工程中的有限元方法 第3版 英文版PDF|Epub|txt|kindle电子书版本网盘下载

工程中的有限元方法 第3版 英文版PDF格式电子书版下载

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Contents1

出版说明1

序1

前言1

PREFACE1

1 FUNDAMENTAL CONCEPTS1

1.1 Introduction1

1.2 Historical Background1

1.3 Outline of Presentation2

1.4 Stresses and Equilibrium2

1.5 Boundary Conditions4

1.6 Strain-Displacement Relations4

1.7 Stress-Strain Relations6

Special Cases,7

1.8 Temperature Effects8

1.9 Potential Energy and Equilibrium;The Rayleigh-Ritz Method9

Potential Energy П,9

Rayleigh-Ritz Method,11

1.10 Galerkin's Method13

1.11 Saint Venant's Principle16

1.12 Von Mises Stress17

1.13 Computer Programs17

1.14 Conclusion18

Historical References18

Problems18

2 MATRIX ALGEBRA AND GAUSSIAN ELIMINATION22

2.1 Matrix Algebra22

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 Elimination29

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 Solving39

Conjugate GradientAlgorithm,40

Problems41

Program Listings,43

3 ONE-DIMENSIONAL PROBLEMS45

3.1 Introduction45

3.2 Finite Element Modeling46

Element Division,46

Numbering Scheme,47

3.3 Coordinates and Shape Functions48

3.4 The Potential-Energy Approach52

Element Stiffness Matrix,53

Force Terms,54

3.5 The Galerkin Approach56

Element Stiffness,56

ForceTerms,57

3.6 Assembly of the Global Stiffness Matrix and Load Vector58

3.7 Properties of K61

3.8 The Finite Element Equations;Treatment of Boundary Conditions62

Types of Boundary Conditions,62

Elimination Approach,63

Penalty Approach,69

Multipoint Constraints,74

3.9 Quadratic Shape Functions78

3.10 Temperature Effects84

Problems88

Input Data File,88

Program Listing,98

4 TRUSSES103

4.1 Introduction103

4.2 Plane Trusses104

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 Trusses114

4.4 Assembly of Global Stiffness Matrix for the Banded and Skyline Solutions116

Assembly for Banded Solution,116

Input Data File,119

Problems120

Program Listing,128

5 TWO-DIMENSIONAL PROBLEMS USING CONSTANT STRAIN TRIANGLES130

5.1 Introduction130

5.2 Finite Element Modeling131

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 Conditions152

Some General Comments on Dividing into Elements,154

5.5 Orthotropic Materials154

TemperatureEffects,157

InputDataFile,160

Problems162

Program Listing,174

6 AXISYMMETRIC SOLIDS SUBJECTED TO AXISYMMETRIC LOADING178

6.1 Introduction178

6.2 Axisymmetric Formulation179

6.3 Finite Element Modeling:Triangular Element181

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 Conditions191

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

Problems198

Program Listing,205

7 TWO-DIMENSIONAL ISOPARAMETRIC ELEMENTS AND NUMERICAL INTEGRATION208

7.1 Introduction208

7.2 The Four-Node Quadrilateral208

Shape Functions,208

Element Stiffness Matrix,211

Element Force Vectors,213

7.3 Numerical Integration214

Stiffness Integration,217

Two-Dimensional Integrals,217

Stress Calculations,218

7.4 Higher Order Elements220

Nine-Node Quadrilateral,220

Eight-Node Quadrilateral,222

Six-Node Triangle,223

7.5 Four-Node Quadrilateral for Axisymmetric Problems225

7.6 Conjugate Gradient Implementation of the Quadrilateral Element226

Concluding Note,227

Input Data File,228

Problems230

Program Listings,233

8 BEAMS AND FRAMES237

8.1 Introduction237

Potential-Energy Approach,238

Galerkin Approach,239

8.2 Finite Element Formulation240

8.3 LoadVector243

8.4 Boundary Considerations244

8.5 Shear Force and Bending Moment245

8.6 Beams on Elastic Supports247

8.7 Plane Frames248

8.8 Three-Dimensional Frames253

8.9 Some Comments257

Input Data File,258

Problems261

Program Listings,267

9 THREE-DIMENSIONAL PROBLEMS IN STRESS ANALYSIS275

9.1 Introduction275

9.2 Finite Element Formulation276

Element Stiffness,279

9.3 Stress Calculations280

Force Terms,280

9.4 Mesh Preparation281

9.5 Hexahedral Elements and Higher Order Elements285

9.6 Problem Modeling287

9.7 Frontal Method for Finite Element Matrices289

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

Problems293

Program Listings,297

10 SCALAR FIELD PROBLEMS306

10.1 Introduction306

10.2 Steady State Heat Transfer308

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 Torsion331

Triangular Element,332

Galerkin Approach,333

10.4 Potential Flow,Seepage,Electric and Magnetic Fields,and Fluid Flow in Ducts336

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 Conclusion348

Input Data File,349

Problems350

Program Listings,361

11.2 Formulation367

11.1 Introduction367

11 DYNAMIC CONSIDERATIONS367

Solid Body with Distributed Mass,368

11.3 Element Mass Matrices370

11.4 Evaluation of Eigenvalues and Eigenvectors375

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 Shafts391

11.6 Guyan Reduction392

11.7 Rigid Body Modes394

11.8 Conclusion396

Input Data File,397

Problems399

Program Listings,404

12 PREPROCESSING AND POSTPROCESSING411

12.1 Introduction411

12.2 Mesh Generation411

Region and Block Representation,411

Block Corner Nodes,Sides,and Subdivisions,412

Deformed Configuration and Mode Shape,419

12.3 Postprocessing419

Contour Plotting,420

Nodal Values from Known Constant Element Values421

for aTriangle,421

Least Squares Fit for a Four-Noded Quadrilateral,423

12.4 Conclusion424

Input Data File,425

Problems425

Program Listings,427

APPENDIX Proof of dA＝det J dξdη440

BIBLIOGRAPHY443

ANSWERS TO SELECTED PROBLEMS447

INDEX449

教师信息反馈表454

时代教育·国外高校优秀教材精选455