Introduction to the Finite Element Method 4E

by Reddy, J.

• ISBN13: 9781259861901
• ISBN10: 1259861902
• eBook ISBN(s): 9781259861918
• Edition: 4th
• Format: Hardcover
• Copyright: 2018-10-08
• Publisher: McGraw Hill
• More Book Details
• Purchase Benefits

Table of Contents

1 General Introduction 

1.1 Background

1.2 Mathematical Model Development 

1.3 Numerical Simulations 

1.4 The Finite Element Method

1.5 The Present Study 

1.6 Summary 

Problems 

References for Additional Reading 

2 Mathematical Preliminaries and Classical Variational Methods

2.1 General Introduction 

2.2 Some Mathematical Concepts and Formulae

2.3 Energy and Virtual Work Principles 

2.4 Integral Formulations of Differential Equations

2.5 Variational Methods

2.6 Equations of Continuum Mechanics

2.7 Summary 

Problems 

References for Additional Reading

3 1-D Finite Element Models of Second-Order Differential Equations

3.1 Introduction 

3.2 Finite Element Analysis Steps 

3.3 Finite Element Models of Discrete Systems

3.4 Finite Element Models of Continuous Systems

3.5 Axisymmetric Problems

3.6 Errors in Finite Element Analysis 

3.7 Summary 

Problems

References for Additional Reading 

4 Applications to 1-D Heat Transfer and Fluid and Solid

Mechanics Problems 

4.1 Preliminary Comments 

4.2 Heat Transfer 

4.3 Fluid Mechanics

4.4 Solid and Structural Mechanics 

4.5 Summary 

Problems

References for Additional Reading

5 Finite Element Analysis of Beams and Circular Plates 

5.1 Introduction 

5.2 Euler–Bernoulli Beam Element 

5.3 Timoshenko Beam Elements

5.4 Axisymmetric Bending of Circular Plates 

5.5 Summary 

Problems 

References for Additional Reading 

6 Plane Trusses and Frames 

6.1 Introduction 

6.2 Analysis of Trusses 

6.3 Analysis of Plane Frame Structures

6.4 Inclusion of Constraint Conditions 

6.5 Summary 

Problems 

References for Additional Reading 

7 Eigenvalue and Time-Dependent Problems in 1-D 

7.1 Introduction 

7.2 Equations of Motion 

7.3 Eigenvalue Problems 

7.4 Transient Analysis

7.5 Summary 

Problems 

References for Additional Reading

8 Numerical Integration and Computer Implementation 

8.1 Introduction 

8.2 Numerical Integration 

8.3 Computer Implementation 

8.4 Applications of Program FEM1D 

8.5 Summary 

Problems

References for Additional Reading 

9 Single-Variable Problems in Two Dimensions 

9.1 Introduction 

9.2 Boundary Value Problems 

9.3 Modeling Considerations 

9.4 Numerical Examples 

9.5 Eigenvalue and Time-Dependent Problems

9.6 Summary 

Problems 

References for Additional Reading 

10 2-D Interpolation Functions, Numerical Integration, and Computer Implementation 

10.1 Introduction 

10.2 2-D Element Library

10.3 Numerical Integration 

10.4 Modeling Considerations 

10.5 Computer Implementation and FEM2D

10.6 Summary

Problems

References for Additional Reading

11 Flows of Viscous Incompressible Fluids

11.1 Introduction

11.2 Governing Equations

11.3 Velocity–Pressure Formulation

11.4 Penalty Function Formulation 

11.5 Computational Aspects 

11.6 Numerical Examples 

11.7 Summary 

Problems 

References for Additional Reading

12 Plane Elasticity 

12.1 Introduction

12.2 Governing Equations 

12.3 Virtual Work and Weak Formulations

12.4 Finite Element Model 

12.5 Elimination of Shear Locking in Linear Elements

12.6 Numerical Examples 

12.7 Summary

Problems 

References for Additional Reading 

13 3-D Finite Element Analysis 

13.1 Introduction 

13.2 Heat Transfer

13.3 Flows of Viscous Incompressible Fluids 

13.4 Elasticity 

13.5 Element Interpolation Functions and Numerical Integration 

13.6 Numerical Examples

13.7 Summary 

Problems

References for Additional Reading 

Index