Contents
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
3.3 Quadratic and Higher-Order Elements
3.4 Elements for three-Dimensional Problems
3.5 Three-dimensional Elements
3.6 Order of Interpolation Functions
1
25
54
CONTENTS
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
6.6 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 Problems
80
120
151
CONTENTS
7 Combination of Regions 180
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
209
This page intentionally left blank
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.