Brebbia / Walker Boundary Element Techniques in Engineering

1. Auflage 2016
ISBN: 978-1-4831-0256-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 220 Seiten, Web PDF

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.

Autoren/Hrsg.

Brebbia, C. A.

Walker, S.

Inhaltsverzeichnis

1;Front Cover;1
2;Boundary Element Techniques in Engineering;4
3;Copyright Page;5
4;Preface;6
5;Table of Contents;8
6;Chapter 1. Approximate Methods;12
6.1;1.1 Introduction;12
6.2;1.2 Weighted Residual Techniques ;14
6.3;1.3 Weak Formulations ;21
6.4;1.4 The Inverse Problem ;25
6.5;1.5 Boundary Methods ;28
6.6;REFERENCES;35
6.7;BIBLIOGRAPHY;35
7;Chapter 2. Potential Problems;36
7.1;2.1 INTRODUCTION;36
7.2;2.2 THE FUNDAMENTAL SOLUTION AND DIRECT FORMULATION;38
7.3;2.3 THE INDIRECT FORMULATION;43
7.4;2.4 MATRIX FORMULATION;46
7.5;2.5 POISSON'S EQUATION;56
7.6;2.6 THE ORTHOTROPIC CASE;58
7.7;2.7 THE HELMHOLTZ EQUATION;61
7.8;REFERENCES;64
8;Chapter 3. Higher-Order Elements;65
8.1;3.1 INTRODUCTION;65
8.2;3.2 LINEAR ELEMENTS FOR TWO-DIMENSIONAL PROBLEMS;66
8.3;3.3 QUADRATIC AND HIGHER-ORDER ELEMENTS;73
8.4;3.4 ELEMENTS FOR THREE-DIMENSIONAL PROBLEMS;76
8.5;3.5 THREE-DIMENSIONAL ELEMENTS;87
8.6;3.6 ORDER OF INTERPOLATION FUNCTIONS;89
8.7;REFERENCES;89
8.8;BIBLIOGRAPHY;90
9;Chapter 4. Fundamental Solutions;91
9.1;4.1 INTRODUCTION;91
9.2;4.2 EIGENFUNCTIONS AND THE DIRAC DELTA FUNCTION;91
9.3;4.3 FUNDAMENTAL SOLUTIONS ON A FINITE REGION;100
9.4;4.4 INFINITE DOMAINS;103
9.5;4.5 THE FUNDAMENTAL SOLUTION IN INFINITE SPACE;106
9.6;4.6 NUMERICAL SOLUTIONS (ANISOTROPIC BODIES);111
9.7;4.7 THE METHOD OF IMAGES;113
9.8;4.8 THE FUNDAMENTAL SOLUTION AND BOUNDARY ELEMENTS;122
9.9;4.9 EXPLICIT FORMS FOR THE FUNDAMENTAL SOLUTION;125
9.10;REFERENCES;130
10;Chapter 5. Elastostatics;131
10.1;5.1 INTRODUCTION;131
10.2;5.2 WEIGHTED RESIDUAL STATEMENTS;134
10.3;5.3 FUNDAMENTAL SOLUTION;135
10.4;5.4 SOURCE APPROACH;137
10.5;5.5 MATRIX FORMULATION;139
10.6;5.6 TWO-DIMENSIONAL ELASTICITY;152
10.7;REFERENCES;160
10.8;BIBLIOGRAPHY;161
11;Chapter 6. Time-Dependent and Non-Linear Problems;162
11.1;6.1 INTRODUCTION;162
11.2;6.2 TRANSFORM METHODS;162
11.3;6.3 FOURIER TRANSFORMS;165
11.4;6.4 LAPLACE TRANSFORMS10;167
11.5;6.5 TRANSIENT ELASTODYNAMICS;171
11.6;6.6 STEADY STATE ELASTODYNAMICS;174
11.7;6.7 VISCOELASTIC PROBLEMS;176
11.8;6.8 TIME INTEGRATION USING TIME STEPPING;178
11.9;6.9 TIME-DEPENDENT FUNDAMENTAL SOLUTION;180
11.10;6.10 NON-LINEAR PROBLEMS;184
11.11;6.11 PLASTICITY AND SOIL MECHANICS PROBLEMS;186
11.12;REFERENCES;189
12;Chapter 7. Combination of Regions;191
12.1;7.1 INTRODUCTION;191
12.2;7.2 DIVISION INTO REGIONS;192
12.3;7.3 APPROXIMATE BOUNDARY SOLUTIONS;198
12.4;7.4 INFINITE ELEMENTS;209
12.5;7.5 COMBINATION OF FINITE AND BOUNDARY ELEMENTS;212
12.6;REFERENCES;218
13;Index;220