10 research outputs found

    Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization

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    This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method. A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing. is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization. The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations. The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort. Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions. Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III I LIST OF ABBREVIATIONS V II LIST OF SYMBOLS V III LIST OF FIGURES XIII IV LIST OF TABLES XVIII 1. INTRODUCTION 1 1.1 RESEARCH DESIGN AND MOTIVATION 6 1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9 2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12 2.1 MATERIAL INTERPOLATION 16 2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17 2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18 3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21 3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22 3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27 3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32 3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36 3.5 CROSS-SECTION COMPARISON 39 4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41 4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43 4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45 4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49 4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54 5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58 5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61 5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66 5.3 SUBDIVISION SURFACES 67 5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71 5.5 CONSTRUCTIVE SOLID GEOMETRY 73 6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75 6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76 6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78 6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82 6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86 7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96 7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97 7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101 7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105 7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110 8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115 8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118 8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120 8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123 9. CONCLUSION 127 10. OUTLOOK 131 LITERATURE 133 APPENDIX 147 A PREVIOUS STUDIES 147 B CROSS-SECTION PROPERTIES 149 C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155 D EXPERIMENTAL SETUP 15

    Robot Manipulators

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    Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Exploitation du potentiel sismique des Ă©toiles naines blanches

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    Le but de cette thĂšse est d’explorer le potentiel sismique des Ă©toiles naines blanches pulsantes, et en particulier celles Ă  atmosphĂšres riches en hydrogĂšne, les Ă©toiles ZZ Ceti. La technique d’astĂ©rosismologie exploite l’information contenue dans les modes normaux de vibration qui peuvent ĂȘtre excitĂ©s lors de phases particuliĂšres de l’évolution d’une Ă©toile. Ces modes modulent le flux Ă©mergent de l’étoile pulsante et se manifestent principalement en termes de variations lumineuses multi-pĂ©riodiques. L’astĂ©rosismologie consiste donc Ă  examiner la luminositĂ© d’étoiles pulsantes en fonction du temps, afin d’en extraire les pĂ©riodes, les amplitudes apparentes, ainsi que les phases relatives des modes de pulsation dĂ©tectĂ©s, en utilisant des mĂ©thodes standards de traitement de signal, telles que des techniques de Fourier. L’étape suivante consiste Ă  comparer les pĂ©riodes de pulsation observĂ©es avec des pĂ©riodes gĂ©nĂ©rĂ©es par un modĂšle stellaire en cherchant l’accord optimal avec un modĂšle physique reconstituant le plus fidĂšlement possible l’étoile pulsante. Afin d’assurer une recherche optimale dans l’espace des paramĂštres, il est nĂ©cessaire d’avoir de bons modĂšles physiques, un algorithme d’optimisation de comparaison de pĂ©riodes efficace, et une puissance de calcul considĂ©rable. Les pĂ©riodes des modes de pulsation de modĂšles stellaires de naines blanches peuvent ĂȘtre gĂ©nĂ©ralement calculĂ©es de maniĂšre prĂ©cise et fiable sur la base de la thĂ©orie linĂ©aire des pulsations stellaires dans sa version adiabatique. Afin de dĂ©finir dans son ensemble un modĂšle statique de naine blanche propre Ă  l’analyse astĂ©rosismologique, il est nĂ©cessaire de spĂ©cifier la gravitĂ© de surface, la tempĂ©rature effective, ainsi que diffĂ©rents paramĂštres dĂ©crivant la disposition en couche de l’enveloppe. En utilisant parallĂšlement les informations obtenues de maniĂšre indĂ©pendante (tempĂ©rature effective et gravitĂ© de surface) par la mĂ©thode spectroscopique, il devient possible de vĂ©rifier la validitĂ© de la solution obtenue et de restreindre de maniĂšre remarquable l’espace des paramĂštres. L’exercice astĂ©rosismologique, s’il est rĂ©ussi, mĂšne donc Ă  la dĂ©termination prĂ©cise des paramĂštres de la structure globale de l’étoile pulsante et fournit de l’information unique sur sa structure interne et l’état de sa phase Ă©volutive. On prĂ©sente dans cette thĂšse l’analyse complĂšte rĂ©ussie, de l’extraction des frĂ©quences Ă  la solution sismique, de quatre Ă©toiles naines blanches pulsantes. Il a Ă©tĂ© possible de dĂ©terminer les paramĂštres structuraux de ces Ă©toiles et de les comparer remarquablement Ă  toutes les contraintes indĂ©pendantes disponibles dans la littĂ©rature, mais aussi d’infĂ©rer sur la dynamique interne et de reconstruire le profil de rotation interne. Dans un premier temps, on analyse le duo d’étoiles ZZ Ceti, GD 165 et Ross 548, afin de comprendre les diffĂ©rences entre leurs propriĂ©tĂ©s de pulsation, malgrĂ© le fait qu’elles soient des Ă©toiles similaires en tout point, spectroscopiquement parlant. L’analyse sismique rĂ©vĂšle des structures internes diffĂ©rentes, et dĂ©voile la sensibilitĂ© de certains modes de pulsation Ă  la composition interne du noyau de l’étoile. Afin de palier Ă  cette sensibilitĂ©, nouvellement dĂ©couverte, et de rivaliser avec les donnĂ©es de qualitĂ© exceptionnelle que nous fournissent les missions spatiales Kepler et Kepler2, on dĂ©veloppe une nouvelle paramĂ©trisation des profils chimiques dans le coeur, et on valide la robustesse de notre technique et de nos modĂšles par de nombreux tests. Avec en main la nouvelle paramĂ©trisation du noyau, on dĂ©croche enfin le ”Saint Graal” de l’astĂ©rosismologie, en Ă©tant capable de reproduire pour la premiĂšre fois les pĂ©riodes observĂ©es Ă  la prĂ©cision des observations, dans le cas de l’étude sismique des Ă©toiles KIC 08626021 et de GD 1212.The goal of this thesis is to explore the seismic potential of pulsating white dwarf stars, and in particular those having an hydrogen-rich atmosphere, the ZZ Ceti stars. The technique of asteroseismology relies on the information contained in the normal modes of vibration that can be excited during specific phases of the evolution of a star. These modes modulate the emerging flux of the pulsating star and mainly present themselves as multi-periodic luminosity variations. Asteroseismology is the science that examines the luminosity of pulsating stars as a function of time, to better extract the periods, apparent amplitudes and relative phases of the detected pulsation modes, using standard methods of signal processing such as Fourier techniques. We then compare the observed pulsation periods to periods generated from a stellar model by searching the optimal match with a physically sound model that best describes the pulsating star. To better search in parameter space, it is primordial to have good physically sound models, an efficient algorithm comparing the periods, and significant computing power. The periods of the pulsation modes of white dwarf stellar models can be generally calculated very precisely on the basis of the linear theory of stellar pulsations in its adiabatic version. To define a static white dwarf model suitable for a seismic analysis, it is necessary to specify the surface gravity, the effective temperature, and the various parameters describing the onion-like structure of the star. By using a posteriori the informations obtained independently (effective temperature and surface gravity) with the spectroscopic technique, it is then possible to confirm the validity of the solution obtained. The asteroseismic exercise, when successful, precisely determines the various parameters of the global structure of the pulsating star, and gives unique information on the internal structure of the star and the current state of its evolutionary phase. We present in this thesis the complete and successful analyses, from frequency extraction to the finding of the seismic solution, of four pulsating white dwarf stars. It was possible to determine the structural parameters of these stars and to compare them to every possible independent constraints found in the literature, but to also infer on the internal dynamic and to reconstruct the internal rotation profile. At first, we analyse the pair of ZZ Ceti stars, GD 165 and Ross 548, to better understand the differences in their pulsation spectra, notwithstanding their identical spectroscopic properties. The seismic analysis reveals different internal structures, and unravels the sensitivity of some pulsation modes to the internal composition of the core of the star. To compensate for this newly discovered sensitivity, and to rival the exceptional quality of the data coming from the spatial missions Kepler and Kepler2, we develop a new parameterization of the core chemical profiles, and we validate the robustness of our technique and our models by various tests. Having in hand the new parameterization of the core, we reach the ”Holy Grail” of asteroseismology, by being capable of reproducing for the first time the observed periods to the precision of the observations, in the study case of the stars KIC 08626021 and GD 1212

    2001-2002 Graduate Catalog

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    2000-2001 Graduate Catalog

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    Aeronautical engineering: A cumulative index to a continuing bibliography (supplement 235)

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    This publication is a cummulative index to the abstracts contained in Supplements 223 through 234 of Aeronautical Engineering: A Continuing Bibliography. The bibliographic series is compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). Seven indexes are included -- subject, personal author, corporate source, foreign technology, contract number, report number and accession number
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