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Boundary Element Techniques in Engineering

Book 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.

Table of Contents

  1. Front Cover
  2. Boundary Element Techniques in Engineering
  3. Copyright Page
  4. Preface
  5. Table of Contents
  6. Chapter 1. Approximate Methods
    1. 1.1 Introduction
    2. 1.2 Weighted Residual Techniques (1/2)
    3. 1.2 Weighted Residual Techniques (2/2)
    4. 1.3 Weak Formulations
    5. 1.4 The Inverse Problem
    6. 1.5 Boundary Methods (1/2)
    7. 1.5 Boundary Methods (2/2)
    8. REFERENCES
    9. BIBLIOGRAPHY
  7. Chapter 2. Potential Problems
    1. 2.1 INTRODUCTION
    2. 2.2 THE FUNDAMENTAL SOLUTION AND DIRECT FORMULATION
    3. 2.3 THE INDIRECT FORMULATION
    4. 2.4 MATRIX FORMULATION (1/2)
    5. 2.4 MATRIX FORMULATION (2/2)
    6. 2.5 POISSON'S EQUATION
    7. 2.6 THE ORTHOTROPIC CASE
    8. 2.7 THE HELMHOLTZ EQUATION
    9. REFERENCES
  8. Chapter 3. Higher-Order Elements
    1. 3.1 INTRODUCTION
    2. 3.2 LINEAR ELEMENTS FOR TWO-DIMENSIONAL PROBLEMS (1/2)
    3. 3.2 LINEAR ELEMENTS FOR TWO-DIMENSIONAL PROBLEMS (2/2)
    4. 3.3 QUADRATIC AND HIGHER-ORDER ELEMENTS
    5. 3.4 ELEMENTS FOR THREE-DIMENSIONAL PROBLEMS (1/3)
    6. 3.4 ELEMENTS FOR THREE-DIMENSIONAL PROBLEMS (2/3)
    7. 3.4 ELEMENTS FOR THREE-DIMENSIONAL PROBLEMS (3/3)
    8. 3.5 THREE-DIMENSIONAL ELEMENTS
    9. 3.6 ORDER OF INTERPOLATION FUNCTIONS
    10. REFERENCES
    11. BIBLIOGRAPHY
  9. Chapter 4. Fundamental Solutions
    1. 4.1 INTRODUCTION
    2. 4.2 EIGENFUNCTIONS AND THE DIRAC DELTA FUNCTION
    3. 4.3 FUNDAMENTAL SOLUTIONS ON A FINITE REGION
    4. 4.4 INFINITE DOMAINS
    5. 4.5 THE FUNDAMENTAL SOLUTION IN INFINITE SPACE
    6. 4.6 NUMERICAL SOLUTIONS (ANISOTROPIC BODIES)
    7. 4.7 THE METHOD OF IMAGES (1/2)
    8. 4.7 THE METHOD OF IMAGES (2/2)
    9. 4.8 THE FUNDAMENTAL SOLUTION AND BOUNDARY ELEMENTS
    10. 4.9 EXPLICIT FORMS FOR THE FUNDAMENTAL SOLUTION
    11. REFERENCES
  10. Chapter 5. Elastostatics
    1. 5.1 INTRODUCTION
    2. 5.2 WEIGHTED RESIDUAL STATEMENTS
    3. 5.3 FUNDAMENTAL SOLUTION
    4. 5.4 SOURCE APPROACH
    5. 5.5 MATRIX FORMULATION (1/3)
    6. 5.5 MATRIX FORMULATION (2/3)
    7. 5.5 MATRIX FORMULATION (3/3)
    8. 5.6 TWO-DIMENSIONAL ELASTICITY (1/2)
    9. 5.6 TWO-DIMENSIONAL ELASTICITY (2/2)
    10. REFERENCES
    11. BIBLIOGRAPHY
  11. Chapter 6. Time-Dependent and Non-Linear Problems
    1. 6.1 INTRODUCTION
    2. 6.2 TRANSFORM METHODS
    3. 6.3 FOURIER TRANSFORMS
    4. 6.4 LAPLACE TRANSFORMS10
    5. 6.5 TRANSIENT ELASTODYNAMICS
    6. 6.6 STEADY STATE ELASTODYNAMICS
    7. 6.7 VISCOELASTIC PROBLEMS
    8. 6.8 TIME INTEGRATION USING TIME STEPPING
    9. 6.9 TIME-DEPENDENT FUNDAMENTAL SOLUTION
    10. 6.10 NON-LINEAR PROBLEMS
    11. 6.11 PLASTICITY AND SOIL MECHANICS PROBLEMS
    12. REFERENCES
  12. Chapter 7. Combination of Regions
    1. 7.1 INTRODUCTION
    2. 7.2 DIVISION INTO REGIONS (1/2)
    3. 7.2 DIVISION INTO REGIONS (2/2)
    4. 7.3 APPROXIMATE BOUNDARY SOLUTIONS (1/3)
    5. 7.3 APPROXIMATE BOUNDARY SOLUTIONS (2/3)
    6. 7.3 APPROXIMATE BOUNDARY SOLUTIONS (3/3)
    7. 7.4 INFINITE ELEMENTS
    8. 7.5 COMBINATION OF FINITE AND BOUNDARY ELEMENTS (1/2)
    9. 7.5 COMBINATION OF FINITE AND BOUNDARY ELEMENTS (2/2)
    10. REFERENCES
  13. Index