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A First Course in Finite Elements Vital Source e-bog
Jacob Fish og Ted Belytschko
(2007)
John Wiley & Sons
599,00 kr.
539,10 kr.
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A First Course in Finite Elements
Jacob Fish og Ted Belytschko
(2007)
Sprog: Engelsk
John Wiley & Sons, Limited
629,00 kr.
566,10 kr.
4 stk på lager
Hvor kan jeg afhente varen?Detaljer om varen
- 1. Udgave
- Vital Source searchable e-book (Fixed pages)
- Udgiver: John Wiley & Sons (April 2007)
- Forfattere: Jacob Fish og Ted Belytschko
- ISBN: 9780470510841
Developed from the authors, combined total of 50 years
undergraduate and graduate teaching experience, this book presents
the finite element method formulated as a general-purpose numerical
procedure for solving engineering problems governed by partial
differential equations.
Focusing on the formulation and application of the finite element
method through the integration of finite element theory, code
development, and software application, the book is both
introductory and self-contained, as well as being a hands-on
experience for any student.
This authoritative text on Finite Elements:
* Adopts a generic approach to the subject, and is not application
specific
* In conjunction with a web-based chapter, it integrates code
development, theory, and application in one book
* Provides an accompanying Web site that includes ABAQUS Student
Edition, Matlab data and programs, and instructor resources
* Contains a comprehensive set of homework problems at the end of
each chapter
* Produces a practical, meaningful course for both lecturers,
planning a finite element module, and for students using the text
in private study.
* Accompanied by a book companion website housing supplementary
material that can be found at
http://www.wileyeurope.com/college/Fish
A First Course in Finite Elements is the ideal practical
introductory course for junior and senior undergraduate students
from a variety of science and engineering disciplines. The
accompanying advanced topics at the end of each chapter also make
it suitable for courses at graduate level, as well as for
practitioners who need to attain or refresh their knowledge of
finite elements through private study.
undergraduate and graduate teaching experience, this book presents
the finite element method formulated as a general-purpose numerical
procedure for solving engineering problems governed by partial
differential equations.
Focusing on the formulation and application of the finite element
method through the integration of finite element theory, code
development, and software application, the book is both
introductory and self-contained, as well as being a hands-on
experience for any student.
This authoritative text on Finite Elements:
* Adopts a generic approach to the subject, and is not application
specific
* In conjunction with a web-based chapter, it integrates code
development, theory, and application in one book
* Provides an accompanying Web site that includes ABAQUS Student
Edition, Matlab data and programs, and instructor resources
* Contains a comprehensive set of homework problems at the end of
each chapter
* Produces a practical, meaningful course for both lecturers,
planning a finite element module, and for students using the text
in private study.
* Accompanied by a book companion website housing supplementary
material that can be found at
http://www.wileyeurope.com/college/Fish
A First Course in Finite Elements is the ideal practical
introductory course for junior and senior undergraduate students
from a variety of science and engineering disciplines. The
accompanying advanced topics at the end of each chapter also make
it suitable for courses at graduate level, as well as for
practitioners who need to attain or refresh their knowledge of
finite elements through private study.
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Bookshelf online: 5 år fra købsdato.
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Detaljer om varen
- 1. Udgave
- Paperback: 336 sider
- Udgiver: John Wiley & Sons, Limited (April 2007)
- Forfattere: Jacob Fish og Ted Belytschko
- ISBN: 9780470035801
The text material evolved from over 50 years of combined teaching experience it deals with a formulation and application of the finite element method. A meaningful course can be constructed from a subset of the chapters in this book for a quarter course; instructions for such use are given in the preface. The course material is organized in three chronological units of one month each: 1) the finite element formulation for one-dimensional problems, 2) the finite element formulation for scalar field problems in two dimensions and 3) finite element programming and application to scalar field problems; and finite element formulation for vector field problems in two dimensions and beams. In conjunction with the book there will be the access and use of ABAQUS software and MATLAB exercises.
Preface xi 1 Introduction 1
1.1 Background 1
1.2 Applications of Finite elements 7 References 9 2 Direct Approach for Discrete Systems 11
2.1 Describing the Behavior of a Single Bar Element 11
2.2 Equations for a System 15
2.2.1 Equations for Assembly 18
2.2.2 Boundary Conditions and System Solution 20
2.3 Applications to Other Linear Systems 24
2.4 Two-Dimensional Truss Systems 27
2.5 Transformation Law 30
2.6 Three-Dimensional Truss Systems 35 References 36 Problems 37 3 Strong andWeak Forms for One-Dimensional Problems 41
3.1 The Strong Form in One-Dimensional Problems 42
3.1.1 The Strong Form for an Axially Loaded Elastic Bar 42
3.1.2 The Strong Form for Heat Conduction in One Dimension 44
3.1.3 Diffusion in One Dimension 46
3.2 TheWeak Form in One Dimension 47
3.3 Continuity 50
3.4 The Equivalence Between theWeak and Strong Forms 51
3.5 One-Dimensional Stress Analysis with Arbitrary Boundary Conditions 58
3.5.1 Strong Form for One-Dimensional Stress Analysis 58
3.5.2 Weak Form for One-Dimensional Stress Analysis 59
3.6 One-Dimensional Heat Conduction with Arbitrary Boundary Conditions 60
3.6.1 Strong Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 60
3.6.2 Weak Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 61
3.7 Two-Point Boundary Value Problem with Generalized Boundary Conditions 62
3.7.1 Strong Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 62
3.7.2 Weak Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 63
3.8 Advection-Diffusion 64
3.8.1 Strong Form of Advection-Diffusion Equation 65
3.8.2 Weak Form of Advection-Diffusion Equation 66
3.9 Minimum Potential Energy 67
3.10 Integrability 71 References 72 Problems 72 4 Approximation of Trial Solutions,Weight Functions and Gauss Quadrature for One-Dimensional Problems 77
4.1 Two-Node Linear Element 79
4.2 Quadratic One-Dimensional Element 81
4.3 Direct Construction of Shape Functions in One Dimension 82
4.4 Approximation of theWeight Functions 84
4.5 Global Approximation and Continuity 84
4.6 Gauss Quadrature 85 Reference 90 Problems 90 5 Finite Element Formulation for One-Dimensional Problems 93
5.1 Development of Discrete Equation: Simple Case 93
5.2 Element Matrices for Two-Node Element 97
5.3 Application to Heat Conduction and Diffusion Problems 99
5.4 Development of Discrete Equations for Arbitrary Boundary Conditions 105
5.5 Two-Point Boundary Value Problem with Generalized Boundary Conditions 111
5.6 Convergence of the FEM 113
5.6.1 Convergence by Numerical Experiments 115
5.6.2 Convergence by Analysis 118
5.7 FEM for Advection-Diffusion Equation 120 References 122 Problems 123 6 Strong andWeak Forms for Multidimensional Scalar Field Problems 131
6.1 Divergence Theorem and Green''s Formula 133
6.2 Strong Form 139
6.3 Weak Form 142
6.4 The Equivalence BetweenWeak and Strong Forms 144
6.5 Generalization to Three-Dimensional Problems 145
6.6 Strong andWeak Forms of Scalar Steady-State Advection-Diffusion in Two Dimensions 146 References 148 Problems 148 7 Approximations of Trial Solutions,Weight Functions and Gauss Quadrature for Multidimensional Problems 151
7.1 Completeness and Continuity 152
7.2 Three-Node Triangular Element 154
7.2.1 Global Approximation and Continuity 157
7.2.2 Higher Order Triangular Elements 159
7.2.3 Derivatives of Shape Functions for the Three-Node Triangular Element 160
7.3 Four-Node Rectangular Elements 161
7.4 Four-Node Quadrilateral Element 164
7.4.1 Continuity of Isoparametric Elements 166
7.4.2 Derivatives of Isoparametric Shape Functions 166
7.5 Higher Order Quadrilateral Elements 168
7.6 Triangular Coordinates 172
7.6.1 Linear Triangular Element 172
7.6.2 Isoparametric Triangular Elements 174
7.6.3 Cubic Element 175
7.6.4 Triangular Elements by Collapsing Quadrilateral Elements 176
7.7 Completeness of Isoparametric Elements 177
7.8 Gauss Quadrature in Two Dimensions 178
7.8.1 Integration Over Quadrilateral Elements 179
7.8.2 Integration Over Triangular Elements 180
7.9 Three-Dimensional Elements 181
7.9.1 Hexahedral Elements 181
7.9.2 Tetrahedral Elements 183 References 185 Problems 186 8 Finite Element Formulation for Multidimensional Scalar Field Problems 189
8.1 Finite Element Formulation for Two-Dimensional Heat Conduction Problems 189
8.2 Verification and Validation 201
8.3 Advection-Diffusion Equation 207 References 209 Problems 209 9 Finite Element Formulation for Vector Field Problems - Linear Elasticity 215
9.1 Linear Elasticity 215
9.1.1 Kinematics 217
9.1.2 Stress and Traction 219
9.1.3 Equilibrium 220
9.1.4 Constitutive Equation 222
9.2 Strong andWeak Forms 223
9.3 Finite Element Discretization 225
9.4 Three-Node Triangular Element 228
9.4.1 Element Body Force Matrix 229
9.4.2 Boundary Force Matrix 230
9.5 Generalization of Boundary Conditions 231
9.6 Discussion 239
9.7 Linear Elasticity Equations in Three Dimensions 240 Problems 241 10 Finite Element Formulation for Beams 249
10.1 Governing Equations of the Beam 249
10.1.1 Kinematics of Beam 249
10.1.2 Stress-Strain Law 252
10.1.3 Equilibrium 253
10.1.4 Boundary Conditions 254
10.2 Strong Form toWeak Form 255
10.2.1 Weak Form to Strong Form 257
10.3 Finite Element Discretization 258
10.3.1 Trial Solution andWeight Function Approximations 258
10.3.2 Discrete Equations 260
10.4 Theorem of Minimum Potential Energy 261
10.5 Remarks on Shell Elements 265 Reference 269 Problems 269 11 Commercial Finite Element Program ABAQUS Tutorials 275
11.1 Introduction 275
11.1.1 Steady-State Heat Flow Example 275
11.2 Preliminaries 275
11.3 Creating a
Part 276
11.4 Creating a Material Definition 278
11.5 Defining and Assigning Section Properties 279
11.6 Assembling the Model 280
11.7 Configuring the Analysis 280
11.8 Applying a Boundary Condition and a Load to the Model 280
11.9 Meshing the Model 282
11.10 Creating and Submitting an Analysis Job 284
11.11 Viewing the Analysis Results 284
11.12 Solving the Problem Using Quadrilaterals 284
11.13 Refining the Mesh 285
11.13.1 Bending of a Short Cantilever Beam 287
11.14 Copying the Model 287
11.15 Modifying the Material Definition 287
11.16 Configuring the Analysis 287
11.17 Applying a Boundary Condition and a Load to the Model 288
11.18 Meshing the Model 289
11.19 Creating and Submitting an Analysis Job 290
11.20 Viewing the Analysis Results 290
11.20.1 Plate with a Hole in Tension 290
11.21 Creating a New Model 292
11.22 Creating a
Part 292
11.23 Creating a Material Definition 293
11.24 Defining and Assigning Section Properties 294
11.25 Assembling the Model 295
11.26 Configuring the Analysis 295
11.27 Applying a Boundary Condition and a Load to the Model 295
11.28 Meshing the Model 297
11.29 Creating and Submitting an Analysis Job 298
11.30 Viewing the Analysis Results 299
11.31 Refining the Mesh 299 Appendix 303 A.1 Rotation of Coordinate System in Three Dimensions 303 A.2 Scalar Product Theorem 304 A.3 Taylor''s Formula with Remainder and the Mean Value Theorem 304 A.4 Green''s Theorem 305 A.5 Point Force (Source) 307 A.6 Static Condensation 308 A.7 Solution Methods 309 Direct Solvers 310 Iterative Solvers 310 Conditioning 311 References 312 Problem 312 Index 313
1.1 Background 1
1.2 Applications of Finite elements 7 References 9 2 Direct Approach for Discrete Systems 11
2.1 Describing the Behavior of a Single Bar Element 11
2.2 Equations for a System 15
2.2.1 Equations for Assembly 18
2.2.2 Boundary Conditions and System Solution 20
2.3 Applications to Other Linear Systems 24
2.4 Two-Dimensional Truss Systems 27
2.5 Transformation Law 30
2.6 Three-Dimensional Truss Systems 35 References 36 Problems 37 3 Strong andWeak Forms for One-Dimensional Problems 41
3.1 The Strong Form in One-Dimensional Problems 42
3.1.1 The Strong Form for an Axially Loaded Elastic Bar 42
3.1.2 The Strong Form for Heat Conduction in One Dimension 44
3.1.3 Diffusion in One Dimension 46
3.2 TheWeak Form in One Dimension 47
3.3 Continuity 50
3.4 The Equivalence Between theWeak and Strong Forms 51
3.5 One-Dimensional Stress Analysis with Arbitrary Boundary Conditions 58
3.5.1 Strong Form for One-Dimensional Stress Analysis 58
3.5.2 Weak Form for One-Dimensional Stress Analysis 59
3.6 One-Dimensional Heat Conduction with Arbitrary Boundary Conditions 60
3.6.1 Strong Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 60
3.6.2 Weak Form for Heat Conduction in One Dimension with Arbitrary Boundary Conditions 61
3.7 Two-Point Boundary Value Problem with Generalized Boundary Conditions 62
3.7.1 Strong Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 62
3.7.2 Weak Form for Two-Point Boundary Value Problems with Generalized Boundary Conditions 63
3.8 Advection-Diffusion 64
3.8.1 Strong Form of Advection-Diffusion Equation 65
3.8.2 Weak Form of Advection-Diffusion Equation 66
3.9 Minimum Potential Energy 67
3.10 Integrability 71 References 72 Problems 72 4 Approximation of Trial Solutions,Weight Functions and Gauss Quadrature for One-Dimensional Problems 77
4.1 Two-Node Linear Element 79
4.2 Quadratic One-Dimensional Element 81
4.3 Direct Construction of Shape Functions in One Dimension 82
4.4 Approximation of theWeight Functions 84
4.5 Global Approximation and Continuity 84
4.6 Gauss Quadrature 85 Reference 90 Problems 90 5 Finite Element Formulation for One-Dimensional Problems 93
5.1 Development of Discrete Equation: Simple Case 93
5.2 Element Matrices for Two-Node Element 97
5.3 Application to Heat Conduction and Diffusion Problems 99
5.4 Development of Discrete Equations for Arbitrary Boundary Conditions 105
5.5 Two-Point Boundary Value Problem with Generalized Boundary Conditions 111
5.6 Convergence of the FEM 113
5.6.1 Convergence by Numerical Experiments 115
5.6.2 Convergence by Analysis 118
5.7 FEM for Advection-Diffusion Equation 120 References 122 Problems 123 6 Strong andWeak Forms for Multidimensional Scalar Field Problems 131
6.1 Divergence Theorem and Green''s Formula 133
6.2 Strong Form 139
6.3 Weak Form 142
6.4 The Equivalence BetweenWeak and Strong Forms 144
6.5 Generalization to Three-Dimensional Problems 145
6.6 Strong andWeak Forms of Scalar Steady-State Advection-Diffusion in Two Dimensions 146 References 148 Problems 148 7 Approximations of Trial Solutions,Weight Functions and Gauss Quadrature for Multidimensional Problems 151
7.1 Completeness and Continuity 152
7.2 Three-Node Triangular Element 154
7.2.1 Global Approximation and Continuity 157
7.2.2 Higher Order Triangular Elements 159
7.2.3 Derivatives of Shape Functions for the Three-Node Triangular Element 160
7.3 Four-Node Rectangular Elements 161
7.4 Four-Node Quadrilateral Element 164
7.4.1 Continuity of Isoparametric Elements 166
7.4.2 Derivatives of Isoparametric Shape Functions 166
7.5 Higher Order Quadrilateral Elements 168
7.6 Triangular Coordinates 172
7.6.1 Linear Triangular Element 172
7.6.2 Isoparametric Triangular Elements 174
7.6.3 Cubic Element 175
7.6.4 Triangular Elements by Collapsing Quadrilateral Elements 176
7.7 Completeness of Isoparametric Elements 177
7.8 Gauss Quadrature in Two Dimensions 178
7.8.1 Integration Over Quadrilateral Elements 179
7.8.2 Integration Over Triangular Elements 180
7.9 Three-Dimensional Elements 181
7.9.1 Hexahedral Elements 181
7.9.2 Tetrahedral Elements 183 References 185 Problems 186 8 Finite Element Formulation for Multidimensional Scalar Field Problems 189
8.1 Finite Element Formulation for Two-Dimensional Heat Conduction Problems 189
8.2 Verification and Validation 201
8.3 Advection-Diffusion Equation 207 References 209 Problems 209 9 Finite Element Formulation for Vector Field Problems - Linear Elasticity 215
9.1 Linear Elasticity 215
9.1.1 Kinematics 217
9.1.2 Stress and Traction 219
9.1.3 Equilibrium 220
9.1.4 Constitutive Equation 222
9.2 Strong andWeak Forms 223
9.3 Finite Element Discretization 225
9.4 Three-Node Triangular Element 228
9.4.1 Element Body Force Matrix 229
9.4.2 Boundary Force Matrix 230
9.5 Generalization of Boundary Conditions 231
9.6 Discussion 239
9.7 Linear Elasticity Equations in Three Dimensions 240 Problems 241 10 Finite Element Formulation for Beams 249
10.1 Governing Equations of the Beam 249
10.1.1 Kinematics of Beam 249
10.1.2 Stress-Strain Law 252
10.1.3 Equilibrium 253
10.1.4 Boundary Conditions 254
10.2 Strong Form toWeak Form 255
10.2.1 Weak Form to Strong Form 257
10.3 Finite Element Discretization 258
10.3.1 Trial Solution andWeight Function Approximations 258
10.3.2 Discrete Equations 260
10.4 Theorem of Minimum Potential Energy 261
10.5 Remarks on Shell Elements 265 Reference 269 Problems 269 11 Commercial Finite Element Program ABAQUS Tutorials 275
11.1 Introduction 275
11.1.1 Steady-State Heat Flow Example 275
11.2 Preliminaries 275
11.3 Creating a
Part 276
11.4 Creating a Material Definition 278
11.5 Defining and Assigning Section Properties 279
11.6 Assembling the Model 280
11.7 Configuring the Analysis 280
11.8 Applying a Boundary Condition and a Load to the Model 280
11.9 Meshing the Model 282
11.10 Creating and Submitting an Analysis Job 284
11.11 Viewing the Analysis Results 284
11.12 Solving the Problem Using Quadrilaterals 284
11.13 Refining the Mesh 285
11.13.1 Bending of a Short Cantilever Beam 287
11.14 Copying the Model 287
11.15 Modifying the Material Definition 287
11.16 Configuring the Analysis 287
11.17 Applying a Boundary Condition and a Load to the Model 288
11.18 Meshing the Model 289
11.19 Creating and Submitting an Analysis Job 290
11.20 Viewing the Analysis Results 290
11.20.1 Plate with a Hole in Tension 290
11.21 Creating a New Model 292
11.22 Creating a
Part 292
11.23 Creating a Material Definition 293
11.24 Defining and Assigning Section Properties 294
11.25 Assembling the Model 295
11.26 Configuring the Analysis 295
11.27 Applying a Boundary Condition and a Load to the Model 295
11.28 Meshing the Model 297
11.29 Creating and Submitting an Analysis Job 298
11.30 Viewing the Analysis Results 299
11.31 Refining the Mesh 299 Appendix 303 A.1 Rotation of Coordinate System in Three Dimensions 303 A.2 Scalar Product Theorem 304 A.3 Taylor''s Formula with Remainder and the Mean Value Theorem 304 A.4 Green''s Theorem 305 A.5 Point Force (Source) 307 A.6 Static Condensation 308 A.7 Solution Methods 309 Direct Solvers 310 Iterative Solvers 310 Conditioning 311 References 312 Problem 312 Index 313
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