We obtain an upper bound for decay rate of p-adic oscillatory integrals of with analytic phase function and constructible amplitude map. / Thesis / Doctor of Philosophy (PhD)

The prediction of settlements in infrastructural design puts high demands on the numerical analysis of the subsoil and the associated constitutive model: complex installation processes and the repetitive character of live loads pose considerable challenges. Although in this context the main focus is on the analytical requirements of a geotechnical problem in order to realistically capture soil behaviour, the needs of engineering practice should not be neglected in constitutive modelling. Along these lines, a new soil model for non-cohesive soils has been developed in the theoretical framework of elastoplasticity. Based on the concept of bounding surface plasticity according to Manzari and Dafalias (1997), soil properties such as strength, stiffness and dilatancy depend on the distance between the current stress state and a corresponding model surface in stress space. This way the multi surface model correctly reproduces elementary behavioural patterns of soil, including for example shear related phenomena such as hardening/softening, contraction/dilation and attainment of critical state (constant volume shear strength). Moreover, the model captures the state dependence of soil behaviour (barotropy and pycnotropy). Thus, with only one set of material parameters, the mechanical behaviour of a wide range of initial soil states with respect to stress and void ratio can be simulated (unified modelling). The kinematic hardening mechanism of the conical yield surface contributes to a realistic stiffness evolution in un- and reloading and is hence essential for stress or strain accumulation due to load reversals. Since the chosen modelling framework is suitable for further development, the original formulation has been extended to adapt the model to the defined needs. In order to adequately simulate geotechnically relevant stress paths of low and higher complexity, first of all, a cap shaped yield surface was added to allow for plastic straining not only in shear, but also in constant stress ratio loading (e. g. isotropic or oedometric compression). When it comes to stress paths of unconventional orientation, to load reversals or composed stress paths with changes in loading direction, a supplementary stiffness increase at small strains and its subsequent strain dependent degradation have proven valuable. Furthermore, an additional mechanism accounts for a regressive accumulation of stresses or strains with increasing number of load cycles (in terms of dissipated energy). In view of its suitability for practical use, all model extensions are structured in a modular fashion, so that the complexity of the model (and hence the amount of parameters) can be adapted to the complexity of the geotechnical problem by activating or deactivating certain features. Most model parameters can be determined by conventional laboratory testing. An internal routine optionally facilitates the parameter choice by calibrating certain bounding surface related parameters from an alternative user input, which is more oriented towards experimental outcome. Since a good understanding of a material model is crucial for its reasonable and responsible use, the present thesis aims at offering a sound documentation. Thus, the first part gives an outline of the underlying bounding surface concept and describes the innovations on the constitutive level with reference to theoretical considerations. It is followed by a detailed analysis of capabilities and limitations of the extended model. The next part is dedicated to the numerical implementation of the soil model and its calibration procedure on the basis of laboratory test results. Moreover, the embedded calibration routine including the applied optimisation algorithm is presented. The subsequent section serves model validation: by means of element test simulations, generation of response envelopes as well as the reproduction of more general (e. g. composed) stress paths the performance of the extended bounding surface model is demonstrated. Finally, the last chapter draws conclusions and discloses potential future perspectives.:1 Introduction 1.1 General aspects on constitutive modelling 1.2 Motivation and outline of the thesis 1.3 Basic assumptions and terminology 2 Literature review 2.1 From elastoplasticity to bounding surface plasticity 2.1.1 Bounding surface model according to Manzari and Dafalias (1997) 2.2 Further development of the original model 2.2.1 Papadimitriou and Bouckovalas (2002) 2.2.2 Taiebat and Dafalias (2008) 2.3 Small strain stiffness 2.3.1 Observations 2.3.2 Micromechanical considerations 2.3.3 Very small strain shear modulus G0 2.3.4 Constitutive modelling approaches 2.4 Dilatancy 3 The extended bounding surface model 3.1 Fundamental capabilities of the bounding surface concept 3.1.1 Elastic region 3.1.2 Critical state 3.1.3 Shear strength 3.1.4 Shear stiffness (monotonic) 3.1.5 Contractancy and dilatancy 3.1.6 Barotropy and pycnotropy 3.1.7 Compressive stiffness 3.1.8 Shear stiffness in reversed loading 3.1.9 Additional features 3.2 New features of the extended bounding surface model 3.2.1 Minor modifications 3.2.2 Dilatancy formulation 3.2.3 Cap yield surface 3.2.4 Small strain stiffness mechanism 3.2.5 Cyclic loading mechanism 3.2.6 Summary 3.3 Limitations of the bounding surface model 3.3.1 Intrinsic insuffciencies of the bounding surface concept 3.3.2 Remaining shortcomings of the advanced model version 3.3.3 Newly introduced deficiencies 4 The numerical model and its calibration procedure 4.1 Octave implementation of an element test programme 4.2 Calibration procedure 4.2.1 Sands for calibration 4.2.2 Calibration of basic parameters 4.2.3 Calibration of extended model parameters 4.3 User friendly calibration routine 4.3.1 Conceptual background 4.3.2 Optimisation algorithm 5 Performance of the extended bounding surface model 5.1 Model performance in element tests 5.1.1 Monotonic drained triaxial compression test 5.1.2 Monotonic undrained triaxial compression test 5.1.3 Monotonic eta-constant tests 5.2 Model performance in non-standard triaxial testing 5.2.1 Concept of response envelopes 5.2.2 Simulation of response envelopes 5.3 Model performance on general stress paths 5.3.1 Triaxial compression at small strains 5.3.2 Cyclic triaxial loading 6 Conclusions and perspectives 6.1 Conclusions 6.2 Future perspectives Bibliography Appendices A Mathematical background A.1 Fundamental equations of elastoplasticity A.2 Compilation of major constitutive equations (multiaxial formulation) A.3 Elastoplastic stiffness matrix for singular yield surfaces A.4 Coefficient matrices S and E for loading constraints A.5 Derivation of Mcap and Hcap A.6 Intergranular strain adjustment A.7 Intergranular strain correlation B Details on particle swarm optimisation C Compilation of simulation results C.1 Monotonic triaxial loading C.1.1 Toyoura sand C.1.2 Sacramento River sand C.1.3 Hostun sand C.2 Monotonic eta-constant loading C.2.1 Sacramento River sand C.2.2 Hostun sand C.3 Cyclic triaxial loading / Die Prognose von Setzungen für die Bemessung von Infrastrukturbauwerken stellt hohe Anforderungen an die numerische Untersuchung des Baugrunds und das damit verbundene Stoffgesetz: komplexe Herstellungsprozesse und zyklisch wiederkehrende Verkehrslasten stellen beachtliche Herausforderungen dar. Während das Hauptaugenmerk zumeist auf der realitätsnahen Abbildung des Bodenverhaltens liegt und damit die analytischen Anforderungen des geotechnischen Problems im Fokus stehen, sollten die Bedürfnisse der Ingenieurspraxis in der Stoffgesetzmodellierung nicht außer Acht gelassen werden. In diesem Sinne wurde im Rahmen der Elastoplastizität ein neues Materialmodell für nichtbindige Böden entwickelt. Auf dem Konzept der Bounding Surface Plastizität nach Manzari und Dafalias (1997) beruhend, sind Eigenschaften wie Festigkeit, Steifigkeit und Dilatanz Funktion des Abstands zwischen aktuellem Spannungszustand und einer zugeordneten Modellfläche im Spannungsraum. Auf diese Weise bildet das Mehrflächenmodell fundamentale Verhaltensmuster von Boden korrekt ab, einschließlich beispielsweise scherbezogener Phänomene wie Ver- und Entfestigung, Kontraktanz und Dilatanz oder das Erreichen des kritischen Zustands (Scherfestigkeit bei konstantem Volumen). Des Weiteren erfasst das Modell die Zustandsabhängigkeit des Bodenverhaltens (Barotropie und Pyknotropie). So kann mit nur einem Parametersatz das mechanische Verhalten einer großen Spannweite unterschiedlicher Anfangszustände hinsichtlich Spannung und Lagerungsdichte simuliert werden. Der kinematische Verfestigungsmechanismus der konusförmigen Fließfläche trägt bei Ent- und Wiederbelastungen zu einer realistischeren Steifigkeitsentwicklung bei und ist damit von essenzieller Bedeutung für die Akkumulation von Spannungen oder Verformungen infolge von Lastwechseln. Da sich der gewählte konstitutive Rahmen für Weiterentwicklungen eignet, wurde die ursprüngliche Formulierung des Stoffgesetzes erweitert, um das Modell an die definierten Anforderungen anzupassen. Um geotechnisch relevante Spannungspfade niedriger und höherer Komplexität adäquat reproduzieren zu können, wurde zunächst eine kappenförmige Fließfläche ergänzt. So können irreversible Verformungen nicht nur bei Scherung, sondern auch bei Belastungen ohne Änderung des Spannungsverhältnisses, wie z. B. bei isotroper oder ödometrischer Kompression, auftreten. Bei Spannungspfaden ungewöhnlicher Orientierung, bei Lastwechseln oder zusammengesetzten Spannungspfaden mit Änderung der Belastungsrichtung hat sich eine erhöhte Steifigkeit bei kleinen Dehnungen mit anschließendem dehnungsabhängigen Abfall als nützlich erwiesen. Darüber hinaus berücksichtigt ein zusätzlicher Mechanismus die rückläufige Akkumulation von Spannung oder Verformung mit zunehmender Zyklenanzahl (mittels dissipierter Energie). Im Hinblick auf die Eignung des Stoffgesetzes für die Praxis ist das Modell modular aufgebaut. So kann die Komplexität des Modells (und damit die Anzahl der Parameter) durch Ein- und Ausschalten bestimmter Erweiterungen an die Komplexität des geotechnischen Problems angepasst werden. Die Mehrzahl der Modellparameter wird mit Hilfe konventioneller Laborversuche bestimmt. Eine interne Routine erleichtert durch die Kalibrierung bestimmter Bounding Surface bezogener Größen anhand eines alternativen, stärker an Versuchsergebnissen orientierten User-Inputs bei Bedarf die Parameterwahl. Da die Kenntnis eines Stoffgesetzes entscheidend ist für dessen vernünftigen und verantwortungsvollen Einsatz, soll die vorliegende Arbeit eine fundierte und umfassende Dokumentation bieten. Der erste Teil vermittelt daher zunächst einen Überblick über das zugrunde liegende Bounding Surface Konzept und beschreibt die Neuerungen auf konstitutiver Ebene mit Bezug auf theoretische Hintergründe. Er wird gefolgt von einer detaillierten Darlegung von Potenzialen und Einschränkungen für die Nutzung des erweiterten Modells. Der nächste Abschnitt widmet sich der numerischen Implementierung des Stoffgesetzes und seiner Kalibrierung auf Basis von Versuchsergebnissen. Des Weiteren wird die Kalibrierungsroutine einschließlich des verwendeten Optimierungsalgorithmus präsentiert. Der nachfolgende Teil dient der Modellvalidierung: durch die Simulation von Elementversuchen, die Erzeugung von Antwortellipsen sowie die Abbildung allgemeinerer (beispielsweise zusammengesetzter) Spannungspfade wird die Leistungsfähigkeit des erweiterten Bounding Surface Modells demonstriert. Abschließend werden Schlussfolgerungen gezogen und potenzielle Perspektiven aufgezeigt.:1 Introduction 1.1 General aspects on constitutive modelling 1.2 Motivation and outline of the thesis 1.3 Basic assumptions and terminology 2 Literature review 2.1 From elastoplasticity to bounding surface plasticity 2.1.1 Bounding surface model according to Manzari and Dafalias (1997) 2.2 Further development of the original model 2.2.1 Papadimitriou and Bouckovalas (2002) 2.2.2 Taiebat and Dafalias (2008) 2.3 Small strain stiffness 2.3.1 Observations 2.3.2 Micromechanical considerations 2.3.3 Very small strain shear modulus G0 2.3.4 Constitutive modelling approaches 2.4 Dilatancy 3 The extended bounding surface model 3.1 Fundamental capabilities of the bounding surface concept 3.1.1 Elastic region 3.1.2 Critical state 3.1.3 Shear strength 3.1.4 Shear stiffness (monotonic) 3.1.5 Contractancy and dilatancy 3.1.6 Barotropy and pycnotropy 3.1.7 Compressive stiffness 3.1.8 Shear stiffness in reversed loading 3.1.9 Additional features 3.2 New features of the extended bounding surface model 3.2.1 Minor modifications 3.2.2 Dilatancy formulation 3.2.3 Cap yield surface 3.2.4 Small strain stiffness mechanism 3.2.5 Cyclic loading mechanism 3.2.6 Summary 3.3 Limitations of the bounding surface model 3.3.1 Intrinsic insuffciencies of the bounding surface concept 3.3.2 Remaining shortcomings of the advanced model version 3.3.3 Newly introduced deficiencies 4 The numerical model and its calibration procedure 4.1 Octave implementation of an element test programme 4.2 Calibration procedure 4.2.1 Sands for calibration 4.2.2 Calibration of basic parameters 4.2.3 Calibration of extended model parameters 4.3 User friendly calibration routine 4.3.1 Conceptual background 4.3.2 Optimisation algorithm 5 Performance of the extended bounding surface model 5.1 Model performance in element tests 5.1.1 Monotonic drained triaxial compression test 5.1.2 Monotonic undrained triaxial compression test 5.1.3 Monotonic eta-constant tests 5.2 Model performance in non-standard triaxial testing 5.2.1 Concept of response envelopes 5.2.2 Simulation of response envelopes 5.3 Model performance on general stress paths 5.3.1 Triaxial compression at small strains 5.3.2 Cyclic triaxial loading 6 Conclusions and perspectives 6.1 Conclusions 6.2 Future perspectives Bibliography Appendices A Mathematical background A.1 Fundamental equations of elastoplasticity A.2 Compilation of major constitutive equations (multiaxial formulation) A.3 Elastoplastic stiffness matrix for singular yield surfaces A.4 Coefficient matrices S and E for loading constraints A.5 Derivation of Mcap and Hcap A.6 Intergranular strain adjustment A.7 Intergranular strain correlation B Details on particle swarm optimisation C Compilation of simulation results C.1 Monotonic triaxial loading C.1.1 Toyoura sand C.1.2 Sacramento River sand C.1.3 Hostun sand C.2 Monotonic eta-constant loading C.2.1 Sacramento River sand C.2.2 Hostun sand C.3 Cyclic triaxial loading

<p>This paper presents techniques for speeding up commonly used algorithms forbounding volume (BV) computation, such as the AABB, sphere and k-DOP. Byexploiting the possibilities of parallelismin modern processors, the result exceedsthe expected theoretical result. The methods focus on data-level-parallelism(DLP) using Intel’s SSE instructions, for operations on 4 parallel independentsingle precision floating point values, with a theoretical speed-up factor of 4 ondata throughput. Still, a speed-up between 7–9 are shown in the computation ofAABBs and k-DOPs. For the computation of tight fitting spheres the speed-upfactor halts at approximately 4 due to a limiting data dependency. In addition,further parallelization by multithreading algorithms on multi-core CPUs showsspeed-up factors of 14 on 2 cores and reaching 25 on 4 cores, compared to nonparallel algorithms.</p>

To teleoperate an unmanned vehicle a rich set of information should be gathered from surroundings.These systems use sensors which sends high amounts of data and processing the data in CPUs can be time consuming. Similarly, the algorithms that use the data may work slow because of the amount of the data. The solution is, preprocessing the data taken from the sensors on the vehicle and transmitting only the necessary parts or the results of the preprocessing. In this thesis a 180 degree laser scanner at the front end of an unmanned ground vehicle (UGV) tilted up and down on a horizontal axis and point clouds constructed from the surroundings. Instead of transmitting this data directly to the path planning or obstacle avoidance algorithms, a preprocessing stage has been run. In this preprocess rst, the points belonging to the ground plane have been detected and a simplied version of ground has been constructed then the obstacles have been detected. At last, a simplied ground plane as ground and simple primitive geometric shapes as obstacles have been sent to the path planning algorithms instead of sending the whole point cloud.

This paper presents techniques for speeding up commonly used algorithms forbounding volume (BV) computation, such as the AABB, sphere and k-DOP. Byexploiting the possibilities of parallelismin modern processors, the result exceedsthe expected theoretical result. The methods focus on data-level-parallelism(DLP) using Intel’s SSE instructions, for operations on 4 parallel independentsingle precision floating point values, with a theoretical speed-up factor of 4 ondata throughput. Still, a speed-up between 7–9 are shown in the computation ofAABBs and k-DOPs. For the computation of tight fitting spheres the speed-upfactor halts at approximately 4 due to a limiting data dependency. In addition,further parallelization by multithreading algorithms on multi-core CPUs showsspeed-up factors of 14 on 2 cores and reaching 25 on 4 cores, compared to nonparallel algorithms.

Ray tracing is a computationally complex global illumination algorithm that is used for producing realistic images. In addition to parallel implementations on commodity PC clusters, recently, Graphics Processing Units (GPU) have also been used to accelerate ray tracing. In this thesis, ray tracing is accelerated on a GPU cluster where the viewing plane is divided into unit tiles. Slave processes work on these tiles in a task parallel manner which are dynamically assigned to them. To decrease the number of ray-triangle intersection tests, Bounding Volume Hierarchies (BVH) are used. It is shown that almost linear speedup can be achieved. On the other hand, it is observed that API and network overheads are obstacles for scalability.

In this study, we consider a resource investment problem with time/resource trade-offs in project environments. We assume each mode of an activity is characterized by its processing time and resource requirement and there is a single renewable resource. Our aim is to minimize the maximum resource usage, hence the total amount invested for the single resource. We formulate the problem as a mixed integer linear model and find optimal solutions for small sized problem instances. We propose several lower bounding procedures to find high quality estimates on the optimal resource investment cost. We use our lower bounds to evaluate the performance of our heuristic procedures. The results of our computational experiments have revealed the satisfactory performances of our lower bounds and heuristic procedures. Projects, Resource Investment Time/Resource Trade-off, Bounding Procedures

Crowd simulations are attracting increasing attention from both academia and the industry field and are implemented across a vast range of applications, from scientific demonstrations to video games and films. As such, the demand for greater realism in their aesthetics and the amount of agents involved is always growing. A successful crowd simulation must simulate large numbers of pedestrians' behaviours as realistically as possible in real-time. The thesis looks at two important aspects of crowd simulation and real-time animation. First, this thesis introduces a new data structure called Extended Oriented Bounding Box (EOBB) and related methods for fast collision detection and obstacle avoidance in the simulation of crowd motion in virtual environments. The EOBB is extended to contain a region whose size is defined based on the instantaneous velocity vector, thus allowing a bounding volume representation of both geometry and motion. Such a representation is also found to be highly effective in motion planning using the location of vertices of bounding boxes in the immediate neighbourhood of the current crowd member. Second, we present a detailed analysis of the effectiveness of spatial subdivision data structures, specifically for large-scale crowd simulation. For large-scale crowd simulation, computational time for collision detection is huge, and many studies use spatial partitioning data structure to reduce the computational time, depicting their strengths and weaknesses, but few compare multiple methods in an effort to present the best solution. This thesis attempts to address this by implementing and comparing four popular spatial partitioning data structures with the EOBB.

[pt] A restituição de modelos tridimensionais complexos de engenharia tem sido um desafio para a computação gráfica desde seus primórdios, pois modelos detalhados são freqüentemente compostos de milhões de polígonos, enquanto as estações gráficas atuais são capazes de exibir, em taxas interativas, apenas algo da ordem de dezenas ou centenas de milhares de polígonos. Uma das formas de melhorar o desempenho de visualizadores de modelos tridimensionais é reduzir o número de polígonos passados para a cadeia de restituição, eliminando grandes grupos de polígonos determinados como não visíveis por estarem fora do volume de visão ou escondidos por outros polígonos. Neste trabalho, realizamos um estudo do uso de volumes envolventes para determinar os conjuntos de polígonos que são potencialmente visíveis, propomos uma forma de estruturar esses polígonos numa hierarquia de forma a diminuir os cálculos necessários para esse fim e compilamos uma série de resultados que permitem nortear o uso de volumes envolventes e a estruturação de modelos. / [en] Rendering complex three-dimensional Engineering models has been a challenge for Computer Graphics ever since its origin, as detailed models are often composed of millions of polygons while current graphic stations are able to display, at interactive rates, only dozens or hundreds of thousands of polygons. A way to increase the performance of viewers of three-dimensional models is to reduce the number of polygons passed to the rendering pipeline by eliminating large groups of polygons classified as non-visible for being out of the viewing frustum or hidden by other polygons. In this work, we study the use of bounding volumes to determine sets of polygons which are potentially visible, propose a way to structure such polygons in a hierarchy so as to restrict the necessary computations for this purpose, and compile a series of results which allow us to take some conclusions on the use of bounding volumes and model structuring.

This work deals with a theoretical analysis of contacting semiconductor chips using wire-bonding method. There are mentioned basic types of chips packages and their contacts. In the thesis is also described software Ansys. The number of the mechanical stress and deformation simulation within micro-wire during thermocompress process were made.