623 research outputs found

    Fluid Vesicles in Flow

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    We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.Comment: 13 pages, 13 figures. Adv. Colloid Interface Sci., 201

    A geometric framework for immersogeometric analysis

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    The purpose of this dissertation is to develop a geometric framework for immersogeometric analysis that directly uses the boundary representations (B-reps) of a complex computer-aided design (CAD) model and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. Using the non-boundary-fitted mesh which does not need to conform to the shape of the object can alleviate the challenge of mesh generation for complex geometries. This also reduces the labor-intensive and time-consuming work of geometry cleanup for the purpose of obtaining watertight CAD models in order to perform boundary-fitted mesh generation. The Dirichlet boundary conditions in the fluid domain are enforced weakly over the immersed object surface in the intersected elements. The surface quadrature points for the immersed object are generated on the parametric and analytic surfaces of the B-rep models. In the case of trimmed surfaces, adaptive quadrature rule is considered to improve the accuracy of the surface integral. For the non-boundary-fitted mesh, a sub-cell-based adaptive quadrature rule based on the recursive splitting of quadrature elements is used to faithfully capture the geometry in intersected elements. The point membership classification for identifying quadrature points in the fluid domain is based on a voxel-based approach implemented on GPUs. A variety of computational fluid dynamics (CFD) simulations are performed using the proposed method to assess its accuracy and efficiency. Finally, a fluid--structure interaction (FSI) simulation of a deforming left ventricle coupled with the heart valves shows the potential advantages of the developed geometric framework for the immersogeomtric analysis with complex moving domains

    Doctor of Philosophy

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    dissertationVolumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research

    CAD-Based Porous Scaffold Design of Intervertebral Discs in Tissue Engineering

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    With the development and maturity of three-dimensional (3D) printing technology over the past decade, 3D printing has been widely investigated and applied in the field of tissue engineering to repair damaged tissues or organs, such as muscles, skin, and bones, Although a number of automated fabrication methods have been developed to create superior bio-scaffolds with specific surface properties and porosity, the major challenges still focus on how to fabricate 3D natural biodegradable scaffolds that have tailor properties such as intricate architecture, porosity, and interconnectivity in order to provide the needed structural integrity, strength, transport, and ideal microenvironment for cell- and tissue-growth. In this dissertation, a robust pipeline of fabricating bio-functional porous scaffolds of intervertebral discs based on different innovative porous design methodologies is illustrated. Firstly, a triply periodic minimal surface (TPMS) based parameterization method, which has overcome the integrity problem of traditional TPMS method, is presented in Chapter 3. Then, an implicit surface modeling (ISM) approach using tetrahedral implicit surface (TIS) is demonstrated and compared with the TPMS method in Chapter 4. In Chapter 5, we present an advanced porous design method with higher flexibility using anisotropic radial basis function (ARBF) and volumetric meshes. Based on all these advanced porous design methods, the 3D model of a bio-functional porous intervertebral disc scaffold can be easily designed and its physical model can also be manufactured through 3D printing. However, due to the unique shape of each intervertebral disc and the intricate topological relationship between the intervertebral discs and the spine, the accurate localization and segmentation of dysfunctional discs are regarded as another obstacle to fabricating porous 3D disc models. To that end, we discuss in Chapter 6 a segmentation technique of intervertebral discs from CT-scanned medical images by using deep convolutional neural networks. Additionally, some examples of applying different porous designs on the segmented intervertebral disc models are demonstrated in Chapter 6

    Analysis and Parameterization of Triangulated Surfaces

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    This dissertation deals with the analysis and parameterization of surfaces represented by triangle meshes, that is, piecewise linear surfaces which enable a simple representation of 3D models commonly used in mathematics and computer science. Providing equivalent and high-level representations of a 3D triangle mesh M is of basic importance for approaching different computational problems and applications in the research fields of Computational Geometry, Computer Graphics, Geometry Processing, and Shape Modeling. The aim of the thesis is to show how high-level representations of a given surface M can be used to find other high-level or equivalent descriptions of M and vice versa. Furthermore, this analysis is related to the study of local and global properties of triangle meshes depending on the information that we want to capture and needed by the application context. The local analysis of an arbitrary triangle mesh M is based on a multi-scale segmentation of M together with the induced local parameterization, where we replace the common hypothesis of decomposing M into a family of disc-like patches (i.e., 0-genus and one boundary component) with a feature-based segmentation of M into regions of 0-genus without constraining the number of boundary components of each patch. This choice and extension is motivated by the necessity of identifying surface patches with features, of reducing the parameterization distortion, and of better supporting standard applications of the parameterization such as remeshing or more generally surface approximation, texture mapping, and compression. The global analysis, characterization, and abstraction of M take into account its topological and geometric aspects represented by the combinatorial structure of M (i.e., the mesh connectivity) with the associated embedding in R^3. Duality and dual Laplacian smoothing are the first characterizations of M presented with the final aim of a better understanding of the relations between mesh connectivity and geometry, as discussed by several works in this research area, and extended in the thesis to the case of 3D parameterization. The global analysis of M has been also approached by defining a real function on M which induces a Reeb graph invariant with respect to affine transformations and best suited for applications such as shape matching and comparison. Morse theory and the Reeb graph were also used for supporting a new and simple method for solving the global parameterization problem, that is, the search of a cut graph of an arbitrary triangle mesh M. The main characteristics of the proposed approach with respect to previous work are its capability of defining a family of cut graphs, instead of just one cut, of bordered and closed surfaces which are treated with a unique approach. Furthermore, each cut graph is smooth and the way it is built is based on the cutting procedure of 0-genus surfaces that was used for the local parameterization of M. As discussed in the thesis, defining a family of cut graphs provides a great flexibility and effective simplifications of the analysis, modeling, and visualization of (time-depending) scalar and vector fields; in fact, the global parameterization of M enables to reduce th

    Continuum Deformation Model for Drug-Eluting Stent (DES) Medical Devices Using Finite Element Analysis (FEA)

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    The development of coronary stent medical devices was originally considered as a major advance in the treatment of obstructive cardiovascular disease. The implantation of stent, however, involves clinical adverse effects such as re-narrowing of arterial wall after stenting. Drug-eluting stents (DES) have been developed to prevent such adverse effects by slowly delivering anti-proliferative and/or anti-inflammatory drugs from coating composites of drug-containing polymers. One of the major issues in DES implantation is, however, that the coatings comprised of drug and polymer composite phases are often fractured or delaminated during the deployment of stent, which can lead to more serious clinical complications. In this study, we developed a computational model employing the finite element analysis (FEA) technique to predict the stress distributions of various components in DES medical devices including coating composites. This work is considered as one of the first attempts to address the stress concentrations of DES medical devices upon implantation using 2D/3D computational approaches. The ABAQUS commercial package (Hibbit Karlsson & Sorences Inc., Pawtucket, RI, USA) was used to perform computational analyses for systems with large elastic/plastic deformations. Designs of three commercial products (SYNERGY, TAXUS Express, and FLEX stents) available in the market have been modeled in this thesis. The displacement control method has been adopted in developing our model for the deployment of DES. Throughout the present thesis, the impacts of geometry and material variables such as stent strut/coating thicknesses and material contents in composites on the mechanical performance of the DES were quantitatively examined. Moreover, to predict the rate of in-stent restenosis (ISR), we developed a model to include the physiological environments, i.e., arterial wall and atherosclerotic plaque, in the system. From the results, it has been monitored that the strut thickness and coating thickness of DES are one of the major factors determining the amount of stress concentration on the inner surfaces of arterial wall and atherosclerotic plaque. The higher von-Mises stress accumulation was observed with thicker strut and coating. The findings indicate that the optimizing geometry of stent and coating is a critical variable to manipulate its mechanical performance and the rate of ISR. The computation results also demonstrate that the stress concentrations in the SYNERGY and FLEX DES are much lower than those observed in the TAXUS Express stents

    Virtuelle endovaskuläre Versorgung von abdominalen Aortenaneurysmen

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    This thesis is focused on computational methods that predict the outcome of endovascular repair of abdominal aortic aneurysms. Novelties include improvements of the aneurysm model, the stent-graft model as well as the in-silico stent-graft placement methodology. The newly developed methods are applied to patient-specific cases and are validated against real-world postinterventional data. Further, directions for using the in-silico model of endovascular aneurysm repair as personalized preinterventional planning tool in clinical practice are provided.Die vorliegende Arbeit beschäftigt sich mit numerischen Methoden um den Ausgang einer endovaskulären Versorgung von abdominalen Aortenaneurysmen vorherzusagen. Neuheiten umfassen Verbesserungen des Aneurysmenmodells, des Stentgraftmodells sowie der virtuellen Platzierungsmethode des Stentgrafts. Die neu entwickelten Methoden werden auf patientenspezifische Fälle angewandt und werden mit realen postoperativen Daten validiert. Weiterhin werden klinische Anwendungen des Modells der endovaskulären Aneurysmenversorgung als personalisiertes präoperatives Planungswerkzeug präsentiert

    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
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