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Historical References 18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