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Transmission Line Matrix (TLM) is a numerical technique which is
based upon establishing an analogue between a space and time
dependent physical problem and an electrical network which includes
transmission lines. By their very nature these enforce time
discretization on the network which can then be solved explicitly
in the time-domain.
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.
A good mathematical model of a physical situation leads to improved understanding. A good model must be robust (its underlying assumptions must not lead to inconsistent results) and it must be predictive anticipating results that can be verified by experiment. This book shows engineers how to construct or choose such models and how to solve them numerically. These are enormously important tasks in practical engineering.
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