Transmission Line Matrix (TLM) in Computational Mechanics

By: Donard de Cogan, William J. O'Connor, Susan Pulko

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Hardcover | 1 November 2005 | Edition Number 1

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272 Pages

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23.4 x 15.6 x 1.91

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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 (R) 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 concepts and illustrate the applications.

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Non-Fiction Computing & I.T.Computer Networking & Communications Engineering & Technology Technology in General Engineering in General Energy Technology & Engineering Electrical Engineering Power Generation & Distribution Science Physics Mechanical Engineering & Materials

Mechanical Engineering Civil Engineering

Introduction	p. 1
TLM and the 1-D Wave Equation	p. 9
Introduction	p. 9
The Vibrating String	p. 10
A Simple TLM Model	p. 11
Boundary and Initial Conditions	p. 13
Wave Media, Impedance, and Speed	p. 15
Transmission Line Junctions	p. 18
Stubs	p. 19
The Forced Wave Equation	p. 20
Waves in Moving Media: The Moving Threadline Equation	p. 21
Gantry Crane Example	p. 21
Rotating String: Differential Equation and Analytical Solution	p. 22
Rotating String: TLM Model	p. 23
Rotating String: Results	p. 24
TLM in 2-D (Extension to Higher Dimensions)	p. 24
Conclusions	p. 25
The Theory of TLM: An Electromagnetic Viewpoint	p. 27
Introduction	p. 27
The Building Blocks: Electrical Components	p. 28
Resistor	p. 28
Capacitor	p. 28
Inductor	p. 30
Transmission Line	p. 31
Basic Network Theory	p. 32
Propagation of a Signal in Space (Maxwell's Equations)	p. 33
Distributed and Lumped Circuits	p. 36
Transmission Lines Revisited	p. 37
Time Discretization	p. 37
Discontinuities	p. 39
TLM Nodal Configurations	p. 40
Boundaries	p. 43
Conclusion	p. 45
TLM Modeling of Acoustic Propagation	p. 47
Introduction	p. 47
1-D TLM Algorithm	p. 47
2-D TLM Algorithm for Acoustic Propagation	p. 52
Driven Sine-Wave Excitation	p. 56
The 2-D Propagation of a Gaussian Wave-Form	p. 60
Moving Sources	p. 63
Propagation in Inhomogeneous Media	p. 66
Incorporation of Stub Lines	p. 68
Boundaries	p. 74
Surface Conforming Boundaries	p. 74
Frequency-Dependent Absorbing Boundaries	p. 77
Open-Boundary Descriptions	p. 80
Absorption within a PML Region	p. 84
Conclusion	p. 85
TLM Modeling of Thermal and Particle Diffusion	p. 87
Introduction	p. 87
Spatial Discretizations and Electrical Networks for Thermal and Particle Diffusion	p. 88
TLM Algorithm for a 1-D Link-line Nodal Arrangement	p. 90
1-D Link-Resistor Formulation	p. 91
Boundaries	p. 92
Insulating Boundary	p. 92
Symmetry Boundary	p. 92
Perfect Heat-Sink Boundary	p. 93
Constant Temperature Boundaries	p. 93
Temperature/Heat/Matter Excitation of the TLM Mesh	p. 95
Constant T Boundary as an Input	p. 95
Single Shot Injection into Bulk Material	p. 96
Flux Injection into Bulk Material	p. 100
Single Heat Source	p. 100
Multiple Flux Sources	p. 101
The Extension to Two and Three Dimensions	p. 102
Link-Line Formulations	p. 102
Link-Resistor Formulations	p. 104
Non-Uniformities in Mesh and Material Properties	p. 106
Stubs and the Avoidance of Internodal Reflections	p. 111
Time-Step Variation	p. 114
Some Aspects of the Theory of Lossy TLM	p. 117
TLM and Finite Difference Formulations for the Telegrapher's and Diffusion Equations	p. 117
Anomalous "Jumps-To-Zero" In Link-Line TLM	p. 121
TLM Diffusion Models as Binary Scattering Processes	p. 126
Mesh Decimation	p. 128
The Statistics of TLM Diffusion Models	p. 130
TLM and Analytical Solutions of the Laplace Equation	p. 132
Solution of the Diffusion Equation with Fixed-Value Boundaries	p. 132
Solution of the Telegrapher's Equation with Fixed-Value Boundaries	p. 133
TLM Models of Elastic Solids	p. 137
The Behavior of Elastic Materials	p. 137
The Analogy between TLM and State Space Control Theory	p. 140
Nodal Structure for Modeling Elastic Behavior	p. 143
Implementation	p. 149
Boundaries	p. 152
Force Boundaries	p. 153
Conclusion	p. 157
Simple TLM Deformation Models	p. 159
Introduction	p. 159
Review of the Behavior of Materials	p. 159
Trouton's Descending Fluid and a TLM Treatment of a Vertically Supported Column	p. 161
A Model of Viscous Bending	p. 165
Numerical Issues and Model Convergence	p. 169
TLM Models of Viscoelastic Deformation	p. 170
The Parallel Viscoelastic Model	p. 170
Conclusion	p. 173
TLM Modeling of Hydraulic Systems	p. 177
Introduction	p. 177
Symbols, Analogues, and Parameters	p. 178
Compressional Waves in Fluids	p. 181
A Transmission Line Analysis of Fluid Flow	p. 181
Time-Domain Transmission Line Models of Fluid Systems	p. 183
Transients in Elastic Pipes	p. 193
Open-Channel Hydraulics	p. 196
Conclusions	p. 198
Application of TLM to Computational Fluid Mechanics	p. 203
Introduction	p. 203
Viscosity	p. 204
Viscosity in the TLM Algorithm	p. 205
Results	p. 206
Incompressible Fluids and Velocity Fields	p. 207
Convective Acceleration and the TLM Model	p. 208
Comments on the Procedure	p. 211
Implementation Issues	p. 212
State of the Art Examples	p. 213
Introduction	p. 213
The Hanging Cable and Gantry Crane Problems	p. 213
Hanging Cable: Analytical Analysis and Results	p. 213
Hanging Cable: TLM Model	p. 214
Gantry Crane: Results	p. 215
The Modeling of Rigid Bodies Joined by Transmission Line Joints	p. 216
Klein-Gordon Equation	p. 220
Acoustic Propagation and Scattering (Two-Dimensions)	p. 223
Condenser Microphone Model	p. 225
Propagation in Polar Meshes	p. 226
Acoustic Propagation in Complex Ducts (A 3-D TLM Model)	p. 227
A 3-D Symmetrical Condensed TLM Node for Acoustic Propagation	p. 229
Waves in Moving Media	p. 233
Some Recent Developments in TLM Modeling of Doppler Effect	p. 235
Simulation of a Thermal Environment for Chilled Foods during Transport: An Example of Three-Dimensional Thermal Diffusion with Phase-Change	p. 237
Recent Advances in Inverse Thermal Modeling using TLM	p. 239
Inverse scattering	p. 239
Amplification Factor	p. 241
TLM and Spatio-Temporal Patterns - The Present and the Future	p. 242
TLM and Diffusion Waves	p. 246
The Logistic Equation in the Presence of Diffusion	p. 248
Index	p. 257
Table of Contents provided by Ingram. All Rights Reserved.

Transmission Line Matrix (TLM) in Computational Mechanics

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Hardcover

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