Strain field in doubly curved surface

This paper presents algorithm for development of structural and continuous curved surface into a planar and non planar (radial) shape in 3D space. The development process is modeled by application of strain in certain plane from the curved surface to its planar development. A doubly curved surface has been generated for the purpose of technical studies. Important features of the approach include formulations of the coefficients of first fundamental form, second fundamental form, Gaussian curvature and Serret Frenet curve. The approximate strain field is obtained by solving a constrained linear and nonlinear problem in algorithm

Optimal development of doubly curved surfaces,

Abstract This paper presents algorithms for optimal development (flattening) of a smooth continuous curved surface embedded in three-dimensional space into a planar shape. The development process is modeled by in-plane strain (stretching) from the curved surface to its planar development. The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming problem. Based on the strain distribution and the coefficients of the first fundamental form of the curved surface, another unconstrained nonlinear programming problem is solved to obtain the optimal developed planar shape. The convergence and complexity properties of our algorithms are analyzed theoretically and numerically. Examples show the effectiveness of the algorithms

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