12 research outputs found
Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization
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
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
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
Generalized averaged Gaussian quadrature and applications
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
Exploitation du potentiel sismique des Ă©toiles naines blanches
Le but de cette thĂšse est dâexplorer 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
dâastĂ©rosismologie exploite lâinformation contenue dans les modes normaux de vibration qui
peuvent ĂȘtre excitĂ©s lors de phases particuliĂšres de lâĂ©volution dâune Ă©toile. Ces modes modulent
le flux Ă©mergent de lâĂ©toile pulsante et se manifestent principalement en termes de
variations lumineuses multi-pĂ©riodiques. LâastĂ©rosismologie consiste donc Ă examiner la luminositĂ© dâĂ©toiles pulsantes en fonction du temps, afin dâen extraire les pĂ©riodes, les amplitudes
apparentes, ainsi que les phases relatives des modes de pulsation détectés, en utilisant des
mĂ©thodes standards de traitement de signal, telles que des techniques de Fourier. LâĂ©tape suivante
consiste à comparer les périodes de pulsation observées avec des périodes générées par
un modĂšle stellaire en cherchant lâaccord optimal avec un modĂšle physique reconstituant le
plus fidĂšlement possible lâĂ©toile pulsante. Afin dâassurer une recherche optimale dans lâespace
des paramĂštres, il est nĂ©cessaire dâavoir de bons modĂšles physiques, un algorithme dâoptimisation
de comparaison de périodes efficace, et une puissance de calcul considérable. Les périodes
des modes de pulsation de modĂšles stellaires de naines blanches peuvent ĂȘtre gĂ©nĂ©ralement
calculées de maniÚre précise et fiable sur la base de la théorie linéaire des pulsations stellaires
dans sa version adiabatique. Afin de définir dans son ensemble un modÚle statique de
naine blanche propre Ă lâanalyse astĂ©rosismologique, il est nĂ©cessaire de spĂ©cifier la gravitĂ©
de surface, la température effective, ainsi que différents paramÚtres décrivant la disposition
en couche de lâenveloppe. En utilisant parallĂšlement les informations obtenues de maniĂšre
indépendante (température effective et gravité de surface) par la méthode spectroscopique,
il devient possible de vérifier la validité de la solution obtenue et de restreindre de maniÚre
remarquable lâespace des paramĂštres. Lâexercice astĂ©rosismologique, sâil est rĂ©ussi, mĂšne donc
Ă la dĂ©termination prĂ©cise des paramĂštres de la structure globale de lâĂ©toile pulsante et fournit
de lâinformation unique sur sa structure interne et lâĂ©tat de sa phase Ă©volutive.
On prĂ©sente dans cette thĂšse lâanalyse complĂšte rĂ©ussie, de lâextraction des frĂ©quences Ă
la solution sismique, de quatre étoiles naines blanches pulsantes. Il a été possible de déterminer
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 dâinfĂ©rer sur la dynamique
interne et de reconstruire le profil de rotation interne. Dans un premier temps, on
analyse le duo dâĂ©toiles ZZ Ceti, GD 165 et Ross 548, afin de comprendre les diffĂ©rences entre
leurs propriĂ©tĂ©s de pulsation, malgrĂ© le fait quâelles soient des Ă©toiles similaires en tout point,
spectroscopiquement parlant. Lâanalyse sismique rĂ©vĂšle des structures internes diffĂ©rentes, et
dévoile la sensibilité de certains modes de pulsation à la composition interne du noyau de
lâĂ©toile. 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 développe une nouvelle paramétrisation 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 âSaint Graalâ de lâastĂ©rosismologie,
en étant capable de reproduire pour la premiÚre fois les périodes observées à la précision des
observations, dans le cas de lâĂ©tude 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 âHoly Grailâ 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
Neural Radiance Fields: Past, Present, and Future
The various aspects like modeling and interpreting 3D environments and
surroundings have enticed humans to progress their research in 3D Computer
Vision, Computer Graphics, and Machine Learning. An attempt made by Mildenhall
et al in their paper about NeRFs (Neural Radiance Fields) led to a boom in
Computer Graphics, Robotics, Computer Vision, and the possible scope of
High-Resolution Low Storage Augmented Reality and Virtual Reality-based 3D
models have gained traction from res with more than 1000 preprints related to
NeRFs published. This paper serves as a bridge for people starting to study
these fields by building on the basics of Mathematics, Geometry, Computer
Vision, and Computer Graphics to the difficulties encountered in Implicit
Representations at the intersection of all these disciplines. This survey
provides the history of rendering, Implicit Learning, and NeRFs, the
progression of research on NeRFs, and the potential applications and
implications of NeRFs in today's world. In doing so, this survey categorizes
all the NeRF-related research in terms of the datasets used, objective
functions, applications solved, and evaluation criteria for these applications.Comment: 413 pages, 9 figures, 277 citation
Robot Manipulators
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
Innovative configurations of thermochemical energy storage devices by topology optimization
One of the main challenges to increasing the share of renewable energy sources in future energy scenarios is the mismatch between energy supply and demand. Thermal energy storage technologies have been identified as one possible solution to this challenge. Among the different thermal energy storage technologies, thermochemical energy storage devices are envisioned to have a large impact due to large theoretical energy density, negligible heat losses and possible heat-upgradation. Such devices rely on reversible chemical reactions where the energy is first stored in the form of chemical compounds generated by means of an endothermic reaction and recovered later on by recombining the compounds to drive an exothermic reaction.
However, several technical limitations still hamper the successful introduction of thermochemical energy storage technologies in the market. In particular, the effective configuring of these devices is a complex engineering challenge due to the intrinsic dynamic operation, the complex multi-physics problems involved and the vast range of system requirements. Furthermore, standard design approaches are often driven by the analystsâ insight and experience, constraining the assessed configurations to a limited number of conceived solutions and precluding the full exploitation of the potential storage material.
To break these barriers, this dissertation explores the use of topology optimization as a systematic design tool for the effective configuration of thermochemical energy storage devices Topology optimization is a form-finding methodology able to identify optimal designs without the need for any guess regarding the initial layout. Compared to conventional design approaches, the key advantage of topology optimization is thus its matchless design freedom. Novel enhancement pathways are identified by the analysis of the emerging design trends, and design solutions that outperform the current state-of-the-art are obtained.
Specifically, this dissertation studies the heat transfer enhancement of reactive beds through the insertion of extended surfaces made of highly conductive material. Design guidelines for practitioners are derived from the analysis of the generated designs for variable bed properties, desired discharge time and bed size. Thus, the mass transfer enhancement of reactive beds is achieved through the generation of non-intuitive flow channel geometries aiming to effectively distribute gas reactants to reactive sites. Finally, the two approaches are combined to generate reactive beds employing optimized flow channel and extended surface geometries, ultimately leading to the concurrent enhancement of heat and mass transfer
Aeronautical engineering: A cumulative index to a continuing bibliography (supplement 235)
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