326 research outputs found
A high-performance boundary element method and its applications in engineering
As a semi-numerical and semi-analytical method, owing to the inherent advantage, of boundary-only discretisation, the boundary element method (BEM) has been widely applied to problems with complicated geometries, stress concentration problems, infinite domain problems, and many others. However, domain integrals and non-symmetrical and dense matrix systems are two obstacles for BEM which have hindered the its further development and application. This thesis is aimed at proposing a high-performance BEM to tackle the above two drawbacks and broaden the application scope of BEM. In this thesis, a detailed introduction to the traditional BEM is given and several popular algorithms are introduced or proposed to enhance the performance of BEM. Numerical examples in heat conduction analysis, thermoelastic analysis and thermoelastic fracture problems are performed to assess the efficiency and correction of the algorithms. In addition, necessary theoretical derivations are embraced for establishing novel boundary integral equations (BIEs) for specific engineering problems. The following three parts are the main content of this thesis. (1) The first part (Part II consisting of two chapters) is aimed at heat conduction analysis by BEM. The coefficient matrix of equations formed by BEM in solving problems is fully-populated which occupy large computer memory. To deal with that, the fast multipole method (FMM) is introduced to energize the line integration boundary element method (LIBEM) to performs better in efficiency. In addition, to compute domain integrals with known or unknown integrand functions which are caused by heat sources or heterogeneity, a novel BEM, the adaptive orthogonal interpolation moving least squares (AOIMLS) method enhanced LIBEM, which also inherits the advantage of boundary-only discretisation, is proposed. Unlike LIBEM, which is an accurate and stable method for computing domain integrals, but only works when the mathematical expression of integral function in domain integrals is known, the AOIMLS enhanced LIBEM can compute domain integrals with known or unknown integral functions, which ensures all the nonlinear and nonhomogeneous problems can be solved without domain discretisation. In addition, the AOIMLS can adaptively avoid singular or ill-conditioned moment matrices, thus ensuring the stability of the calculation results. (2) In the second part (Part III consisting of four chapters), the thermoelastic problems and fracture problems are the main objectives. Due to considering thermal loads, domain integrals appear in the BIEs of the thermoelastic problems, and the expression of integrand functions is known or not depending on the temperature distribution given or not, the AOIMLS enhanced LIBEM is introduced to conduct thermoelasticity analysis thereby. Besides, a series of novel unified boundary integral equations based on BEM and DDM are derived for solving fracture problems and thermoelastic fracture problems in finite and infinite domains. Two sets of unified BIEs are derived for fracture problems in finite and infinite domains based on the direct BEM and DDM respectively, which can provide accurate and stable results. Another two sets of BIEs are addressed by employing indirect BEM and DDM, which cannot ensure a stable result, thereby a modified indirect BEM is proposed which performs much more stable. Moreover, a set of novel BIEs based on the direct BEM and DDM for cracked domains under thermal stress is proposed. (3) In the third part (Part IV consisting of one chapter), a high-efficiency combined BEM and discrete element method (DEM) is proposed to compute the inner stress distribution and particle breakage of particle assemblies based on the solution mapping scheme. For the stress field computation of particles with similar geometry, a template particle is used as the representative particle, so that only the related coefficient matrices of one template particle in the local coordinate system are needed to be calculated, while the coefficient matrices of the other particles, can be obtained by mapping between the local and global coordinate systems. Thus, the combined BEM and DEM is much more effective when modelling a large-scale particle system with a small number of distinct possible particle shapes. Furthermore, with the help of the Hoek-Brown criterion, the possible cracks or breakage paths of a particle can be obtained
Algorithms for Triangles, Cones & Peaks
Three different geometric objects are at the center of this dissertation: triangles, cones and peaks.
In computational geometry, triangles are the most basic shape for planar subdivisions.
Particularly, Delaunay triangulations are a widely used for manifold applications in engineering, geographic information systems, telecommunication networks, etc.
We present two novel parallel algorithms to construct the Delaunay triangulation of a given point set.
Yao graphs are geometric spanners that connect each point of a given set to its nearest neighbor in each of cones drawn around it.
They are used to aid the construction of Euclidean minimum spanning trees
or in wireless networks for topology control and routing.
We present the first implementation of an optimal -time sweepline algorithm to construct Yao graphs.
One metric to quantify the importance of a mountain peak is its isolation.
Isolation measures the distance between a peak and the closest point of higher elevation.
Computing this metric from high-resolution digital elevation models (DEMs) requires efficient algorithms.
We present a novel sweep-plane algorithm that can calculate the isolation of all peaks on Earth in mere minutes
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
Simulation of fracture slip and propagation in hydraulic stimulation of geothermal reservoirs
Rollen til hydraulisk stimulering i å øke produksjonen fra geotermiske reservoarer, og muliggjøre kommersiell utnyttelse av et større spekter av geotermiske ressurser, har fått økt oppmerksomhet de siste tiårene. Under stimulering kan eksisterende sprekker sideforskyves, forplante seg og koble seg til andre sprekker og der igjennom øke permeabiliteten i reservoaret. Prosessene er preget av sterke hydromekaniske interaksjoner, som vi har begrensede muligheter til å overvåke. Numeriske simuleringer er derfor et viktig verktøy for å hjelpe oss til å bedre forstå mekanismene som er i spill.
Avhandlingen tar sikte på å utvikle en omfattende matematisk modell og en numerisk tilnærming for å analysere bruddmekanismer og undersøke koblede hydromekaniske prosesser som forekommer i oppsprukne porøse medier. Den foreslåtte modellen benytter en blandet-dimensjonal konseptuell modell, som inkluderer porelastisitet i det porøse mediet og kontaktmekanikk for sprekkene. Modellen tillater også forplantning og koalescens av eksisterende sprekker.
Et nytt diskretiseringsskjema for å løse den foreslåtte matematiske modellen presenteres. Den foreslåtte metoden bruker en to-nivå simuleringstilnærming, kategorisert i grove og fine nivåer, for å redusere beregningskostnader og sikre nøyaktighet. En endelig volummetode kombineres med en aktiv-sett løsningsstrategi for å diskretisere porelastisitet og bruddkontaktmekanikk på det grove nivået. Sprekkeforplantning betraktes på et fint nivå, der en endelig elementmetode kombineres med kollapsede kvartpunktselementer for å approksimere singulariteten i spenningen ved enden av sprekkene. Adaptiv gitring basert på en feilestimator og Laplace-glatting av gitteret introduseres på begge nivåer for effektivt å håndtere sprekkepropagering og koalescens. Simuleringene utført i denne avhandlingen forbedrer vår forståelse av hydraulisk stimulering og dens effekt på forbedring av sprekkepermeabilitet og konnektivitet i geotermiske reservoarer.The role of hydraulic stimulation in enhancing geothermal reservoir production and allowing for commercial exploitation of a larger range of geothermal resources has attracted attention from researchers in recent decades. During stimulation, preexisting fractures may slip, propagate, and connect to other fractures to enhance permeability. The processes are characterized by strong hydromechanical interactions, which have limited monitoring opportunities. Therefore, numerical simulations provide a powerful tool to help us better understand the mechanisms.
This thesis aims to develop a comprehensive mathematical model and a numerical approach to analyze fracture mechanisms, and to investigate the coupled hydromechanical processes occurring in fractured porous media. The proposed model will employ a mixed-dimensional conceptual model, incorporating the concepts of poroelasticity and fracture contact mechanics. The model will also allow for the growth and coalescence of preexisting fractures.
A novel discretization scheme for solving the proposed mathematical model is presented. The proposed scheme employs a two-level simulation approach, categorized into coarse and fine levels, to reduce the computational costs and ensure accuracy. A finite volume method is combined with an active set strategy to discretize poroelasticity and fracture contact mechanics on the coarse level. Fracture propagation is considered on a fine level, in which a finite element method is combined with collapsed quarter-point elements to capture the stress singularity at the fracture tips. Adaptive remeshing based on an error estimator and Laplacian smoothing is introduced on both levels to effectively capture fracture propagation and coalescence in the computational grid. The simulations conducted in this thesis improve our understanding of hydraulic stimulation and its effect on enhancing fracture permeability and connectivity in geothermal reservoirs.Doktorgradsavhandlin
In-situ monitoring and intermittent controller for adaptive trajectory generation during laser directed energy deposition via powder feeding
Laser Directed Energy Deposition (LDED) is one of the advanced manufacturing technologies for building near-net-shaped engineering components in a layer-by-layer fashion using high-power lasers as an energy source. LDED using powder feeding (LDED-PF) is widely used due to its higher dimensional accuracy and ability to build fine features. The quality and performance of LDED-PF-built components are dependent on several factors such as process parameters, process conditions, feedstock properties, system configuration, tool-path generation, etc. Among the above, trajectory control is one of the emerging and active areas of research. Generally, trajectories are developed offline for printing the parts. However, some of the major challenges involved in conventional trajectory development for LDED-PF are the propensity for collision between the deposition head/ nozzle and the part being built and challenges in building components with variable overhang.
The major goal of this work is the development of adaptive trajectory control of the LDED-PF process using online and offline techniques to build high-quality components. The work involves the offline trajectory development to build complex-shaped components with variable overhang angles by considering collision between the nozzle head and the part; adaptive layer thickness for higher dimensional accuracy. In addition, the work is extended to the development of online and intermittent trajectory control using a combination of in-situ surface quality monitoring and machine learning technique.
Offline trajectory planning is performed for two complex-shaped geometries such as a hemispherical dome and a bent pipe. Offline adaptive trajectory planning for hemispherical dome involves the development of an algorithm including the deposition parameters with variable overhang and collision checking, while the trajectory planning for building bent pipe structures includes the deployment of adaptive slicing in addition to the collision check and overhang angle deposition. To manufacture the dome, the tilt angle is used to avoid the collision between the nozzle and previously built material with a condition that the tilt angle cannot exceed the maximum allowable overhang angle. The algorithm verifies the tilt angle suitable to build the dome and the angle is transferred from the tilt angle to the tilt angle of the rotary table. In order to build the bent pipe geometry, the variation in scanning speed is used to realize the adaptive slicing, which aids in having point-to-point variable layer height thereby permitting non-parallel deposition. In addition, changing the tool orientation during the deposition permits the manufacturing of support-free bent pipe parts as observed for dome structures. LDED-PF of the hemispherical dome and bent pipe was performed using the developed algorithms and the built geometries have good dimensional stability and density.
In the case of online trajectory planning, a novel in-situ monitoring software platform was developed for the online surface anomaly detection of LDED-PF parts using machine learning techniques. The above starts with the development of a novel method to calibrate the laser line scanner with respect to the robotic end-effector with sub 0.5 mm accuracy. Subsequently, 2D surface profiles obtained from the LDED-PF built part surface using the laser scanner are stitched together to create an accurate 3D point cloud representation. Further, the point cloud data is processed, and defect detection is carried out using unsupervised learning and supervised (deep) learning techniques. Further, the developed defect detection software platform was used to create an online adaptive toolpath trajectory control platform to correct the dimensional inaccuracies in-situ. It uses a laser line scanner to scan the part after the deposition of the definite number of layers followed by the detection of concave, convex, and flat surfaces using deep learning. Further, the developed adaptive trajectory planning algorithm is deployed by using three different strategies to control material deposition on concave, convex, and flat surfaces. The material deposition is controlled by using adaptive scanning speed, and a combination of laser on-off and scanning speed. Subsequently, the built geometries are subjected to geometric, microstructure, and mechanical characterizations. The study offers an integrated and complete methodology for developing high-quality components using LDED-PF with a minimal dimensional deviation from the original CAD model
VOLMAP: a Large Scale Benchmark for Volume Mappings to Simple Base Domains
Correspondences between geometric domains (mappings) are ubiquitous in computer graphics and engineering, both for a variety of downstream applications and as core building blocks for higher level algorithms. In particular, mapping a shape to a convex or star-shaped domain with simple geometry is a fundamental module in existing pipelines for mesh generation, solid texturing, generation of shape correspondences, advanced manufacturing etc. For the case of surfaces, computing such a mapping with guarantees of injectivity is a solved problem. Conversely, robust algorithms for the generation of injective volume mappings to simple polytopes are yet to be found, making this a fundamental open problem in volume mesh processing. VOLMAP is a large scale benchmark aimed to support ongoing research in volume mapping algorithms. The dataset contains 4.7K tetrahedral meshes, whose boundary vertices are mapped to a variety of simple domains, either convex or star-shaped. This data constitutes the input for candidate algorithms, which are then required to position interior vertices in the domain to obtain a volume map. Overall, this yields more than 22K alternative test cases. VOLMAP also comprises tools to process this data, analyze the resulting maps, and extend the dataset with new meshes, boundary maps and base domains. This article provides a brief overview of the field, discussing its importance and the lack of effective techniques. We then introduce both the dataset and its major features. An example of comparative analysis between two existing methods is also present
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