Boundary Element Techniques in Engineering

1 Approximate Methods 1.1 Introduction 1.2 Weighted Residual Techniques 1.3 Weak Formulations 1.4 The Inverse Problem 1.5 Boundary Methods2 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 Equation3 Higher-Order Elements 3.1 Introduction 3.2 Linear Elements for Two-Dimensional Problems 3.3 Quadratic and Higher-Order Elements 3.4 Elements for Three-Dimensional Problems 3.5 Three-Dimensional Elements 3.6 Order of Interpolation Functions4 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 Solution5 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 Elasticity6 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 6.6 Steady State 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 Problems7 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 ElementsIndex