ABSTRACT
This much-anticipated second edition introduces the fundamentals of the finite element method featuring clear-cut examples and an applications-oriented approach. Using the transport equation for heat transfer as the foundation for the governing equations, this new edition demonstrates the versatility of the method for a wide range of applications,
Preface
1. INTRODUCTION
1.1 Background
1.2 History
1.3 Orientation
1.4 Closure
References
2. THE METHOD OF WEIGHTED RESIDUALS AND
GALERKIN APPROXIMATIONS
2.1 Background
2.2 Classical Solutions
2.3 The "Weak" Statement
2.4 Closure
Exercises
References
3. THE FINITE ELEMENT METHOD IN ONE DIMENSION
3.1 Overview
3.2 Shape Functions
3.2.1 Linear Elements
3.2.2 Quadratic Elements
3.2.3 Cubic Elements
3.3 Steady Conduction Equation
3.3.1 Galerkin Formulation
3.3.2 Variable Diffusion and Boundary Convection
3.4 Axisymmetric Heat Conduction
3.5 Natural Coordinate System
3.6 Time Dependence
3.6.1 Spatial Discretization
3.6.2 Time Discretization
3.7 Matrix Formulation
3.8 Solution Methods
3.9 Closure
Exercises
References
4. THE TWO-DIMENSIONAL TRIANGULAR ELEMENT
4.1 Overview
4.2 The Mesh
4.3 Shape Functions (Linear, Quadratic)
4.3.1 Linear Shape Functions
4.3.2 Quadratic Shape Functions
4.4 Area Coordinates
4.5 Numerical Integration
4.6 Diffusion in a Triangular Element
4.7 Steady-State Diffusion with Boundary Convection
4.8 The Axisymmetric Conduction Equation
4.9 The Quadratic Triangular Element
4.10 Time-Dependent Diffusion Equation
4.11 Bandwidth
4.12 Mass Lumping
4.13 Closure
Exercises
References
5. THE TWO-DIMENSIONAL QUADRILATERAL ELEMENT
5.1 Background
5.2 Element Mesh
5.3 Shape Functions
5.3.1 Bilinear Rectangular Element
5.3.2 Quadratic Rectangular Elements
5.4 Natural Coordinate System
5.5 Numerical Integration using Gaussian Quadratures
5.6 Steady-State Conduction with Boundary Convection
5.7 The Quadratic Quadrilateral Element
5.8 Time-Dependent Diffusion
5.9 Computer Program Exercises
5.10 Closure
Exercises
References
6. ISOPARAMETRIC TWO-DIMENSIONAL ELEMENTS
