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Boundary Element Methods for Engineers: Part I

Potential Problems

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Language:  English
The book is presented in two Parts. Part I describes boundary element treatments of problems of the potential type, using both constant and quadratic boundary elements.
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The book offers a deliberately simple introduction to boundary element methods applicable to a wide range of engineering problems. The mathematics are kept as simple as reasonably possible. Several boundary element computer programs, written in both Fortran and Matlab, suitable for use on desktops or laptops are presented and described in detail and their uses are illustrated with the aid of a number of practical examples. Problems, with solutions, are provided at the ends of the chapters, for readers to solve for themselves. The book is presented in two Parts. Part I starts with a brief review of the problems encountered in engineering, showing that they of two broad types. It then describes boundary element treatments of problems of the potential type, using both constant and quadratic boundary elements. Part II is concerned with elastic stress analysis problems of the plane strain and plane stress types.

  1. Introduction
    1. Continuum Mechanics Problems
    2. Some Practical Engineering Problems
    3. Methods for Solving Harmonic and Biharmonic Equations
  2. Boundary Element Analysis of Potential Problems
    1. Fundamental Solution
    2. Boundary Integral Equation
    3. Discretisation of the Boundary Integral Equation
    4. Constant Boundary Elements
    5. Quadratic Boundary Elements
    6. Scaling
    7. Solving the Linear Equations
    8. Solving Poisson’s Equation
  3. Constant Boundary Element Program for Potential Problems
    1. Program BEM2PC
    2. Some Test Problems for BEM2PC
    3. An Example: Downstream Viscous Flow in a Rectangular Channel
  4. Quadratic Boundary Element Program for Potential Problems
    1. Program BEM2PQ
    2. Some Test Problems for BEM2PQ
    3. An Example: Downstream Viscous Flow in a Rectangular Channel
    4. An Example: Heat Conduction in a Domain of Complex Shape
    5. Discussion

  • Appendix A: Gaussian Quadrature
  • Appendix B: Gaussian Elimination
  • Appendix C: Matlab Version of Constant Boundary Element Program for Potential Problems
  • Appendix D: Matlab Version of Quadratic Boundary Element Program for Potential Problems
  • Solutions to Problems – Part 1

The programming language used in the main text is Fortran. Although it is somewhat unfashionable these days for general programming purposes, Fortran is still very widely used in engineering computation. Matlab versions of the programs are also provided in Appendices. Full listings of all the programs, both Fortran and Matlab, are available for download here.

About the Author

Roger Fenner

Roger Fenner is Professor of Engineering Computation in the Department of Mechanical Engineering at Imperial College London. For the last forty years his research interests have focussed on numerical techniques, principally boundary element and finite element methods, applied to engineering problems. Such problems have ranged from large scale structures such as offshore oil rigs and mine winding drums, through very high pressure equipment used in the chemical industry, to fluid flows encountered in the processing of plastics. His previous books include Finite Element Methods for Engineers (2nd Edition, 2013, Imperial College Press), Mechanics of Solids and Structures (2nd Edition, 2012, CRC Press), Engineering Elasticity (1986, Ellis Horwood), Principles of Polymer Processing (1979, Macmillan) and Computing for Engineers (1974, Macmillan).