Introduction To The Finite Element Method 4e

By (author) Reddy J.
Description:
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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


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 
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