The Boundary Element Method: 27 (Solid Mechanics and Its Applications, 27) - Hardcover

Hall, W.S.

Hardcover

ISBN 10: 079232580X ISBN 13: 9780792325802

Publisher: Springer, 1993

Synopsis

The Boundary Element Method is a simple, efficient and cost effective computational technique which provides numerical solutions - for objects of any shap- for a wide range of scientific and engineering problems. In dealing with the development of the mathematics of the Boundary Element Method the aim has been at every stage, only to present new material when sufficient experience and practice of simpler material has been gained. Since the usual background of many readers will be of differential equations, the connection of differential equations with integral equations is explained in Chapter 1, together with analytical and numerical methods of solution. This information on integral equations provides a base for the work of subsequent chapters. The mathematical formulation of boundary integral equations for potential problems - derived from the more familiar Laplace partial differential equation which governs many important physical problems - is set out in Chapter 2. It should be noted here that this initial formulation of the boundary integral equations reduces the dimensionality of the problem. In the key Chapter 3, the essentials of the Boundary Element Method are presented. This first presentation of the Boundary Element Method is in its simplest and most approachable form - two dimensional, with the shape of the boundary approximated by straight lines and the functions approximated by constants over each of the straight lines.

About this title

Synopsis

This work sets out a simple, efficient and cost-effective computational technique which provides numerical solutions, for objects of any shape, to a wide range of scientific and engineering problems. It provides a complete approach to formulating boundary integral equations for scientific and engineering problems and solving them numerically using an element approximation. Only a knowledge of elementary calculus is required, since the text begins by relating familiar differential equations to integral equations and then moves on to the simple solution of integral equations. From this starting point, the mathematics of formulation and numerical approximation are developed progressively with every mathematical step being provided. Particular attention is paid to the problem of accurate evaluation of singular integrands and to the use of increasing levels of accuracy provided by constant, linear and quadratic approximations. This enables a full solution to be given for both two-dimensional and three-dimensional potential problems and finally, for the two-dimensional elastostatics problem.

"The Boundary Element Method" develops the mathematics of the text progressively both within chapters and from chapter to chapter. It is a self-contained, step-by-step exposition of the boundary element method, leading to its application to the key problem of elastostatics. The text may be used as a standard introductory reference text for the mathematics of this method and is suitable for final year undergraduate study as well as for postgraduates, scientists and engineers new to the subject. Worked examples and exercises are provided throughout the text.

Edition details

• Publisher: Springer
• Publication date: 1993
• Language: English
• ISBN 10: 079232580X
• ISBN 13: 9780792325802
• Binding: Hardcover
• Number of pages: 240