# Boundary Element Techniques in Engineering

1st Edition - March 6, 1980

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• Authors: C. A. Brebbia, S. Walker
• eBook ISBN: 9781483102566

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## Description

Boundary Element Techniques in Engineering deals with solutions of two- and three-dimensional problems in elasticity and the potential theory where finite elements are inefficient. The book discusses approximate methods, higher-order elements, elastostatics, time-dependent problems, non-linear problems, and combination of regions. Approximate methods include weighted residual techniques, weak formulations, the inverse formulation, and boundary methods. The text also explains Laplace's equation, indirect formulation, matrix formulation, Poisson's equation, and the Helmholtz equation. It describes how elements with linear variations of u and q (i.e. linear elements) can be developed for two dimensional problems, as well as for quadratic and higher order elements for two-dimensional problems. The text investigates the Dirac delta function as a sum of Eigen functions, including some methods to determine the explicit form of fundamental solutions for recurrent problems. The book also tackles the application of boundary elements to problems with both material and certain types of geometric non-linearities, and also the applications of boundary elements to plasticity problems. The text is ideal for mathematicians, students, and professor of calculus or advanced mathematics.

• 1 Approximate Methods

1.1 Introduction

1.2 Weighted Residual Techniques

1.3 Weak Formulations

1.4 The Inverse Problem

1.5 Boundary Methods

2 Potential Problems

2.1 Introduction

2.2 The Fundamental Solution and Direct Formulation

2.3 The Indirect Formulation

2.4 Matrix Formulation

2.5 Poisson's Equation

2.6 The Orthotropic Case

2.7 The Helmholtz Equation

3 Higher-Order Elements

3.1 Introduction

3.2 Linear Elements for Two-Dimensional Problems

3.4 Elements for Three-Dimensional Problems

3.5 Three-Dimensional Elements

3.6 Order of Interpolation Functions

4 Fundamental Solutions

4.1 Introduction

4.2 Eigenfunctions and the Dirac Delta Function

4.3 Fundamental Solutions on a Finite Region

4.4 Infinite Domains

4.5 The Fundamental Solution in Infinite Space

4.6 Numerical Solutions (Anisotropie Bodies)

4.7 The Method of Images

4.8 The Fundamental Solution and Boundary Elements

4.9 Explicit Forms for the Fundamental Solution

5 Elastostatics

5.1 Introduction

5.2 Weighted Residual Statements

5.3 Fundamental Solution

5.4 Source Approach

5.5 Matrix Formulation

5.6 Two-Dimensional Elasticity

6 Time-Dependent and Non-Linear Problems

6.1 Introduction

6.2 Transform Methods

6.3 Fourier Transforms

6.4 Laplace Transforms

6.5 Transient Elastodynamics

6.7 Viscoelastic Problems

6.8 Time Integration Using Time Stepping

6.9 Time-Dependent Fundamental Solution

6.10 Non-Linear Problems

6.11 Plasticity and Soil Mechanics Problems

7 Combination of Regions

7.1 Introduction

7.2 Division into Regions

7.3 Approximate Boundary Solutions

7.4 Infinite Elements

7.5 Combination of Finite and Boundary Elements

Index

## Product details

• No. of pages: 220
• Language: English
• Published: March 6, 1980
• Imprint: Newnes
• eBook ISBN: 9781483102566

### C. A. Brebbia

#### Affiliations and Expertise

Computational Mechanics Institute and University of Southampton

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