Watertight conversion of trimmed CAD surfaces to Clough-Tocher splines

The boundary representations (B-reps) that are used to represent shape in Computer-Aided Design systems create unavoidable gaps at the face boundaries of a model. Although these inconsistencies can be kept below the scale that is important for visualisation and manufacture, they cause problems for many downstream tasks, making it difficult to use CAD models directly for simulation or advanced geometric analysis, for example. Motivated by this need for watertight models, we address the problem of converting B-rep models to a collection of cubic C1C1 Clough–Tocher splines. These splines allow a watertight join between B-rep faces, provide a homogeneous representation of shape, and also support local adaptivity. We perform a comparative study of the most prominent Clough–Tocher constructions and include some novel variants. Our criteria include visual fairness, invariance to affine reparameterisations, polynomial precision and approximation error. The constructions are tested on both synthetic data and CAD models that have been triangulated. Our results show that no construction is optimal in every scenario, with surface quality depending heavily on the triangulation and parameterisation that are used.This research was supported by the Engineering and Physical Sciences Research Council through Grant EP/K503757/1.This is the final version. It was first published by Elsevier at http://www.sciencedirect.com/science/article/pii/S0167839615000795

Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures

A novel surface interrogation technique is proposed to compute the intersection of curves with spline surfaces in isogeometric analysis. The intersection points are determined in one-shot without resorting to a Newton-Raphson iteration or successive refinement. Surface-curve intersection is required in a wide range of applications, including contact, immersed boundary methods and lattice-skin structures, and requires usually the solution of a system of nonlinear equations. It is assumed that the surface is given in form of a spline, such as a NURBS, T-spline or Catmull-Clark subdivision surface, and is convertible into a collection of B\'ezier patches. First, a hierarchical bounding volume tree is used to efficiently identify the B\'ezier patches with a convex-hull intersecting the convex-hull of a given curve segment. For ease of implementation convex-hulls are approximated with k-dops (discrete orientation polytopes). Subsequently, the intersections of the identified B\'ezier patches with the curve segment are determined with a matrix-based implicit representation leading to the computation of a sequence of small singular value decompositions (SVDs). As an application of the developed interrogation technique the isogeometric design and analysis of lattice-skin structures is investigated. The skin is a spline surface that is usually created in a computer-aided design (CAD) system and the periodic lattice to be fitted consists of unit cells, each containing a small number of struts. The lattice-skin structure is generated by projecting selected lattice nodes onto the surface after determining the intersection of unit cell edges with the surface. For mechanical analysis, the skin is modelled as a Kirchhoff-Love thin-shell and the lattice as a pin-jointed truss. The two types of structures are coupled with a standard Lagrange multiplier approach

A Line/Trimmed NURBS Surface Intersection Algorithm Using Matrix Representations

International audienceWe contribute a reliable line/surface intersection method for trimmed NURBS surfaces, based on a novel matrix-based implicit representation and numerical methods in linear algebra such as singular value decomposition and the computation of generalized eigenvalues and eigenvectors. A careful treatment of degenerate cases makes our approach robust to intersection points with multiple pre-images. We then apply our intersection algorithm to mesh NURBS surfaces through Delaunay refinement. We demonstrate the added value of our approach in terms of accuracy and treatment of degenerate cases, by providing comparisons with other intersection approaches as well as a variety of meshing experiments

Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

An entire design-through-analysis workflow solution for isogeometric B-Rep analysis (IBRA), including both the interface to existing CADs and the analysis procedure, is presented. Possible approaches are elaborated for the full scope of structural analysis solvers ranging from low to high isogeometric simulation fidelity. This is based on a systematic investigation of solver designs suitable for IBRA. A theoretically ideal IBRA solver has all CAD capabilities and information accessible at any point, however, realistic scenarios typically do not allow this level of information. Even a classical FE solver can be included in the CAD-integrated workflow, which is achieved by a newly proposed meshless approach. This simple solution eases the implementation of the solver backend. The interface to the CAD is modularized by defining a database, which provides IO capabilities on the base of a standardized data exchange format. Such database is designed to store not only geometrical quantities but also all the numerical information needed to realize the computations. This feature allows its use also in codes which do not provide full isogeometric geometrical handling capabilities. The rough geometry information for computation is enhanced with the boundary topology information which implies trimming and coupling of NURBS-based entities. This direct use of multi-patch trimmed CAD geometries follows the principle of embedding objects into a background parametrization. Consequently, redefinition and meshing of geometry is avoided. Several examples from illustrative cases to industrial problems are provided to demonstrate the application of the proposed approach and to explain in detail the proposed exchange formats.Peer ReviewedPostprint (published version

Feature-based decomposition of trimmed surface.

Wu Yiu-Bun.Thesis submitted in: September 2004.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 122-123).Abstracts in English and Chinese.Chapter Chapter 1. --- Introduction --- p.1Chapter Chapter 2. --- Previous Works --- p.2Chapter 2.1. --- Surface Patch ApproachChapter 2.2. --- Triangular Facet ApproachChapter Chapter 3. --- The Decomposition Algorithm --- p.7Chapter 3.1. --- Input to the AlgorithmChapter 3.2. --- Overview of the AlgorithmChapter 3.2.1. --- Voronoi Diagram DevelopmentChapter 3.2.2. --- Feature Point DeterminationChapter 3.2.3. --- Correspondence EstablishmentChapter 3.2.4. --- Surface ApproximationChapter 3.3. --- Output of the AlgorithmChapter Chapter 4. --- Voronoi Diagram Development --- p.16Chapter 4.1. --- Triangulation of the Parametric SpaceChapter 4.1.1. --- Degree of TriangulationChapter 4.2. --- Locating BisectorsChapter 4.2.1. --- Bisector CentroidsChapter 4.2.2. --- Sub-triangulationChapter 4.3. --- Finalizing BisectorsChapter Chapter 5. --- Feature Point Determination --- p.31Chapter 5.1. --- Definition of Feature PointsChapter 5.1.1. --- Continuous Sharp TurnsChapter 5.1.2. --- Discrete Sharp TurnsChapter 5.2. --- Parametric Coordinates of Feature PointsChapter Chapter 6. --- Vertices Correspondence Attachment --- p.42Chapter 6.1. --- Validity of CorrespondencesChapter 6.2. --- Shape NormalizationChapter 6.2.1. --- Normalization with Relative PositionChapter 6.3. --- Ranking ProcessChapter 6.3.1. --- Forward and Backward AttachmentChapter 6.3.2. --- Singly Linked Bisector VerticesChapter Chapter 7. --- Surface Fitting --- p.58Chapter 7.1. --- Parametric PatchesChapter 7.1.1. --- Definition of Parametric Patch RegionChapter 7.1.2. --- Local Parametric Coordinate SystemChapter 7.2. --- Parametric GridsChapter 7.2.1. --- Sample Points on the Patch BoundaryChapter 7.2.2. --- Grid GenerationChapter 7.3. --- Surface Patches ConstructionChapter 7.3.1. --- Knot VectorsChapter 7.3.2. --- Control VerticesChapter Chapter 8. --- Worked Example --- p.71Chapter 8.1. --- Example 1: Deformed Plane 1Chapter 8.2. --- Example 2: Deformed Plane 2Chapter 8.3. --- Example 3: SphereChapter 8.4. --- Example 4: Hemisphere 1Chapter 8.5. --- Example 5: Hemisphere 2Chapter 8.6. --- Example 6: ShoeChapter 8.7. --- Example 7: Shark Main BodyChapter 8.8. --- Example 8: Mask 1Chapter 8.9. --- Example 9: Mask 2Chapter 8.10. --- Example 10: Toy CarChapter Chapter 9. --- Result and Analysis --- p.101Chapter 9.1. --- Continuity between PatchesChapter 9.2. --- Special Cases --- p.102Chapter 9.2.1. --- Degenerated PatchChapter 9.2.2. --- S-Shaped FeatureChapter 9.3. --- Comparison --- p.105Chapter 9.3.1. --- Example 1: Deformed Plane 1Chapter 9.3.2. --- Example 2: Deformed Plane 2Chapter 9.3.3. --- Example 3: SphereChapter 9.3.4. --- Example 4: Hemisphere 1Chapter 9.3.5. --- Example 5: Hemisphere 2Chapter 9.3.6. --- Example 6: ShoeChapter 9.3.7. --- Example 7: Shark Main BodyChapter 9.3.8. --- Example 8: Mask 1Chapter 9.3.9. --- Example 9: Mask 2Chapter 9.3.10. --- Example 10: Toy CarChapter Chapter 10. --- Conclusion --- p.119References --- p.12

Integrated modeling and analysis methodologies for architecture-level vehicle design.

In order to satisfy customer expectations, a ground vehicle must be designed to meet a broad range of performance requirements. A satisfactory vehicle design process implements a set of requirements reflecting necessary, but perhaps not sufficient conditions for assuring success in a highly competitive market. An optimal architecture-level vehicle design configuration is one of the most important of these requirements. A basic layout that is efficient and flexible permits significant reductions in the time needed to complete the product development cycle, with commensurate reductions in cost. Unfortunately, architecture-level design is the most abstract phase of the design process. The high-level concepts that characterize these designs do not lend themselves to traditional analyses normally used to characterize, assess, and optimize designs later in the development cycle. This research addresses the need for architecture-level design abstractions that can be used to support ground vehicle development. The work begins with a rigorous description of hierarchical function-based abstractions representing not the physical configuration of the elements of a vehicle, but their function within the design space. The hierarchical nature of the abstractions lends itself to object orientation - convenient for software implementation purposes - as well as description of components, assemblies, feature groupings based on non-structural interactions, and eventually, full vehicles. Unlike the traditional early-design abstractions, the completeness of our function-based hierarchical abstractions, including their interactions, allows their use as a starting point for the derivation of analysis models. The scope of the research in this dissertation includes development of meshing algorithms for abstract structural models, a rigid-body analysis engine, and a fatigue analysis module. It is expected that the results obtained in this study will move systematic design and analysis to the earliest phases of the vehicle development process, leading to more highly optimized architectures, and eventually, better ground vehicles. This work shows that architecture level abstractions in many cases are better suited for life cycle support than geometric CAD models. Finally, substituting modeling, simulation, and optimization for intuition and guesswork will do much to mitigate the risk inherent in large projects by minimizing the possibility of incorporating irrevocably compromised architecture elements into a vehicle design that no amount of detail-level reengineering can undo

Investigation of charged aerosol transport and deposition in human airway models

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Several theoretical and experimental studies of charged aerosol deposition in human airways have been reported. These studies suggest that higher charge values on particles lead to improve deposition efficiency in the human lung, especially in the alveolar region. Most of the previous numerical studies in realistic 3D geometrical models have been investigated only for uncharged particles. Hence, this research was aimed at numerically investigating aerosol transport and deposition by including the effect of electrostatic forces (both space and image charge forces). The numerical models that have been developed and presented in this thesis, treat the aerodynamics and electrodynamics as a coupled problem and successfully integrate both mechanisms. The physical model of the human lung used for this research consists of three sub-models: a 3D bifurcation airway model, a 3D reconstructed airway model representing the tracheobronchial region, and a 2D alveolar airway model representing the alveolar region. The airflow dynamics in these geometrical models were carried out using a Computational Fluid Dynamic software (CFD) with given boundary conditions related to corresponding breathing conditions. The space charge force was calculated using the Particle Mesh (PM) method, and the image charge force was computed using the mesh configuration. Both airflow dynamics and electrodynamics are integrated in the newly developed software, and the particle trajectories are then calculated. The numerical study of electrostatic forces is primarily focused on the submicron particle. The numerical study in the 3D tubular airway model gives a better understanding of parameters affecting the predicted deposition efficiency. The numerical study in the 3D tubular airway model focuses on the transport and deposition of particles near the branching regions between the parent and daughter tubes, where airflow profile is significantly altered, and secondary airflow also arises. Many charged particles are deposited near the carinae by the strong skewed axial velocity and image charge force. The space charge will influence the deposition efficiency if the number concentration of particles is high. Similarly, the charged particles in the 3D reconstructed airway model tends to have the deposition pattern near the branching regions, depending on the local airflow and charge value. In the 2D alveolar model, the image charge force can improve deposition efficiency. The outcome of this research clearly shows how the electrostatic forces play an important role in aerosol transport and deposition in human airways. The integrated numerical model provides a valuable tool for respiratory clinicians and the pharmaceutical industry to study the complex mechanism of drug aerosol deposition in human airways. Although this model is adequate for the intended purpose, it can be further improved by extending this work to develop a complete 3D model of entire human airways incorporating the full breathing cycle. Such a model would require extensive computing facilities, nevertheless it would be an enormous benefit to develop a better treatment for respiratory diseases.Financial support obtained from the Overseas Research Students Awards Scheme (ORS)and System Engineering department

Investigation of charged aerosol transport and deposition in human airway models

Several theoretical and experimental studies of charged aerosol deposition in human airways have been reported. These studies suggest that higher charge values on particles lead to improve deposition efficiency in the human lung, especially in the alveolar region. Most of the previous numerical studies in realistic 3D geometrical models have been investigated only for uncharged particles. Hence, this research was aimed at numerically investigating aerosol transport and deposition by including the effect of electrostatic forces (both space and image charge forces). The numerical models that have been developed and presented in this thesis, treat the aerodynamics and electrodynamics as a coupled problem and successfully integrate both mechanisms. The physical model of the human lung used for this research consists of three sub-models: a 3D bifurcation airway model, a 3D reconstructed airway model representing the tracheobronchial region, and a 2D alveolar airway model representing the alveolar region. The airflow dynamics in these geometrical models were carried out using a Computational Fluid Dynamic software (CFD) with given boundary conditions related to corresponding breathing conditions. The space charge force was calculated using the Particle Mesh (PM) method, and the image charge force was computed using the mesh configuration. Both airflow dynamics and electrodynamics are integrated in the newly developed software, and the particle trajectories are then calculated. The numerical study of electrostatic forces is primarily focused on the submicron particle. The numerical study in the 3D tubular airway model gives a better understanding of parameters affecting the predicted deposition efficiency. The numerical study in the 3D tubular airway model focuses on the transport and deposition of particles near the branching regions between the parent and daughter tubes, where airflow profile is significantly altered, and secondary airflow also arises. Many charged particles are deposited near the carinae by the strong skewed axial velocity and image charge force. The space charge will influence the deposition efficiency if the number concentration of particles is high. Similarly, the charged particles in the 3D reconstructed airway model tends to have the deposition pattern near the branching regions, depending on the local airflow and charge value. In the 2D alveolar model, the image charge force can improve deposition efficiency. The outcome of this research clearly shows how the electrostatic forces play an important role in aerosol transport and deposition in human airways. The integrated numerical model provides a valuable tool for respiratory clinicians and the pharmaceutical industry to study the complex mechanism of drug aerosol deposition in human airways. Although this model is adequate for the intended purpose, it can be further improved by extending this work to develop a complete 3D model of entire human airways incorporating the full breathing cycle. Such a model would require extensive computing facilities, nevertheless it would be an enormous benefit to develop a better treatment for respiratory diseases.EThOS - Electronic Theses Online ServiceGBUnited Kingdo