Transmission Line Matrix (TLM) in Computational Mechanics[推荐]: TT.jpg

Transmission Line Matrix (TLM) in Computational Mechanics
By Donard de Cogan, William J. O’Connor, Susan Pulko




Publisher: CRC
Number Of Pages: 272
Publication Date: 2005-11-01
ISBN-10 / ASIN: 0415327172
ISBN-13 / EAN: 9780415327176
Binding: Hardcover



The finite element method reigns as the dominant technique for modeling mechanical systems. Originally developed to model electromagnetic systems, the Transmission Line Matrix (TLM) method proves to match, and in some cases exceed, the effectiveness of finite elements for modeling several types of physical systems. Transmission Line Matrix in Computational Mechanics provides a tutorial approach to applying TLM for modeling mechanical and other physical systems. Transmission Line Matrix in Computational Mechanics begins with the history of TLM, an introduction to the theory using mechanical engineering concepts, and the electromagnetic basics of TLM. The authors then demonstrate the theory for use in acoustic propagation, along with examples of MATLAB® code. The remainder of the book explores the application of TLM to problems in mechanics, specifically heat and mass transfer, elastic solids, simple deformation models, hydraulic systems, and computational fluid dynamics. A discussion of state-of-the-art techniques concludes the book, offering a look at the current research undertaken by the authors and other leading experts to overcome the limitations of TLM in applying the method to diverse types of systems. This valuable reference introduces students, engineers, and researchers to a powerful, accurate, and stable alternative to finite elements, providing case studies and examples to reinforce the

This is a new book,thank you for the job

Table of Contents
Chapter 1 Introduction................................................................................................1
Chapter 2 TLM and the 1-D Wave Equation.......................................................9
2.1 Introduction ....................................................................................................9
2.2 The Vibrating String ....................................................................................10
2.3 A Simple TLM Model..................................................................................11
2.4 Boundary and Initial Conditions...............................................................13
2.5 Wave Media, Impedance, and Speed........................................................15
2.6 Transmission Line Junctions ......................................................................18
2.7 Stubs...............................................................................................................19
2.8 The Forced Wave Equation ........................................................................20
2.9 Waves in Moving Media: The Moving Threadline Equation................21
2.10 Gantry Crane Example................................................................................21
2.11 Rotating String: Differential Equation and Analytical Solution ...........22
2.11.1 Rotating String: TLM Model..........................................................23
2.11.2 Rotating String: Results ..................................................................24
2.12 TLM in 2-D (Extension to Higher Dimensions).......................................24
2.13 Conclusions...................................................................................................25
Chapter 3 The Theory of TLM: An Electromagnetic Viewpoint................27
3.1 Introduction ..................................................................................................27
3.2 The Building Blocks: Electrical Components...........................................28
3.2.1 Resistor..............................................................................................28
3.2.2 Capacitor...........................................................................................28
3.2.3 Inductor.............................................................................................30
3.2.4 Transmission Line ...........................................................................31
3.3 Basic Network Theory.................................................................................32
3.4 Propagation of a Signal in Space (Maxwell’s Equations).......................33
3.5 Distributed and Lumped Circuits .............................................................36
3.6 Transmission Lines Revisited ....................................................................37
3.6.1 Time Discretization .........................................................................37
3.7 Discontinuities..............................................................................................39
3.8 TLM Nodal Configurations........................................................................40
3.9 Boundaries ....................................................................................................43
3.10 Conclusion ....................................................................................................45
Chapter 4 TLM Modeling of Acoustic Propagation........................................47
4.1 Introduction ..................................................................................................47
4.2 1-D TLM Algorithm.....................................................................................47
4.3 2-D TLM Algorithm for Acoustic Propagation ......................................52
4.4 Driven Sine-Wave Excitation .....................................................................56
4.5 The 2-D Propagation of a Gaussian Wave-Form.....................................60
4.6 Moving Sources............................................................................................63
4.7 Propagation in Inhomogeneous Media ....................................................66
4.8 Incorporation of Stub Lines........................................................................68
4.9 Boundaries ....................................................................................................74
4.10 Surface Conforming Boundaries ...............................................................74
4.11 Frequency-Dependent Absorbing Boundaries........................................77
4.12 Open-Boundary Descriptions ....................................................................80
4.13 Absorption within a PML Region .............................................................84
4.14 Conclusion ....................................................................................................85
Chapter 5 TLM Modeling of Thermal and Particle Diffusion....................87
5.1 Introduction ..................................................................................................87
5.2 Spatial Discretizations and Electrical Networks
for Thermal and Particle Diffusion ...........................................................88
5.3 TLM Algorithm for a 1-D Link-line Nodal Arrangement......................90
5.4 1-D Link–Resistor Formulation .................................................................91
5.5 Boundaries ....................................................................................................92
5.5.1 Insulating Boundary .......................................................................92
5.5.2 Symmetry Boundary.......................................................................92
5.5.3 Perfect Heat-Sink Boundary ..........................................................93
5.5.4 Constant Temperature Boundaries...............................................93
5.6 Temperature/Heat/Matter Excitation of the TLM Mesh......................95
5.6.1 Constant T Boundary as an Input .................................................95
5.6.2 Single Shot Injection into Bulk Material.......................................96
5.7 Flux Injection into Bulk Material .............................................................100
5.7.1 Single Heat Source ........................................................................100
5.8 Multiple Flux Sources................................................................................101
5.9 The Extension to Two and Three Dimensions.......................................102
5.9.1 Link-Line Formulations................................................................102
5.9.2 Link-Resistor Formulations .........................................................104
5.10 Non-Uniformities in Mesh and Material Properties.............................106
5.11 Stubs and the Avoidance of Internodal Reflections..............................111
5.12 Time-Step Variation...................................................................................114
5.13 Some Aspects of the Theory of Lossy TLM............................................117
5.13.1 TLM and Finite Difference Formulations
for the Telegrapher’s and Diffusion Equations.........................117
5.13.2 Anomalous “Jumps-To-Zero” In Link-Line TLM.....................121
5.13.3 TLM Diffusion Models as Binary Scattering Processes ...........126
5.13.4 Mesh Decimation...........................................................................128
5.14 The Statistics of TLM Diffusion Models .................................................130
5.15 TLM and Analytical Solutions of the Laplace Equation ......................132
5.15.1 Solution of the Diffusion Equation
with Fixed-Value Boundaries ......................................................132
5.15.2 Solution of the Telegrapher’s Equation
with Fixed-Value Boundaries ......................................................133
Chapter 6 TLM Models of Elastic Solids..........................................................137
6.1 The Behavior of Elastic Materials ............................................................137
6.2 The Analogy between TLM and State Space Control Theory.............140
6.3 Nodal Structure for Modeling Elastic Behavior ....................................143
6.4 Implementation..........................................................................................149
6.5 Boundaries ..................................................................................................152
6.6 Force Boundaries........................................................................................153
6.7 Conclusion ..................................................................................................157
Chapter 7 Simple TLM Deformation Models ................................................159
7.1 Introduction ................................................................................................159
7.2 Review of the Behavior of Materials .......................................................159
7.3 Trouton’s Descending Fluid and a TLM Treatment
of a Vertically Supported Column ..........................................................161
7.4 A Model of Viscous Bending....................................................................165
7.5 Numerical Issues and Model Convergence ...........................................169
7.6 TLM Models of Viscoelastic Deformation..............................................170
7.6.1 The Parallel Viscoelastic Model...................................................170
7.7 Conclusion ..................................................................................................173
Chapter 8 TLM Modeling of Hydraulic Systems..........................................177
8.1 Introduction ................................................................................................177
8.2 Symbols, Analogues, and Parameters.....................................................178
8.3 Compressional Waves in Fluids ..............................................................181
8.4 A Transmission Line Analysis of Fluid Flow ........................................181
8.5 Time-Domain Transmission Line Models of Fluid Systems ...............183
8.6 Transients in Elastic Pipes ........................................................................193
8.7 Open-Channel Hydraulics........................................................................196
8.8 Conclusions.................................................................................................198
Chapter 9 Application of TLM to Computational Fluid Mechanics.......203
9.1 Introduction ................................................................................................203
9.2 Viscosity ......................................................................................................204
9.3 Viscosity in the TLM Algorithm..............................................................205
9.4 Results..........................................................................................................206
9.5 Incompressible Fluids and Velocity Fields ............................................207
9.6 Convective Acceleration and the TLM Model.......................................208
9.7 Comments on the Procedure....................................................................211
9.8 Implementation Issues ..............................................................................212
Chapter 10 State of the Art Examples................................................................213
10.1 Introduction ................................................................................................213
10.2 The Hanging Cable and Gantry Crane Problems .................................213
10.2.1 Hanging Cable: Analytical Analysis and Results.....................213
10.2.2 Hanging Cable: TLM Model ........................................................214
10.2.3 Gantry Crane: Results...................................................................215
10.3 The Modeling of Rigid Bodies Joined by Transmission Line Joints ...216
10.4 Klein–Gordon Equation ............................................................................220
10.5 Acoustic Propagation and Scattering (Two-Dimensions)....................223
10.6 Condenser Microphone Model................................................................225
10.7 Propagation in Polar Meshes ...................................................................226
10.8 Acoustic Propagation in Complex Ducts (A 3-D TLM Model)...........227
10.9 A 3-D Symmetrical Condensed TLM Node
for Acoustic Propagation ..........................................................................229
10.10 Waves in Moving Media..........................................................................233
10.11 Some Recent Developments in TLM Modeling of Doppler Effect ....235
10.12 Simulation of a Thermal Environment for Chilled Foods
during Transport: An Example of Three-Dimensional Thermal
Diffusion with Phase-Change ..................................................................237
10.12.1Recent Advances in Inverse Thermal Modeling using TLM 239
10.12.2 Inverse scattering..........................................................................239
10.12.3 Amplification Factor.....................................................................241
10.12.4 TLM and Spatio-Temporal Patterns — The Present
and the Future................................................................................242
10.12.5 TLM and Diffusion Waves ..........................................................246
10.12.6 The Logistic Equation in the Presence of Diffusion.................248
Index .....................................................................................................................257

Transmission Line Matrix (TLM) in Computational Mechanics.part1

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[ 本帖最后由 drjiachen 于 2008-12-24 09:57 编辑 ]

Transmission Line Matrix (TLM) in Computational Mechanics.part2

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