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Introduction to the Finite Element Method 4E
Introduction to the Finite Element Method 4E

Introduction to the Finite Element Method 4E, 4th Edition

ISBN10: 1259861902 | ISBN13: 9781259861901
By J. Reddy
© 2019

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* The estimated amount of time this product will be on the market is based on a number of factors, including faculty input to instructional design and the prior revision cycle and updates to academic research-which typically results in a revision cycle ranging from every two to four years for this product. Pricing subject to change at any time.

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An up-to-date, self-contained introduction to the theory and applications of the finite element method

This thoroughly revised classic engineering textbook offers a broad-based overview of the finite element method. Written by a world-renowned mechanical engineering researcher and author, the book shows, step-by-step, how to calculate numerical solutions to steady-state as well as time-dependent problems. You also get detailed problems with worked-out solutions and downloadable programs that can be used and modified for real-world situations. Special attention is paid to applications that are important in bioengineering, fluid and thermal sciences, structural mechanics, and a host of applied sciences.

Introduction to the Finite Element Method, Fourth Edition, covers:
Mathematical preliminaries and classical variational methods
1-D finite element models of second-order differential equations
Applications to 1-D heat transfer and fluid and solid mechanics problems
Finite element analysis of beams and circular plates
Plane trusses and frames
Eigenvalue and time-dependent problems in 1-D
Numerical integration and computer implementation in 1-D
Single-variable problems in two dimensions
2-D interpolation functions, numerical integration, and computer implementation in 2-D
Flows of viscous incompressible fluids
Plane elasticity
3-D finite element analysis

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 
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 
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 
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 
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 
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 
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 
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 
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 
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
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 
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
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 
References for Additional Reading 


About the Author

J. Reddy

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