Finite elements for analysis and design

목차 (Table of Contents)

• CONTENTS
• Preface = xii
• 1. Introduction = 1
• 1.1 Finite Element Methods = 1
• 1.2 Capabilities of FEA = 1
• 1.3 Outline of Finite Element Procedures = 5
• 1.4 Optimization Concepts = 9
• 1.5 References = 14
• 2. Mathematical Preliminaries = 15
• 2.1 Introduction = 15
• 2.2 Linear Space and Norms = 17
• 2.3 Sobolev Norms$$^＊$$ = 19
• 2.4 Self-Adjointness$$^＊$$ = 19
• 2.5 Weighted Residuals = 20
• 2.6 Essential Boundary Conditions = 27
• 2.7 Elliptic Boundary Value problems = 28
• 2.7.1 One-Dimensional Equations = 28
• 2.7.2 Two-Dimensional Equations = 31
• 2.7.3 Equivalent Forms$$^＊$$ = 34
• 2.8 References = 37
• 3. Variational Methods = 38
• 3.1 Introduction = 38
• 3.2 Structural Mechanics = 38
• 3.3 Finite Element Analysis = 40
• 3.4 Continuous Elastic Bar = 46
• 3.5 Flux Recoverty for an Element = 52
• 3.6 Thermal Loads on a Bar$$^＊$$ = 54
• 3.7 Heat Transfer in a Rod = 55
• 3.8 Gradient Estimates = 57
• 3.9 Element Validation$$^＊$$ = 62
• 3.10 Element Distortion$$^＊$$ = 65
• 3.11 Euler's Equations of Variational Calculus$$^＊$$ = 67
• 3.12 System Validation$$^＊$$ = 71
• 3.13 References = 71
• 4. Element Interpolation and Local Coordinates = 72
• 4.1 Introduction = 72
• 4.2 Linear Interpolation = 72
• 4.3 quadratic Interpolation = 75
• 4.4 Lagrange Interpolation = 77
• 4.5 hermitian Interpolation = 78
• 4.6 Hierarchical Interpolation = 79
• 4.7 Interpolation Error$$^＊$$ = 86
• 4.8 References = 87
• 5. One-Dimensional Integration = 88
• 5.1 Introduction = 88
• 5.2 local Coordinate Jacobian = 88
• 5.3 Exact Polynomial Integration$$^＊$$ = 89
• 5.4 Numerical Integration = 90
• 5.5 Variable Jacobians = 95
• 5.6 References = 97
• 6. Beam Analysis = 98
• 6.1 Introduction = 98
• 6.2 Vriational procedure = 99
• 6.3 hermite Element Matrices = 101
• 6.4 Sample Appliction = 104
• 6.5 Gradient Estimates$$^＊$$ = 106
• 6.6 Element Equations via Galerkin's Method$$^＊$$ = 108
• 6.7 Beams on an Elastic Foundtion$$^＊$$ = 108
• 6.7.1 Foundtion models = 109
• 6.7.2 Element Stiffness Matrices = 110
• 6.7.3 Cubic Beam Elements = 110
• 6.7.4 Fifth Order Beam Element = 111
• 6.7.5 Member and Foundtion Reaction Recovery = 111
• 6.7.6 The Treatment for Gaps = 112
• 6.7.7 Numerical Example = 113
• 6.8 Exact Analytic Elements$$^＊$$ = 114
• 6.9 References = 117
• 7. Truss Elements and Axis Transformations$$^＊$$ = 118
• 7.1 Introduction = 118
• 7.2 Direction Cosines = 118
• 7.3 Transformation of Displacement Components = 119
• 7.4 Transformation of Element Matrices = 120
• 7.5 Example Structures = 122
• 7.6 References = 125
• 8. Cylindrical Analysis Problems = 126
• 8.1 Introduction = 126
• 8.2 Heat Conduction in a Cylinder = 126
• 8.3 Cylindrical Stress Analysis = 129
• 8.4 References = 132
• 9. General Interpolation = 133
• 9.1 Introduction = 133
• 9.2 Unit Coordinate Interpolation = 133
• 9.3 Natural Coordinates = 140
• 9.4 Isoparametric and Subparametric Elements = 140
• 9.5 Hierarchical Interpolation = 151
• 9.6 Differential Geometry$$^＊$$ = 156
• 9.7 parametric Extrapolation$$^＊$$ = 161
• 9.8 Mass Properties, Equivalent Geometry$$^＊$$ = 163
• 9.9 Interpolation Error$$^＊$$ = 165
• 9.10 References = 167
• 10. Adpative Analysis = 168
• 10.1 Introduction = 168
• 10.2 H-Adaptivity = 172
• 10.3 P-Adaptivity = 175
• 10.4 HP-Adaptivity = 176
• 10.5 Adaptive Example = 181
• 10.6 References = 189
• 11. Integration Methods = 190
• 11.1 Introduction = 190
• 11.2 Unit Coordinate Integration = 191
• 11.3 Simplex Coordinate Integration = 195
• 11.4 Numerical Integration = 195
• 11.4.1 Unit Coordinate Quadrature = 195
• 11.4.2 Natural Coordinate Quadrature = 196
• 11.5 Typical Source Distribution Integrals$$^＊$$ = 198
• 11.6 Minimal, Optimal, Rduced and Selected Integration$$^＊$$ = 201
• 11.7 References = 206
• 12. Heat Transfer = 208
• 12.1 Introduction = 208
• 12.2 Variational Formulation = 208
• 12.3 Element and Boundary Matrices = 210
• 12.3.1 Linear Triangle = 211
• 12.3.2 Rectangular Bilinear Element$$^＊$$ = 212
• 12.3.3 General Elements = 215
• 12.4 Example Application = 218
• 12.5 References = 218
• 13. Elasticity = 219
• 13.1 Introduction = 219
• 13.2 Minimum total Potential Energy = 221
• 13.2.1 Displacement Interpolations = 221
• 13.2.2 Strain-Displacement Relations = 222
• 13.2.3 Stress-Strain Law = 223
• 13.3 matrices for the Constant Strain Triangle = 224
• 13.4 Stress and Strain Transformations$$^＊$$ = 233
• 13.5 Anisotropic Materials$$^＊$$ = 236
• 13.6 Axisymmetric Solids$$^＊$$ = 238
• 13.7 General Solids$$^＊$$ = 240
• 13.8 References = 241
• 14. Error Measures for Elliptic Problems = 242
• 14.1 Introduction = 242
• 14.2 Error Estimates = 245
• 14.3 Adaptive Process = 251
• 14.4 Hierarchical Error Indicator = 254
• 14.5 Example Error Calculations$$^＊$$ = 255
• 14.6 Flux Balancing Methods = 259
• 14.7 References = 261
• 15. Sensitivity Analysis$$^＊$$ = 263
• 15.1 Introduction = 263
• 15.2 Structural Models = 263
• 15.3 Optimal Design Problem = 265
• 15.4 Yield Criteria Sensitivity = 265
• 15.5 Yield Criteria Sensitivity = 267
• 15.6 Computing Stiffness Sensitivity = 270
• 15.6.1 Exact Sensitivity = 270
• 15.6.2 Finite Difference Approximations = 271
• 15.7 Isoparametric Elements = 272
• 15.8 Shape Sensitivity = 273
• 15.9 References = 276
• 16. Special Elements$$^＊$$ = 277
• 16.1 Introduction = 277
• 16.2 Interpolation Enhancement for C$$^0$$ Transition Elements = 277
• 16.3 Singularity Elements = 280
• 16.4 Semi-infinite Elements = 285
• 16.5 Upwind Elements = 286
• 16.6 Gap-Contact Elements = 287
• 16.7 References = 288
• 17. Time-Dependent Problems = 290
• 17.1 Introduction = 290
• 17.2 Parabolic Equations = 290
• 17.2.1 Simple Approximations = 292
• 17.2.2 Examples = 296
• 17.3 Hyperbolic Equations = 297
• 17.3.1 Simple Approximations = 299
• 17.3.2 Lumped Mass Forced Vibration Example = 304
• 17.4 Diagonal "Mass" Matrices$$^＊$$ = 304
• 17.5 Units Diagonal Scaling$$^＊$$ = 309
• 17.6 References = 312
• 18. Computational Fluid Dynamics$$^＊$$ with Dr. Bala Ramaswamy = 313
• 18.1 Introduction = 313
• 18.2 Mathematical Formulation = 314
• 18.3 Solution Procedure Outline = 315
• 18.4 Algorithm Details = 318
• 18.5 Examples = 330
• 18.5.1 Lid-Driven Cavity Problem = 330
• 18.5.2 Sudden Expansion Problem = 334
• 18.6 References = 340
• 19. Automatic Mesh Generation = 342
• 19.1 Introduction = 342
• 19.2 Automatic Mesh Generation = 342
• 19.3 Tree Structure Methods = 343
• 19.4 Mapping Methods$$^＊$$ = 350
• 19.4.1 Mapping Functions = 350
• 19.4.2 Higher Order Elements = 353
• 19.4.3 MESH2D Program = 354
• 19.5 References = 358
• 20. Compuational Procedures = 359
• 20.1 Introduction = 359
• 20.2 Element Calculations = 369
• 20.3 Condensation of Internal Degrees of Freedom$$^＊$$ = 383
• 20.4 Assembly into the System = 387
• 20.4.1 Introduction = 387
• 20.4.2 Assembly Programs = 389
• 20.4.3 Example = 395
• 20.5 Essential Boundary Conditions and Constraints = 400
• 20.5.1 Application of Essential Boundary Conditions = 400
• 20.5.2 Matrix Manipulations = 401
• 20.5.3 Constraints Applied at the Element Level$$^＊$$ = 405
• 20.5.4 Penalty Modifications for Nodal Constraints$$^＊$$ = 405
• 20.6 Economical Solution of the System Equations = 406
• 20.6.1 Efficient Node Numbering = 407
• 20.6.2 Equaton Solving Techniques = 408
• 20.6.3 Programming the Solution = 412
• 20.7 Frontal Assembly and Solution Procedures$$^＊$$ = 414
• 20.8 Iterative Solvers$$^＊$$ = 417
• 20.9 Programming Parametric Elements = 419
• 20.10 Output of Results = 421
• 20.11 Post-solution Calculations Within the Elements = 424
• 20.12 Sample Graphical Outputs = 429
• 20.13 References = 429
• 21. MODEL Applications in 1-D = 431
• 21.1 Introduction = 431
• 21.2 Conductive and Convective Heat Transfer = 431
• 21.3 Plane Truss Structures$$^＊$$ = 437
• 21.4 Slider Bearing Lubrication = 444
• 21.5 Ordinary Differential Equations$$^＊$$ = 449
• 21.5.1 Linear Example = 449
• 21.5.2 Nonlinear Example = 449
• 21.6 Plane Frame Structures = 453
• 21.7 References = 460
• 22. MODEL Applications in 2-and 3-D = 461
• 22.1 Introduction = 461
• 22.2 Plane Stress Analysis = 461
• 22.3 Heat Conduction = 471
• 22.4 Viscous Flow in Straight Ducts = 477
• 22.5 Potential Flow = 480
• 22.6 Electromagnetic Waveguides$$^＊$$ = 492
• 22.7 Axisymmetric Plasma Equilibria$$^＊$$ = 494
• 22.8 Neutron Diffusion$$^＊$$ = 498
• 22.9 Axisymmetric Solenoid Magnet$$^＊$$ = 501
• 22.10 Three-Dimensional Applications = 507
• 22.11 References = 513
• Appendices :
• Ⅰ. Matrix Notation and Operations = 515
• Ⅱ. Subroutines in MODEL library = 523
• Ⅲ. Notation in MODEL = 528
• Ⅳ. Program Disk Directory = 531
• INDEX = 542