目录 · · · · · ·
1. A Brief Overview of MATLAB s Programming Language 1
1.1 Introduction 2
1.2 Variables 3
1.3 Vectors 4
1.4 Matrices 6
1.5 Export and import data 12
· · · · · · (更多)
1.1 Introduction 2
1.2 Variables 3
1.3 Vectors 4
1.4 Matrices 6
1.5 Export and import data 12
· · · · · · (更多)
1. A Brief Overview of MATLAB s Programming Language 1
1.1 Introduction 2
1.2 Variables 3
1.3 Vectors 4
1.4 Matrices 6
1.5 Export and import data 12
1.6 Loops 12
1.7 Conditional statements 14
1.8 The switch function 16
1.9 2D and 3D Plotting 17
1.10 Programming a function 20
1.11 Chapter overview 27
Exercises 27
References 28
2. Matrix Analysis of Framed Structures 29
2.1 Introduction 30
2.2 EXAMPLE 2.1: Determining the general form of the stiffness matrix 36
2.3 Plane trusses 37
2.4 EXAMPLE 2.2: Matrix analysis of a plane truss 43
2.5 EXAMPLE 2.3: Matrix analysis of a plane truss 45
2.6 Space trusses 48
2.7 EXAMPLE 2.4: Matrix analysis of a space truss 51
2.8 EXAMPLE 2.5: Matrix analysis of a space truss 53
2.9 Plane frames 56
2.10 EXAMPLE 2.6: Matrix analysis of a plane frame 59
2.11 EXAMPLE 2.7: Matrix analysis of a plane frame 62
2.12 Space frames 65
2.13 EXAMPLE 2.8: Matrix analysis of a space frame 70
2.14 EXAMPLE 2.9: Matrix analysis of a space frame 74
2.15 Grids 77
2.16 EXAMPLE 2.10: Matrix analysis of a grid structure 80
2.17 EXAMPLE 2.11: Matrix analysis of a grid structure 83
2.18 Special cases 86
2.19 EXAMPLE 2.12: Matrix analysis of a plane frame subjected to a distributed member loading 89
2.20 EXAMPLE 2.13: Matrix analysis of a plane frame subjected to support settlements 94
2.21 EXAMPLE 2.14: Matrix analysis of a plane frame subjected to temperature variations 99
2.22 EXAMPLE 2.15: Matrix analysis of a plane truss frame affected by member mismatch 103
2.23 EXAMPLE 2.16: Matrix analysis of a plane frame with released members 106
2.24 EXAMPLE 2.17: Matrix analysis of a plane frame having an elastic support 110
2.25 Chapter overview 112
Exercises 112
References 116
3. Elastic analysis of structures using finite element procedure 117
3.1 Introduction 118
3.2 FEM programming for continuum elements 127
3.3 EXAMPLE 3.1: Obtaining the stiffness matrix of a two-node truss member 128
3.4 EXAMPLE 3.2: Obtaining the stiffness matrix of a three-node truss member 131
3.5 EXAMPLE 3.3: Linear-elastic analysis of a one-dimensional structure with 133
3.6 EXAMPLE 3.4: Linear-elastic analysis of a one-dimensional structure with varying cross-sections 136
3.7 EXAMPLE 3.5: Linear-elastic analysis of a plane truss using FEM 139
3.8 EXAMPLE 3.6: Linear-elastic analysis of plane stress structure subjected to 153
3.9 EXAMPLE 3.7: Linear-elastic analysis of plane stress structure subjected to 155
3.10 EXAMPLE 3.8: Linear-elastic analysis of a plane strain structure using quadrilateral elements 158
3.11 EXAMPLE 3.9: Linear-elastic analysis of an axisymmetric structure using quadrilateral elements 161
3.12 EXAMPLE 3.10: Linear-elastic analysis of a plane stress structure using triangular elements 163
3.13 EXAMPLE 3.11: Linear-elastic analysis of a plane stress structure elements 166
3.14 EXAMPLE 3.12: Linear-elastic analysis of a three-dimensional structure subjected to a surface load 174
3.15 EXAMPLE 3.13: Linear-elastic analysis of a three-dimensional structure subjected to a body load 177
3.16 FEM programming for structural elements 179
3.17 EXAMPLE 3.14: Linear-elastic analysis of a clamped Timoshenko beam 183
3.18 EXAMPLE 3.15: Linear-elastic analysis of a Timoshenko beam having 185
3.19 EXAMPLE 3.16: Linear-elastic analysis of a simply supported Mindlin?Reissner plate 192
3.20 EXAMPLE 3.17: Linear-elastic analysis of a clamped supported Mindlin?Reissner plate 195
3.21 Chapter overview 196
Exercises 197
References 198
4. Elastoplastic Analysis of Structures Using Finite Element
Procedure 199
4.1 Introduction 201
4.2 Basics 202
4.3 Elastoplasticity 205
4.4 Yield criteria 210
4.5 Hardening laws 214
4.6 Stress integration using the von Mises yield criterion 219
4.7 Solving nonlinear problems 224
4.8 Finite element programming considering the nonlinear behavior of materials 226
4.9 EXAMPLE 4.1: Elastoplastic analysis of structure with plane strain 230
EXAMPLE 4.2: Elastoplastic analysis of structure with plane strain 235
EXAMPLE 4.3: Elastoplastic analysis of structure with plane strain
condition and isotropic hardening using four-node rectangular
quadrilaterals subjected to a uniform surface load 238
EXAMPLE 4.4: Elastoplastic analysis of structure with plane strain
condition and combined hardening using four-node rectangular
quadrilaterals subjected to a uniform surface load 243
EXAMPLE 4.5: Elastoplastic analysis of structure with plane strain
condition and power-law isotropic hardening using four-node 246
4.10 Extension to three-dimensional elements 249
4.11 Elastoplastic tangent operator 250
4.12 Convergence criteria 253
4.13 Chapter overview 255
Exercises 255
References 256
Further reading 256
5. Finite deformation and hyperelasticity 257
5.1 Introduction 258
5.2 Strain and stress measures in finite deformation 259
5.3 EXAMPLE 5.1: Programming for obtaining the deformation gradient,
the Lagrangian strain, and the second Piola?Kirchhoff stress 267
5.4 Analysis procedures 269
5.5 EXAMPLE 5.2: Finite strain analysis of a uniaxial truss element
subjected to a tension load using the TL formulation 273
5.6 EXAMPLE 5.3: Finite strain analysis of a uniaxial truss element
subjected to a tension load using the UL formulation 276
5.7 Hyperelastic materials 279
5.8 EXAMPLE 5.4: Fitting test data to the neo-Hookean model 295
5.9 EXAMPLE 5.5: Fitting test data to the Mooney?Rivlin model 298
5.10 EXAMPLE 5.6: Fitting test data to the Yeoh model 300
5.11 EXAMPLE 5.7: Fitting test data to the Ogden model 302
5.12 EXAMPLE 5.8: Finite deformation analysis of a structure with plane 310
5.13 EXAMPLE 5.9: Step-by-step finite deformation analysis of a structure 312
5.14 EXAMPLE 5.10: Step-by-step finite deformation analysis of a structure 316
5.15 Chapter overview 319
Exercises 319
References 320
Further reading 320
6. Finite strain 321
6.1 Introduction 322
6.2 Finite rotation and objective rates 323
6.3 EXAMPLE 6.1: Step-by-step finite strain analysis of a structure with 332
6.4 EXAMPLE 6.2: Step-by-step finite strain analysis of a structure 340
6.5 Finite deformation elastoplasticity 344
6.6 Chapter overview 353
Exercises 353
References 353
Further reading 354
7. Solution to systems of linear equations 355
7.1 Introduction 357
7.2 Solution to systems of linear equations 358
7.3 EXAMPLE 7.1: Programming for the LDL T decomposition 373
7.4 EXAMPLE 7.2: Programming of the Gauss?Seidel iterative algorithm 376
7.5 EXAMPLE 7.3: Programming of the successive overrelaxation algorithm 378
7.6 EXAMPLE 7.4: Programming of the modified Richardson iterative algorithm 380
7.7 EXAMPLE 7.5: Programming of the conjugate gradient iterative algorithm 384
7.8 EXAMPLE 7.6: Programming of the conjugate residual iterative algorithm 385
7.9 EXAMPLE 7.7: Programming of the preconditioned conjugate gradient iterative algorithm 388
7.10 EXAMPLE 7.8: Programming of the MINRES iterative algorithm 390
7.11 EXAMPLE 7.9: Programming of the BiCG iterative algorithm 392
7.12 EXAMPLE 7.10: Programming of the BiCG stabilized iterative algorithm 393
7.13 EXAMPLE 7.11: Programming of the CGS iterative algorithm 395
7.14 EXAMPLE 7.12: Programming of the QMR iterative algorithm 396
7.15 EXAMPLE 7.13: Programming of the TFQMR iterative algorithm 397
7.16 EXAMPLE 7.14: Programming of the GMRES iterative algorithm 398
7.17 Solution to eigenproblems 398
7.18 EXAMPLE 7.15: Programming for transforming a general eigenproblem into the standard form 401
7.19 EXAMPLE 7.16: Programming of the Jacobi method 403
7.20 EXAMPLE 7.17: Programming of the generalized Jacobi method 407
7.21 EXAMPLE 7.18: Programming of the HQRI method 410
7.22 EXAMPLE 7.19: Programming of the vector inverse method 414
7.23 EXAMPLE 7.20: Programming of the forward iteration method 415
7.24 EXAMPLE 7.21: Programming of the shifted vector iteration method 417
7.25 EXAMPLE 7.22: Programming of the Rayleigh Quotient iteration method 419
7.26 EXAMPLE 7.23: Programming of the Rayleigh Quotient iteration algorithm with the Gram?Schmidt method 421
7.27 EXAMPLE 7.24: Programming of the implicit polynomial iteration method 423
7.28 EXAMPLE 7.25: Programming for solving a generalized eigenproblem using the Lanczos transformation method 426
7.29 EXAMPLE 7.26: Programming of the convergence check for the Lanczos transformation method 428
7.30 EXAMPLE 7.27: Programming of the subspace method 431 7.31 Chapter overview 434
References 434
Further reading 434
· · · · · · (收起)
1.1 Introduction 2
1.2 Variables 3
1.3 Vectors 4
1.4 Matrices 6
1.5 Export and import data 12
1.6 Loops 12
1.7 Conditional statements 14
1.8 The switch function 16
1.9 2D and 3D Plotting 17
1.10 Programming a function 20
1.11 Chapter overview 27
Exercises 27
References 28
2. Matrix Analysis of Framed Structures 29
2.1 Introduction 30
2.2 EXAMPLE 2.1: Determining the general form of the stiffness matrix 36
2.3 Plane trusses 37
2.4 EXAMPLE 2.2: Matrix analysis of a plane truss 43
2.5 EXAMPLE 2.3: Matrix analysis of a plane truss 45
2.6 Space trusses 48
2.7 EXAMPLE 2.4: Matrix analysis of a space truss 51
2.8 EXAMPLE 2.5: Matrix analysis of a space truss 53
2.9 Plane frames 56
2.10 EXAMPLE 2.6: Matrix analysis of a plane frame 59
2.11 EXAMPLE 2.7: Matrix analysis of a plane frame 62
2.12 Space frames 65
2.13 EXAMPLE 2.8: Matrix analysis of a space frame 70
2.14 EXAMPLE 2.9: Matrix analysis of a space frame 74
2.15 Grids 77
2.16 EXAMPLE 2.10: Matrix analysis of a grid structure 80
2.17 EXAMPLE 2.11: Matrix analysis of a grid structure 83
2.18 Special cases 86
2.19 EXAMPLE 2.12: Matrix analysis of a plane frame subjected to a distributed member loading 89
2.20 EXAMPLE 2.13: Matrix analysis of a plane frame subjected to support settlements 94
2.21 EXAMPLE 2.14: Matrix analysis of a plane frame subjected to temperature variations 99
2.22 EXAMPLE 2.15: Matrix analysis of a plane truss frame affected by member mismatch 103
2.23 EXAMPLE 2.16: Matrix analysis of a plane frame with released members 106
2.24 EXAMPLE 2.17: Matrix analysis of a plane frame having an elastic support 110
2.25 Chapter overview 112
Exercises 112
References 116
3. Elastic analysis of structures using finite element procedure 117
3.1 Introduction 118
3.2 FEM programming for continuum elements 127
3.3 EXAMPLE 3.1: Obtaining the stiffness matrix of a two-node truss member 128
3.4 EXAMPLE 3.2: Obtaining the stiffness matrix of a three-node truss member 131
3.5 EXAMPLE 3.3: Linear-elastic analysis of a one-dimensional structure with 133
3.6 EXAMPLE 3.4: Linear-elastic analysis of a one-dimensional structure with varying cross-sections 136
3.7 EXAMPLE 3.5: Linear-elastic analysis of a plane truss using FEM 139
3.8 EXAMPLE 3.6: Linear-elastic analysis of plane stress structure subjected to 153
3.9 EXAMPLE 3.7: Linear-elastic analysis of plane stress structure subjected to 155
3.10 EXAMPLE 3.8: Linear-elastic analysis of a plane strain structure using quadrilateral elements 158
3.11 EXAMPLE 3.9: Linear-elastic analysis of an axisymmetric structure using quadrilateral elements 161
3.12 EXAMPLE 3.10: Linear-elastic analysis of a plane stress structure using triangular elements 163
3.13 EXAMPLE 3.11: Linear-elastic analysis of a plane stress structure elements 166
3.14 EXAMPLE 3.12: Linear-elastic analysis of a three-dimensional structure subjected to a surface load 174
3.15 EXAMPLE 3.13: Linear-elastic analysis of a three-dimensional structure subjected to a body load 177
3.16 FEM programming for structural elements 179
3.17 EXAMPLE 3.14: Linear-elastic analysis of a clamped Timoshenko beam 183
3.18 EXAMPLE 3.15: Linear-elastic analysis of a Timoshenko beam having 185
3.19 EXAMPLE 3.16: Linear-elastic analysis of a simply supported Mindlin?Reissner plate 192
3.20 EXAMPLE 3.17: Linear-elastic analysis of a clamped supported Mindlin?Reissner plate 195
3.21 Chapter overview 196
Exercises 197
References 198
4. Elastoplastic Analysis of Structures Using Finite Element
Procedure 199
4.1 Introduction 201
4.2 Basics 202
4.3 Elastoplasticity 205
4.4 Yield criteria 210
4.5 Hardening laws 214
4.6 Stress integration using the von Mises yield criterion 219
4.7 Solving nonlinear problems 224
4.8 Finite element programming considering the nonlinear behavior of materials 226
4.9 EXAMPLE 4.1: Elastoplastic analysis of structure with plane strain 230
EXAMPLE 4.2: Elastoplastic analysis of structure with plane strain 235
EXAMPLE 4.3: Elastoplastic analysis of structure with plane strain
condition and isotropic hardening using four-node rectangular
quadrilaterals subjected to a uniform surface load 238
EXAMPLE 4.4: Elastoplastic analysis of structure with plane strain
condition and combined hardening using four-node rectangular
quadrilaterals subjected to a uniform surface load 243
EXAMPLE 4.5: Elastoplastic analysis of structure with plane strain
condition and power-law isotropic hardening using four-node 246
4.10 Extension to three-dimensional elements 249
4.11 Elastoplastic tangent operator 250
4.12 Convergence criteria 253
4.13 Chapter overview 255
Exercises 255
References 256
Further reading 256
5. Finite deformation and hyperelasticity 257
5.1 Introduction 258
5.2 Strain and stress measures in finite deformation 259
5.3 EXAMPLE 5.1: Programming for obtaining the deformation gradient,
the Lagrangian strain, and the second Piola?Kirchhoff stress 267
5.4 Analysis procedures 269
5.5 EXAMPLE 5.2: Finite strain analysis of a uniaxial truss element
subjected to a tension load using the TL formulation 273
5.6 EXAMPLE 5.3: Finite strain analysis of a uniaxial truss element
subjected to a tension load using the UL formulation 276
5.7 Hyperelastic materials 279
5.8 EXAMPLE 5.4: Fitting test data to the neo-Hookean model 295
5.9 EXAMPLE 5.5: Fitting test data to the Mooney?Rivlin model 298
5.10 EXAMPLE 5.6: Fitting test data to the Yeoh model 300
5.11 EXAMPLE 5.7: Fitting test data to the Ogden model 302
5.12 EXAMPLE 5.8: Finite deformation analysis of a structure with plane 310
5.13 EXAMPLE 5.9: Step-by-step finite deformation analysis of a structure 312
5.14 EXAMPLE 5.10: Step-by-step finite deformation analysis of a structure 316
5.15 Chapter overview 319
Exercises 319
References 320
Further reading 320
6. Finite strain 321
6.1 Introduction 322
6.2 Finite rotation and objective rates 323
6.3 EXAMPLE 6.1: Step-by-step finite strain analysis of a structure with 332
6.4 EXAMPLE 6.2: Step-by-step finite strain analysis of a structure 340
6.5 Finite deformation elastoplasticity 344
6.6 Chapter overview 353
Exercises 353
References 353
Further reading 354
7. Solution to systems of linear equations 355
7.1 Introduction 357
7.2 Solution to systems of linear equations 358
7.3 EXAMPLE 7.1: Programming for the LDL T decomposition 373
7.4 EXAMPLE 7.2: Programming of the Gauss?Seidel iterative algorithm 376
7.5 EXAMPLE 7.3: Programming of the successive overrelaxation algorithm 378
7.6 EXAMPLE 7.4: Programming of the modified Richardson iterative algorithm 380
7.7 EXAMPLE 7.5: Programming of the conjugate gradient iterative algorithm 384
7.8 EXAMPLE 7.6: Programming of the conjugate residual iterative algorithm 385
7.9 EXAMPLE 7.7: Programming of the preconditioned conjugate gradient iterative algorithm 388
7.10 EXAMPLE 7.8: Programming of the MINRES iterative algorithm 390
7.11 EXAMPLE 7.9: Programming of the BiCG iterative algorithm 392
7.12 EXAMPLE 7.10: Programming of the BiCG stabilized iterative algorithm 393
7.13 EXAMPLE 7.11: Programming of the CGS iterative algorithm 395
7.14 EXAMPLE 7.12: Programming of the QMR iterative algorithm 396
7.15 EXAMPLE 7.13: Programming of the TFQMR iterative algorithm 397
7.16 EXAMPLE 7.14: Programming of the GMRES iterative algorithm 398
7.17 Solution to eigenproblems 398
7.18 EXAMPLE 7.15: Programming for transforming a general eigenproblem into the standard form 401
7.19 EXAMPLE 7.16: Programming of the Jacobi method 403
7.20 EXAMPLE 7.17: Programming of the generalized Jacobi method 407
7.21 EXAMPLE 7.18: Programming of the HQRI method 410
7.22 EXAMPLE 7.19: Programming of the vector inverse method 414
7.23 EXAMPLE 7.20: Programming of the forward iteration method 415
7.24 EXAMPLE 7.21: Programming of the shifted vector iteration method 417
7.25 EXAMPLE 7.22: Programming of the Rayleigh Quotient iteration method 419
7.26 EXAMPLE 7.23: Programming of the Rayleigh Quotient iteration algorithm with the Gram?Schmidt method 421
7.27 EXAMPLE 7.24: Programming of the implicit polynomial iteration method 423
7.28 EXAMPLE 7.25: Programming for solving a generalized eigenproblem using the Lanczos transformation method 426
7.29 EXAMPLE 7.26: Programming of the convergence check for the Lanczos transformation method 428
7.30 EXAMPLE 7.27: Programming of the subspace method 431 7.31 Chapter overview 434
References 434
Further reading 434
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