reviewing relevant literature, it is apparent that one aspect of aerodynamic sensitivity analysis, namely grid sensitivity, has not been investigated extensively. The grid sensitivity algorithms in most of these studies are based on structural design models. Such models, although sufficient for preliminary or conceptional design, are not acceptable for detailed design analysis. Careless grid sensitivity evaluations, would introduce gradient errors within the sensitivity module, therefore, infecting the overall optimization process. Development of an efficient and reliable grid sensitivity module with special emphasis on aerodynamic applications appear essential. The organization of this study is as follows. The physical and geometric representations of a typical model are derived in chapter 2. The grid generation algorithm and boundary grid distribution are developed in chapter 3. Chapter 4 discusses the theoretical formulation and aerodynamic sensitivity equation. The method of solution is provided in chapter 5. The results are presented and discussed in chapter 6. Finally, some concluding remarks are provided in chapter 7

Feedback Control Design for MARLO, a 3D-Bipedal Robot.

This work develops feedback controllers for bipedal walking in 3D on level ground, both in simulation and experimentally. MARLO is a new robot that has been designed for the study of 3D-bipedal locomotion, with the aim of combining energy efficiency, speed, and robustness with respect to natural terrain variations in a single platform. The robot is highly underactuated, having six actuators and, in single support, 13 degrees of freedom. Its sagittal plane dynamics are designed to embody the spring loaded inverted pendulum (SLIP), which has been shown to provide a dynamic model of the body center of mass during steady running gaits in a wide diversity of terrestrial animals. A detailed dynamic model is used to optimize walking gaits with respect to the cost of mechanical transport (cmt), a dimensionless measure of energetic efficiency. A feedback controller is designed that balances the robot during the quiet standing mode, and another feedback policy is developed such that the robot can take a transition step from quiet standing to walking. A feedback controller is designed that stabilizes steady-state 3D walking gaits, despite the high degree of underactuation of the robot. These controllers are combined through a state machine that handles switching among the three controllers controllers. In experiments on planarized (2D) and untethered (3D) versions of the robot with point feet and passive feet (prosthetic feet) walking over flat ground or on a ramp with a shallow slope, the adaptability of the designed controller to the environment (planar or untethered, flat ground or ramp), and to the morphology of the robot (point feet or passive feet), is demonstrated. In experiments on a planarized version of the robot with passive feet, the controller yielded stable walking after starting from quiet standing, autonomously and without any intervention from the operator. In experiments on an untethered (3D) version of the robot, the controller was able to balance the robot over flat ground or on a shallow ramp during the quiet standing mode. In addition, the controller yielded six-untethered ``human-like'' steps after starting from quiet standing, autonomously without any intervention from the operator.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/102339/1/aramez_1.pd

Multiscale Modelling of Urban Climate

Climate Modelling is a complex task. One of the most important reasons is the presence of a large variety of spatio-temporal scales. There are climatic changes that take place over a time period of a few months and then there are gusts which might last only a few seconds. Similarly there can be a strong influence on the weather of a city due to the presence of a large water body like a sea or of a mountain having a dimension of a few tens or hundreds of kilometres and then there can be a local influence due to the presence of urban structures like buildings and canopies having dimensions of the order of a few meters only. It is not computationally tractable to handle all of these scales in a single climate model. However, we can solve this issue by an integration of a global, meso and micro scale model capable of handling each of the different scales of interest. In this paper we describe in detail one such approach, along with some sample results demonstrating the capabilities of this tool

Wear analysis of hip explants, dual mobility concept: Comparison of quantitative and qualitative analyses

International audienceTotal hip replacement (THR) fails mainly because of wear. It is of interest to analyze wear to be able to increase the longevity of the hip implants. One way to achieve it is to use instruments on explants but the most suitable depends on the application. This paper aims at comparing several methods of surface analysis in the particular application of wear determination in a series of dual mobility explants. Wear measurement could help understand the wear mechanism only partially known. A CMM, Coordinate Measuring Machine, is used to get 3D points representing the explants, then Pro/Engineer ® and Matlab ® are used to calculate wear. A mechanical (SOMICRONIC®) and an optical profilometer (Bruker nanoscope Wyko® NT 9100, ex. Veeco) are used to access roughness parameters. The comparisons of the two software showed similar results for wear calculation except in a few cases where differences are due to the theoretical volumes calculation. The comparison of the two profiling techniques resulted in similar results particularly for Sa and Sdr. The comparison of the results showed that wear is present for four explants; it is relevant with the observed characteristics. The mechanical profilometer showed better accuracy than the optical one which enable to conclude that it must not be neglected for that particular application, even if measurements need more time

Automatic tool path generation for numerically controlled machining of sculptured surfaces

This dissertation presents four new tool path generation approaches for numerically controlled machining of sculptured surfaces: TRI\sb-XYINDEX, FINISH, FIVEX\sb-INDEX, FIX\sb-AXIS\sb-INDEX. All of the above systems index the tool across the object surface in the Cartesian space so that evenly distributed tool paths are accomplished. TRI\sb-XYINDEX is a three-axis tool path generation system which uses a surface triangle set (STS) representation of the surface for tool position calculations. Surface edges are detected with local searching algorithms. Quick tool positioning is achieved by selecting candidate elements of polygons. Test results show that TRI\sb-XYINDEX is more efficient when machining surfaces which are relatively flat while the discrete point approach is faster for highly curved surfaces. FINISH was developed for generating three-axis ball-end tool paths for local surface finishing. It was based on the SPS. Given a surface with excess material represented by a set of discrete points, FINISH automatically identifies the undercut areas. Results show that FINISH provides significant improvements in machining efficiency. FIVEX\sb-INDEX is developed for generating five-axis flat-end tool paths. It uses an STS approximation. Contact points on the surface are derived from edge lists obtained from the intersections of vertical cutting planes with the polygon set. The distances between adjacent end points set an initial step-forward increment between surface contact points. To verify tool movements, some intermediate tool positions are interpolated. The key features of FIVEX\sb-INDEX are: (1) a polygon set representing an object which may be composed of multiple surfaces; (2) Surface contact point generation by cutting plane intersection; (3) simple tool incrementing and positioning algorithms; (4) minimal user interaction; (5) user controlled accuracy of resulting tool paths. FIX\sb-AXIS\sb-INDEX is a subsystem of FIVEX\sb-INDEX, generating tool paths for a tool with fixed orientations. Surface contact points are generated similar to FIVEX\sb-INDEX while tool positions are corrected with the highest point technique along the tool axis direction. Linear fitting is applied to output tool positions. FIX\sb-AXIS\sb-INDEX is preferred for machining surfaces curved in one direction, such as ruled surfaces. Test results show that FIX\sb-AXIS\sb-INDEX can serve as a three-axis tool path generation system but a five-axis machine is required to do it. (Abstract shortened by UMI.)