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Introduction to the Finite Element Method, Third Edition /

J.N. Reddy's, An Introduction to the Finite Element Method, third edition is an update of one of the most popular FEM textbooks available. The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering ap...

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Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Reddy, J. N. (Autor)
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	New York, N.Y. : McGraw-Hill Education, [2006].
Edición:	3rd edition.
Temas:	Finite element method. Electronic books.
Acceso en línea:	Texto completo

Tabla de Contenidos:

Preface
1 Introduction
1.1 General Comments
1.2 Mathematical Models
1.3 Numerical Simulations
1.4 The Finite Element Method
1.4.1 The Basic Idea
1.4.2 The Basic Features
1.4.3 Some Remarks
1.4.4 A Brief Review of History and Recent Developments
1.5 The Present Study
1.6 Summary
Problems
References for Additional Reading
2 Mathematical Preliminaries, Integral Formulations, and Variational Methods
2.1 General Introduction
2.1.1 Variational Principles and Methods
2.1.2 Variational Formulations
2.1.3 Need for Weighted-Integral Statements
2.2 Some Mathematical Concepts and Formulae
2.2.1 Coordinate Systems and the Del Operator
2.2.2 Boundary Value, Initial Value, and Eigenvalue Problems
2.2.3 Integral Identities
2.2.4 Linear and Bilinear Functionals
2.3 Elements of Calculus of Variations
2.3.1 Introduction
2.3.2 Variational Operator and First Variation
2.3.3 Fundamental Lemma of Variational Calculus
2.3.4 The Euler Equations
2.3.5 Natural and Essential Boundary Conditions
2.3.6 Hamilton?s Principle
2.4 Integral Formulations
2.4.1 Introduction
2.4.2 Weighted-Integral and Weak Formulations
2.4.3 Linear and Bilinear Forms and Quadratic Functionals
2.4.4 Examples
2.5 Variational Methods
2.5.1 Introduction
2.5.2 The Ritz Method
2.5.3 Approximation Functions
2.5.4 Examples
2.5.5 The Method of Weighted Residuals
2.6 Summary
Problems
References for Additional Reading
3 Second-Order Differential Equations in One Dimension: Finite Element Models
3.1 Background
3.2 Basic Steps of Finite Element Analysis
3.2.1 Model Boundary Value Problem
3.2.2 Discretization of the Domain
3.2.3 Derivation of Element Equations
3.2.4 Connectivity of Elements
3.2.5 Imposition of Boundary Conditions
3.2.6 Solution of Equations
3.2.7 Postcomputation of the Solution.
3.3 Some Remarks
3.4 Axisymmetric Problems
3.4.1 Model Equation
3.4.2 Weak Form
3.4.3 Finite Element Model
3.5 Summary
Problems
References for Additional Reading
4 Second-Order Differential Equations in One Dimension: Applications
4.1 Preliminary Comments
4.2 Discrete Systems
4.2.1 Linear Elastic Spring
4.2.2 Torsion of Circular Shafts
4.2.3 Electrical Resistor Circuits
4.2.4 Fluid Flow through Pipes
4.3 Heat Transfer
4.3.1 Governing Equations
4.3.2 Finite Element Models
4.3.3 Numerical Examples
4.4 Fluid Mechanics
4.4.1 Governing Equations
4.4.2 Finite Element Model
4.5 Solid and Structural Mechanics
4.5.1 Preliminary Comments
4.5.2 Finite Element Model of Bars and Cables
4.5.3 Numerical Examples
4.6 Plane Trusses
4.6.1 Introduction
4.6.2 Basic Truss Element
4.6.3 General Truss Element
4.6.4 Constraint Equations: Penalty Approach
4.6.5 Constraint Equations: A Direct Approach
4.7 Summary
Problems
References for Additional Reading
5 Beams and Frames
5.1 Introduction
5.2 Euler?Bernoulli Beam Element
5.2.1 Governing Equation
5.2.2 Discretization of the Domain
5.2.3 Derivation of Element Equations
5.2.4 Assembly of Element Equations
5.2.5 Imposition of Boundary Conditions
5.2.6 Postprocessing of the Solution
5.2.7 Numerical Examples
5.3 Timoshenko Beam Elements
5.3.1 Governing Equations
5.3.2 Weak Form
5.3.3 General Finite Element Model
5.3.4 Consistent Interpolation Elements
5.3.5 Reduced Integration Element
5.3.6 Numerical Examples
5.4 Plane Frame Elements
5.4.1 Introductory Comments
5.4.2 Frame Element
5.5 Summary
Problems
References for Additional Reading
6 Eigenvalue and Time-Dependent Problems
6.1 Eigenvalue Problems
6.1.1 Introduction.
6.1.2 Formulation of Eigenvalue Problems
6.1.3 Finite Element Formulation
6.2 Time-Dependent Problems
6.2.1 Introduction
6.2.2 Semidiscrete Finite Element Models
6.2.3 Parabolic Equations
6.2.4 Hyperbolic Equations
6.2.5 Mass Lumping
6.2.6 Applications
6.3 Summary
Problems
References for Additional Reading
7 Computer Implementation
7.1 Numerical Integration
7.1.1 Background
7.1.2 Natural Coordinates
7.1.3 Approximation of Geometry
7.1.4 Isoparametric Formulations
7.1.5 Numerical Integration
7.2 Computer Implementation
7.2.1 Introductory Comments
7.2.2 General Outline
7.2.3 Preprocessor
7.2.4 Calculation of Element Matrices (Processor)
7.2.5 Assembly of Element Equations (Processor)
7.2.6 Imposition of Boundary Conditions (Processor)
7.2.7 Solving Equations and Postprocessing
7.3 Applications of Program FEM1D
7.3.1 General Comments
7.3.2 Illustrative Examples
7.4 Summary
Problems
References for Additional Reading
8 Single-Variable Problems in Two Dimensions
8.1 Introduction
8.2 Boundary Value Problems
8.2.1 The Model Equation
8.2.2 Finite Element Discretization
8.2.3 Weak Form
8.2.4 Finite Element Model
8.2.5 Derivation of Interpolation Functions
8.2.6 Evaluation of Element Matrices and Vectors
8.2.7 Assembly of Element Equations
8.2.8 Postcomputations
8.2.9 Axisymmetric Problems
8.3 A Numerical Example
8.4 Some Comments on Mesh Generation and Imposition of Boundary Conditions
8.4.1 Discretization of a Domain
8.4.2 Generation of Finite Element Data
8.4.3 Imposition of Boundary Conditions
8.5 Applications
8.5.1 Conduction and Convection Heat Transfer
8.5.2 Fluid Mechanics
8.5.3 Solid Mechanics
8.6 Eigenvalue and Time-Dependent Problems
8.6.1 Introduction
8.6.2 Parabolic Equations
8.6.3 Hyperbolic Equations
8.7 Summary
Problems
References for Additional Reading
9 Interpolation Functions, Numerical Integration, and Modeling Considerations
9.1 Introduction
9.2 Element Library
9.2.1 Triangular Elements
9.2.2 Rectangular Elements
9.2.3 The Serendipity Elements
9.2.4 Hermite Cubic Interpolation Functions
9.3 Numerical Integration
9.3.1 Preliminary Comments
9.3.2 Coordinate Transformations
9.3.3 Integration over a Master Rectangular Element
9.3.4 Integration over a Master Triangular Element
9.4 Modeling Considerations
9.4.1 Preliminary Comments
9.4.2 Element Geometries
9.4.3 Mesh Generation
9.4.4 Load Representation
9.5 Summary
Problems
References for Additional Reading
10 Flows of Viscous Incompressible Fluids
10.1 Preliminary Comments
10.2 Governing Equations
10.3 Velocity-Pressure Formulation
10.3.1 Weak Formulation
10.3.2 Finite Element Model
10.4 Penalty Function Formulation
10.4.1 Preliminary Comments
10.4.2 Formulation of the Flow Problem as a Constrained Problem
10.4.3 Lagrange Multiplier Model
10.4.4 Penalty Model
10.4.5 Time Approximation
10.5 Computational Aspects
10.5.1 Properties of the Matrix Equations
10.5.2 Choice of Elements
10.5.3 Evaluation of Element Matrices in the Penalty Model
10.5.4 Postcomputation of Stresses
10.6 Numerical Examples
10.7 Summary
Problems
References for Additional Reading
11 Plane Elasticity
11.1 Introduction
11.2 Governing Equations
11.2.1 Plane Strain
11.2.2 Plane Stress
11.2.3 Summary of Equations
11.3 Weak Formulations
11.3.1 Preliminary Comments
11.3.2 Principle of Virtual Displacements in Vector Form.
11.3.3 Weak Form of the Governing Differential Equations
11.4 Finite Element Model
11.4.1 General Model
11.4.2 Eigenvalue and Transient Problems
11.5 Evaluation of Integrals
11.6 Assembly of Finite Element Equations
11.7 Examples
11.8 Summary
Problems
References for Additional Reading
12 Bending of Elastic Plates
12.1 Introduction
12.2 Classical Plate Theory
12.2.1 Displacement Field
12.2.2 Virtual Work Statement
12.2.3 Finite Element Model
12.2.4 Plate Bending Elements
12.3 Shear Deformation Plate Theory
12.3.1 Displacement Field
12.3.2 Virtual Work Statement
12.3.3 Finite Element Model
12.3.4 Shear Locking and Reduced Integration
12.4 Eigenvalue and Time-Dependent Problems
12.5 Examples
12.6 Summary
Problems
References for Additional Reading
13 Computer Implementation of Two-Dimensional Problems
13.1 Introduction
13.2 Preprocessor
13.3 Element Computations (Processor)
13.4 Applications of the Computer Program FEM2D
13.4.1 Introduction
13.4.2 Description of Mesh Generators
13.4.3 Applications (Illustrative Examples)
13.5 Summary
Problems
References for Additional Reading
14 Prelude to Advanced Topics
14.1 Introduction
14.2 Alternative Finite Element Models
14.2.1 Introductory Comments
14.2.2 Weighted Residual Finite Element Models
14.2.3 Mixed Formulations
14.3 Three-Dimensional Problems
14.3.1 Heat Transfer
14.3.2 Flows of Viscous Incompressible Fluids
14.3.3 Elasticity
14.3.4 Three-Dimensional Finite Elements
14.3.5 A Numerical Example
14.4 Nonlinear Problems
14.4.1 General Comments
14.4.2 Bending of Euler?Bernoulli Beams
14.4.3 The Navier?Stokes Equations in Two Dimensions
14.4.4 Solution Methods for Nonlinear Algebraic Equations
14.4.5 Numerical Examples
14.5 Errors in Finite Element Analysis
14.5.1 Types of Errors
14.5.2 Measures of Errors
14.5.3 Convergence and Accuracy of Solutions
14.6 Summary
Problems
References for Additional Reading
Index.

Introduction to the Finite Element Method, Third Edition /

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