工程中的有限元方法 第3版 英文版PDF电子书下载

Contents 1

出版说明 1

序 1

前言 1

PREFACE 1

1 FUNDAMENTAL CONCEPTS 1

1.1 Introduction 1

1.2 Historical Background 1

1.3 Outline of Presentation 2

1.4 Stresses and Equilibrium 2

1.5 Boundary Conditions 4

1.6 Strain-Displacement Relations 4

1.7 Stress-Strain Relations 6

Special Cases, 7

1.8 Temperature Effects 8

1.9 Potential Energy and Equilibrium;The Rayleigh-Ritz Method 9

Potential Energy П, 9

Rayleigh-Ritz Method, 11

1.10 Galerkin's Method 13

1.11 Saint Venant's Principle 16

1.12 Von Mises Stress 17

1.13 Computer Programs 17

1.14 Conclusion 18

Historical References 18

Problems 18

2 MATRIX ALGEBRA AND GAUSSIAN ELIMINATION 22

2.1 Matrix Algebra 22

Multiplication by a Scalar, 23

Matrix Multiplication, 23

Addition and Subtraction, 23

Row and Column Vectors, 23

Transposition, 24

Differentiation and Integration, 24

Square Matrix, 25

Diagonal Matrix, 25

Identity Matrix, 25

Symmetric Matrix, 25

UpperTriangularMatrix, 26

Determinant ofa Matrix, 26

Matrix Inversion, 26

Eigenvalues and Eigenvectors, 27

Positive Definite Matrix, 28

Cholesky Decomposition, 29

2.2 Gaussian Elimination 29

GeneralAlgorithm for Gaussian Elimination, 30

Symmetric Matrix, 33

Symmetric Banded Matrices, 33

Solution with Multiple Right Sides, 35

Gaussian Elimination with Column Reduction, 36

Skyline Solution, 38

Frontal Solution, 39

2.3 Conjugate Gradient Method for Equation Solving 39

Conjugate GradientAlgorithm, 40

Problems 41

Program Listings, 43

3 ONE-DIMENSIONAL PROBLEMS 45

3.1 Introduction 45

3.2 Finite Element Modeling 46

Element Division, 46

Numbering Scheme, 47

3.3 Coordinates and Shape Functions 48

3.4 The Potential-Energy Approach 52

Element Stiffness Matrix, 53

Force Terms, 54

3.5 The Galerkin Approach 56

Element Stiffness, 56

ForceTerms, 57

3.6 Assembly of the Global Stiffness Matrix and Load Vector 58

3.7 Properties of K 61

3.8 The Finite Element Equations;Treatment of Boundary Conditions 62

Types of Boundary Conditions, 62

Elimination Approach, 63

Penalty Approach, 69

Multipoint Constraints, 74

3.9 Quadratic Shape Functions 78

3.10 Temperature Effects 84

Problems 88

Input Data File, 88

Program Listing, 98

4 TRUSSES 103

4.1 Introduction 103

4.2 Plane Trusses 104

Local and Global Coordinate Systems, 104

Formulas for Calculating e and m, 105

Element Stiffness Matrix, 106

Stress Calculations, 107

TemperatureEffects, 111

4.3 Three-Dimensional Trusses 114

4.4 Assembly of Global Stiffness Matrix for the Banded and Skyline Solutions 116

Assembly for Banded Solution, 116

Input Data File, 119

Problems 120

Program Listing, 128

5 TWO-DIMENSIONAL PROBLEMS USING CONSTANT STRAIN TRIANGLES 130

5.1 Introduction 130

5.2 Finite Element Modeling 131

5.3 Constant-Strain Triangle（CST） 133

Isoparametric Representation, 135

Potential-Energy Approach, 139

Element Stiffness, 140

Force Terms, 141

Galerkin Approach, 146

Stress Calculations, 148

Temperature Effects, 150

5.4 Problem Modeling and Boundary Conditions 152

Some General Comments on Dividing into Elements, 154

5.5 Orthotropic Materials 154

TemperatureEffects, 157

InputDataFile, 160

Problems 162

Program Listing, 174

6 AXISYMMETRIC SOLIDS SUBJECTED TO AXISYMMETRIC LOADING 178

6.1 Introduction 178

6.2 Axisymmetric Formulation 179

6.3 Finite Element Modeling:Triangular Element 181

Potential-Energy Approach, 183

Body Force Term, 184

Rotating Flywheel, 185

Surface Traction, 185

Galerkin Approach, 187

Stress Calculations, 190

Temperature Effects, 191

6.4 Problem Modeling and Boundary Conditions 191

Cylinder Subjected to Internal Pressure, 191

Press Fit on a Rigid Shaft, 192

Infinite Cylinder, 192

Press Fit on an Elastic Shaft, 193

Belleville Spring, 194

Thermal Stress Problem, 195

Input Data File, 197

Problems 198

Program Listing, 205

7 TWO-DIMENSIONAL ISOPARAMETRIC ELEMENTS AND NUMERICAL INTEGRATION 208

7.1 Introduction 208

7.2 The Four-Node Quadrilateral 208

Shape Functions, 208

Element Stiffness Matrix, 211

Element Force Vectors, 213

7.3 Numerical Integration 214

Stiffness Integration, 217

Two-Dimensional Integrals, 217

Stress Calculations, 218

7.4 Higher Order Elements 220

Nine-Node Quadrilateral, 220

Eight-Node Quadrilateral, 222

Six-Node Triangle, 223

7.5 Four-Node Quadrilateral for Axisymmetric Problems 225

7.6 Conjugate Gradient Implementation of the Quadrilateral Element 226

Concluding Note, 227

Input Data File, 228

Problems 230

Program Listings, 233

8 BEAMS AND FRAMES 237

8.1 Introduction 237

Potential-Energy Approach, 238

Galerkin Approach, 239

8.2 Finite Element Formulation 240

8.3 LoadVector 243

8.4 Boundary Considerations 244

8.5 Shear Force and Bending Moment 245

8.6 Beams on Elastic Supports 247

8.7 Plane Frames 248

8.8 Three-Dimensional Frames 253

8.9 Some Comments 257

Input Data File, 258

Problems 261

Program Listings, 267

9 THREE-DIMENSIONAL PROBLEMS IN STRESS ANALYSIS 275

9.1 Introduction 275

9.2 Finite Element Formulation 276

Element Stiffness, 279

9.3 Stress Calculations 280

Force Terms, 280

9.4 Mesh Preparation 281

9.5 Hexahedral Elements and Higher Order Elements 285

9.6 Problem Modeling 287

9.7 Frontal Method for Finite Element Matrices 289

Connectivity and Prefront Routine, 290

Element Assembly and Consideration of Specified dof, 290

Elimination of Completed dof, 291

Backsubstitution, 291

Consideration of Multipoint Constraints, 291

Input Data File, 292

Problems 293

Program Listings, 297

10 SCALAR FIELD PROBLEMS 306

10.1 Introduction 306

10.2 Steady State Heat Transfer 308

One-Dimensional Heat Conduction, 309

One-Dimensional Heat Transfer in Thin Fins, 316

Two-Dimensional Steady-State Heat Conduction, 320

Two-Dimensional Fins, 329

Preprocessing for Program Heat2D, 330

10.3 Torsion 331

Triangular Element, 332

Galerkin Approach, 333

10.4 Potential Flow,Seepage,Electric and Magnetic Fields,and Fluid Flow in Ducts 336

PotentialFlow, 336

Seepage, 338

Electrical and Magnetic Field Problems, 339

Fluid Flow in Ducts, 341

Acoustics, 343

One-Dimensional Acoustics, 344

Boundary Conditions, 344

1-D Axial Vibrations, 345

Two-Dimensional Acoustics, 348

10.5 Conclusion 348

Input Data File, 349

Problems 350

Program Listings, 361

11.2 Formulation 367

11.1 Introduction 367

11 DYNAMIC CONSIDERATIONS 367

Solid Body with Distributed Mass, 368

11.3 Element Mass Matrices 370

11.4 Evaluation of Eigenvalues and Eigenvectors 375

Properties of Eigenvectors, 376

Eigenvalue-Eigenvector Evaluation, 376

Generalized Jacobi Method, 382

Bringing Generalized Problem to Standard Form, 386

Tridiagonalization and Implicit Shift Approach, 386

Tridiagonalization, 387

Implicit Symmetric QR Step with Wilkinson Shift for Diagonalization, 390

11.5 Interfacing with Previous Finite Element Programs and a Program for Determining Critical Speeds of Shafts 391

11.6 Guyan Reduction 392

11.7 Rigid Body Modes 394

11.8 Conclusion 396

Input Data File, 397

Problems 399

Program Listings, 404

12 PREPROCESSING AND POSTPROCESSING 411

12.1 Introduction 411

12.2 Mesh Generation 411

Region and Block Representation, 411

Block Corner Nodes,Sides,and Subdivisions, 412

Deformed Configuration and Mode Shape, 419

12.3 Postprocessing 419

Contour Plotting, 420

Nodal Values from Known Constant Element Values 421

for aTriangle, 421

Least Squares Fit for a Four-Noded Quadrilateral, 423

12.4 Conclusion 424

Input Data File, 425

Problems 425

Program Listings, 427

APPENDIX Proof of dA＝det J dξdη 440

BIBLIOGRAPHY 443

ANSWERS TO SELECTED PROBLEMS 447

INDEX 449

教师信息反馈表 454

时代教育·国外高校优秀教材精选 455