Potential Problems

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333 pages

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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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Description

Content

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.

- Introduction
- Continuum Mechanics Problems
- Some Practical Engineering Problems
- Methods for Solving Harmonic and Biharmonic Equations

- Boundary Element Analysis of Potential Problems
- Fundamental Solution
- Boundary Integral Equation
- Discretisation of the Boundary Integral Equation
- Constant Boundary Elements
- Quadratic Boundary Elements
- Scaling
- Solving the Linear Equations
- Solving Poisson’s Equation

- Constant Boundary Element Program for Potential Problems
- Program BEM2PC
- Some Test Problems for BEM2PC
- An Example: Downstream Viscous Flow in a Rectangular Channel

- Quadratic Boundary Element Program for Potential Problems
- Program BEM2PQ
- Some Test Problems for BEM2PQ
- An Example: Downstream Viscous Flow in a Rectangular Channel
- An Example: Heat Conduction in a Domain of Complex Shape
- 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.