Visualization of Fields and Applications in Engineering

1. Auflage 2011
ISBN: 978-0-470-97397-4
Verlag: Wiley

Buch, Englisch, 384 Seiten, Format (B × H): 157 mm x 236 mm, Gewicht: 703 g

Driven by advances in computer technology, engineering analysis has developed rapidly and extensively in recent times; Visualization of Fields and Applications in Engineering presents the basic techniques for tensor field visualization and mapping of engineering data. Focusing on the fundamental aspects of post processing databases and applications outputs, the author explores existing theories and their integration in tensor field visualization and analysis. The subject covers fundamental theories through to integrated, multi-disciplinary technologies with practical applications in engineering, computer /general sciences.

Visualization of Fields and Applications in Engineering is suitable for academic use and to serve as a source of reference. It will appeal to those who work in the engineering and science professions or in pursuit of academic training/ research.
- Offers a unique engineering approach to basic techniques for tensor field visualization and mapping
- Collates together material currently disseminated throughout the literature into one accessible point of reference
- Presents examples with applications beyond and across many disciplines.

Autoren/Hrsg.

Tou, Stephen

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau
• Technische Wissenschaften Technik Allgemein Konstruktionslehre und -technik
• Technische Wissenschaften Bauingenieurwesen Mathematische Methoden, Computeranwendungen (Bauingenieurwesen)
• Mathematik | Informatik EDV | Informatik Informatik Mensch-Maschine-Interaktion Informationsvisualisierung

Inhaltsverzeichnis

Preface ix

1 Introduction 1

1.1 A General View 1

1.2 Historical Development and Progress in Visual Science 3

1.3 Scientific Visualization Philosophy, Techniques and Challenges 7

2 Field Descriptions and Kinematics 11

2.1 Lagrangian/Eulerian Description and Transformation 11

2.2 Curvilinear Coordinates 15

2.2.1 Polar Coordinate 24

2.2.2 Streamline (Flux Line) Coordinates 29

2.2.3 Potential-Stream Function Coordinates 43

2.3 Field Kinematics and Visual Attributes 49

2.3.1 Field Line Trajectory 49

2.3.2 Field Line Integral Curves 50

2.3.3 Field Lines, Material Lines and Path Lines 54

2.3.4 Streamlines (Flux Lines) 56

3 Field Model, Representation and Visualization 63

3.1 Field Models and Concepts 63

3.2 Scalar Fields and Representation 65

3.3 Vector Fields and Representation 68

3.4 Vector Icons and Classifications 69

3.4.1 Classification Based on Domain Configurations 70

3.4.2 Classification Based on Information Levels 70

3.4.3 Classification Based on Topological Skeleton 71

3.5 Scalar Potential 71

3.6 Vector Potential 74

3.7 Vector Field Specification 77

3.7.1 Helmholtz’s Theorem 77

3.8 Tensor Contraction and Transport Process Visualization 79

3.8.1 Mechanical Energy Function and Heatfunction 80

3.8.2 Strain Energy Trajectory and Strain Function 84

3.9 Multiple Fields 85

4 Complex Analysis and Complex Potentials 97

4.1 Complex Variables/Functions and Applications 97

4.2 Complex Analysis and Cauchy–Riemann Equation 100

4.3 Differentiation of Complex Function 101

4.4 Integration of Complex Functions 104

4.5 Visualization of Complex Potentials 107

4.5.1 Trajectory Method 107

4.5.2 Method of Curvilinear Squares 108

4.5.3 Transfer Characteristics and Field Property Evaluation 111

4.6 Example 4.1a Visualization of Heat and Fluid Transport in a Corner 114

5 Field Mapping and Applications 127

5.1 Introduction 127

5.2 Mapping of Euclidean Geometry 129

5.2.1 Congruent Mapping 129

5.2.2 Similitude Mapping 131

5.2.3 Affine Mapping 132

5.3 Inversion Mapping 133

5.3.1 Circle Inversion 134

5.4 Mapping with Complex Functions 135

5.5 Conformal Mapping and Applications 137

5.6 Hodograph Method and Mapping 147

5.6.1 Conjugate Hodograph 148

5.6.2 Hodograph 149

5.7 Hodograph Representations and Applications 149

5.7.1 Straight Boundaries 156

5.7.2 Free Surface 158

5.7.3 Special Field Patterns 160

5.7.4 Projectile Trajectory in Constant Force Fields 163

5.7.5 Motion Trajectory in Central Force Fields 169

5.7.6 Trajectory of Charged Particles in Uniform Magnetic Fields 179

5.8 Example 4.1b Mapping of Field Patterns and Image Warping 183

6 Tensor Representation, Contraction and Visualization 199

6.1 Introduction 199

6.2 Development of Tensor Visualization Techniques 200

6.2.1 Mohr’s Circle 200

6.2.2 Tensor Field Line Trajectories (Lines of Principal Stress) 200

6.2.3 Isochromatics 201

6.2.4 Isoclines 201

6.2.5 Stress Trajectories 201

6.2.6 Slip Lines 201

6.2.7 Isopachs 201

6.3 Tensor Description and Representation 201

6.3.1 Tensor Icons and Classification 204

6.4 Tensor Decomposition and Tensor Rank Reduction 204

6.4.1 Strain Tensor and Stress Tensor 206

6.4.2 Rotation Tensor 207

6.4.3 Rate of Strain Tensor and Viscous Stress Tensor 208

6.4.4 Vorticity Tensor 210

6.4.5 Tensor Contractions: Tensor Vector on a Reference Plane 213

6.4.6 Tensor Contractions: Tensor Vector at a Point 214

6.5 Visualization of Symmetric Tensors 214

6.5.1 Tensor Invariants 214

6.5.2 Tensor Transformation 217

6.5.3 Principal States and Eigenana

Über Autor(innen)

Stephen Tou, National University, San Diego, USA
Dr Stephen Tou joined the National University in San Diego, USA as an Adjunct Professor in 2006, having previously been with the Department of Mechanical and Aerospace Engineering at Nanyang Technological University, Singapore as an associate professor for 20 years. He teaches a graduate course in transport phenomena and undergraduate courses in fluid mechanics, energy systems & heat transfer, environmental fluid mechanics, energy conversion systems and machinery, and engineering mathematics. He has published circa 60 refereed journal papers and 20 conference papers.