Boundary Element Techniques in Engineering (eBook)

C. A. Brebbia, S. Walker (Autoren)

eBook Download: PDF

2016 | 1. Auflage
220 Seiten
Elsevier Science (Verlag)
978-1-4831-0256-6 (ISBN)

Infos

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.

Inhalt

Front Cover 1
Boundary Element Techniques in Engineering 4
Copyright Page 5
Preface 6
Table of Contents 8
Chapter 1. Approximate Methods 12
1.1 Introduction 12
1.2 Weighted Residual Techniques 14
1.3 Weak Formulations 21
1.4 The Inverse Problem 25
1.5 Boundary Methods 28
REFERENCES 35
BIBLIOGRAPHY 35
Chapter 2. Potential Problems 36
2.1 INTRODUCTION 36
2.2 THE FUNDAMENTAL SOLUTION AND DIRECT FORMULATION 38
2.3 THE INDIRECT FORMULATION 43
2.4 MATRIX FORMULATION 46
2.5 POISSON'S EQUATION 56
2.6 THE ORTHOTROPIC CASE 58
2.7 THE HELMHOLTZ EQUATION 61
REFERENCES 64
Chapter 3. Higher-Order Elements 65
3.1 INTRODUCTION 65
3.2 LINEAR ELEMENTS FOR TWO-DIMENSIONAL PROBLEMS 66
3.3 QUADRATIC AND HIGHER-ORDER ELEMENTS 73
3.4 ELEMENTS FOR THREE-DIMENSIONAL PROBLEMS 76
3.5 THREE-DIMENSIONAL ELEMENTS 87
3.6 ORDER OF INTERPOLATION FUNCTIONS 89
REFERENCES 89
BIBLIOGRAPHY 90
Chapter 4. Fundamental Solutions 91
4.1 INTRODUCTION 91
4.2 EIGENFUNCTIONS AND THE DIRAC DELTA FUNCTION 91
4.3 FUNDAMENTAL SOLUTIONS ON A FINITE REGION 100
4.4 INFINITE DOMAINS 103
4.5 THE FUNDAMENTAL SOLUTION IN INFINITE SPACE 106
4.6 NUMERICAL SOLUTIONS (ANISOTROPIC BODIES) 111
4.7 THE METHOD OF IMAGES 113
4.8 THE FUNDAMENTAL SOLUTION AND BOUNDARY ELEMENTS 122
4.9 EXPLICIT FORMS FOR THE FUNDAMENTAL SOLUTION 125
REFERENCES 130
Chapter 5. Elastostatics 131
5.1 INTRODUCTION 131
5.2 WEIGHTED RESIDUAL STATEMENTS 134
5.3 FUNDAMENTAL SOLUTION 135
5.4 SOURCE APPROACH 137
5.5 MATRIX FORMULATION 139
5.6 TWO-DIMENSIONAL ELASTICITY 152
REFERENCES 160
BIBLIOGRAPHY 161
Chapter 6. Time-Dependent and Non-Linear Problems 162
6.1 INTRODUCTION 162
6.2 TRANSFORM METHODS 162
6.3 FOURIER TRANSFORMS 165
6.4 LAPLACE TRANSFORMS10 167
6.5 TRANSIENT ELASTODYNAMICS 171
6.6 STEADY STATE ELASTODYNAMICS 174
6.7 VISCOELASTIC PROBLEMS 176
6.8 TIME INTEGRATION USING TIME STEPPING 178
6.9 TIME-DEPENDENT FUNDAMENTAL SOLUTION 180
6.10 NON-LINEAR PROBLEMS 184
6.11 PLASTICITY AND SOIL MECHANICS PROBLEMS 186
REFERENCES 189
Chapter 7. Combination of Regions 191
7.1 INTRODUCTION 191
7.2 DIVISION INTO REGIONS 192
7.3 APPROXIMATE BOUNDARY SOLUTIONS 198
7.4 INFINITE ELEMENTS 209
7.5 COMBINATION OF FINITE AND BOUNDARY ELEMENTS 212
REFERENCES 218
Index 220

Produkt-Details

• Erscheint lt. Verlag: 29.1.2016
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• ISBN-10: 1-4831-0256-4 / 1483102564
• ISBN-13: 978-1-4831-0256-6 / 9781483102566