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

This authoritative and thoroughly revised, classic mechanical engineering textbook
offers a broad-based overview and applications of the finite element method. This
revision updates and expands the already large number of problems and worked-out
examples and brings the technical coverage in line with current practices. Readers will
get details on non-traditional applications in bioengineering, fluid, and thermal
sciences, in addition to solid and structural mechanics.
Written by a recognized mechanical engineering expert, An Introduction to the Finite
Element Method, Fourth Edition, teaches, step-by-step, how to determine numerical
solutions to equilibrium as well as time-dependent problems from fluid and thermal
sciences and structural mechanics. Beginning with differential equations, the book
presents a self-contained approach to the construction of weak forms, interpolation
theory, finite element equations and their solution, and computer implementation. The
author provides a solutions manual as well as computer programs that are available
for download.