β Scribed by Chandra A., Mukherjee S.
No coin nor oath required. For personal study only.
This book focuses on analysis of manufacturing processes, and its integration into the design cycle of these processes using the boundary element method (BEM) as the computational model of choice.
Contents......Page 12
1.1 Deformation Processes......Page 20
1.2 Material Removal Processes......Page 22
1.3 Phase Change Processes......Page 24
1.4 Salient Features of Manufacturing Processes and the Boundary Element Method......Page 25
2.1.1 Kinematics in Cartesian Coordinates......Page 32
2.1.2 Kinetics in Cartesian Coordinates......Page 36
2.1.3 Kinematics and Kinetics in General Curvilinear Coordinates......Page 41
2.1.4 Objective Rates of Tensors......Page 45
2.2 Boundary Element Formulations......Page 51
2.2.1 Constitutive Assumptions......Page 52
2.2.2 Three-Dimensional BEM Formulation for Velocities......Page 53
2.2.3 Stress Rates and Velocity Gradients on the Boundary......Page 59
2.2.4 Internal Stress Rates and Velocity Gradients......Page 60
2.2.6 Plane Stress......Page 63
2.2.7 Axisymmetric Problems......Page 64
2.2.8 Derivative Boundary Integral Equations (DBEM) for Plane Strain Problems......Page 72
2.2.9 Derivative Boundary Integral Equations (DBEM) for Plane Stress Problems......Page 74
2.2.10 Sharp Corners for Planar Problems......Page 75
2.3 Finite Element Formulations......Page 76
2.3.1 A Three-Dimensional FEM in an Updated Lagrangian Formulation......Page 77
2.4.1 Viscoplastic Constitutive Models......Page 80
2.4.2 Planar Problems......Page 83
2.4.3 Axisymmetric Problems......Page 92
3.1.1 Direct Formulation......Page 103
3.1.2 Alternative Complex Variable Approach......Page 105
3.1.3 A Derivative BEM (DBEM) Formulation......Page 107
3.2.1 Formulation......Page 111
3.2.2 Numerical Implementation......Page 115
3.2.3 Evaluation of Singular Integrals......Page 119
3.2.4 Numerical Results and Verification......Page 120
3.3.1 Formulation......Page 148
3.4.1 Formulation......Page 154
3.4.2 Numerical Implementation......Page 157
3.4.3 Example Problems and Numerical Results......Page 162
3.5 Thermal Stresses and Thermomechanical Aspects......Page 168
3.5.1 Constitutive Laws......Page 169
3.5.2 Stationary Thermoplasticity in Nonhomogeneous Media......Page 173
3.5.3 Nonstationary Thermoelasticity......Page 185
3.5.4 Nonstationary Thermoplasticity......Page 196
4.1 Design Sensitivity Coefficients (DSCs)......Page 201
4.1.3 The Direct Differentiation Approach (DDA)......Page 202
4.1.5 Nonlinear Problems in Solid Mechanics......Page 203
4.2 DBEM Sensitivity Formulation......Page 204
4.2.1 Boundary Integral Equations for Sensitivities......Page 205
4.2.2 Boundary Condition Sensitivities......Page 207
4.2.3 Sensitivities of Inelastic Constitutive Model Equations......Page 208
4.2.4 Kinematic and Geometric Sensitivities......Page 209
4.2.5 Stress Rates and Velocity Gradient Sensitivities on the Boundary......Page 211
4.2.6 Sensitivities of Integral Equations at an Internal Point......Page 212
4.2.8 Sensitivities of Corner and Compatibility Equations......Page 214
4.2.9 Special CasesβSmall-Strain Elasto-viscoplasticity and Linear Elasticity......Page 215
4.2.10 Leibnitz Rule, Calculation of Geometric Sensitivities, and Related Issues......Page 216
4.3.1 Discretization of Equations......Page 222
4.3.2 Solution Strategy......Page 223
4.4.1 One-Dimensional Problems......Page 226
4.4.2 A 2D ProblemβSimple Shearing Motion......Page 235
4.4.3 Axisymmetric Problems......Page 239
4.5 Design Optimization......Page 244
4.6.2 Objective Functions and Constraints......Page 248
4.6.3 Elastic Shape Optimization......Page 249
4.6.4 Elasto-viscoplastic Shape Optimization......Page 252
5.1 Introduction......Page 267
5.2 Interface Conditions in Planar Forming Problems......Page 269
5.2.1 General Equations......Page 270
5.2.3 Sheet Forming......Page 272
5.2.5 Slab Rolling......Page 273
5.3 Numerical Implementation for Planar Cases......Page 274
5.3.1 Objective Stress Rates for Problems Involving Large Shear Strains......Page 275
5.4 Applications to Forming Problems......Page 281
5.4.1 Plane Strain Extrusion......Page 282
5.4.2 Profile Rolling of Gears......Page 287
5.4.3 Plane Strain Slab Rolling......Page 296
5.4.4 Plane Strain Sheet Forming......Page 303
5.5 Concurrent Preform and Process Design for Formed Products......Page 307
5.5.1 The Concept of Reverse Forming......Page 309
5.5.2 Integrated Design Algorithm......Page 311
6.1 Introduction......Page 323
6.2 Interface Conditions for Axisymmetric Forming Problems......Page 324
6.2.1 Axisymmetric Ring Compression......Page 325
6.2.2 Axisymmetric Extrusion......Page 326
6.3 Numerical Implementation for Axisymmetric Cases......Page 328
6.4.1 Axisymmetric Upsetting and Ring Compression......Page 334
6.4.2 Axisymmetric Extrusion......Page 338
6.5 Design Sensitivity and Optimization Issues......Page 342
7.1 Introduction......Page 344
7.2.1 Governing Differential Equations......Page 346
7.2.2 Integral Formulation......Page 348
7.2.3 Numerical Implementation......Page 349
7.2.4 Evaluation of Integrals......Page 351
7.2.6 Matrix Formulation......Page 352
7.3.1 The Problem......Page 354
7.3.2 Future Information and Spatial Regularization Methods......Page 355
7.3.3 Calculation of the Sensitivity Coefficients......Page 357
7.4.2 The Direct Problem......Page 359
7.4.3 The Design Problem......Page 363
8.1 Introduction......Page 371
8.2 Boundary Element Formulation......Page 375
8.2.1 Numerical Implementation......Page 377
8.2.2 Verification of the Conduction-Convection Algorithm......Page 380
8.3 Modeling of Machining Processes......Page 381
8.3.1 Mathematical Formulation......Page 382
8.3.2 Matching Scheme......Page 387
8.4 Results from BEM Analyses......Page 391
8.5 BEM Sensitivity Formulation......Page 397
8.6 Sensitivities of Machining Processes......Page 406
8.6.1 Matching Boundary Conditions for Sensitivity Calculations......Page 407
8.6.2 Matching Scheme for the Sensitivity Problem......Page 409
8.7 Results from BEM Sensitivity Analysis......Page 411
8.8 Discussion and Conclusion......Page 422
9.1 Introduction......Page 426
9.2 Background of Strength Degradation in Ceramic Grinding......Page 429
9.3 Indentation Fracture Mechanics Model for Monolithic Ceramics......Page 431
9.3.1 An Integral Equation Formulation for Grinding of Monolithic Ceramics......Page 432
9.3.2 Numerical Solution Procedure......Page 439
9.4 Determination of Effective Elastic Properties......Page 442
9.4.1 Numerical Results for Monolithic Ceramics......Page 443
9.5 Grinding of Ceramic Composites......Page 459
9.5.1 Fundamental Fields due to Point Loads and Point Dislocations......Page 463
9.5.2 An Integral Equation Formulation for General Crack-Anticrack Systems......Page 469
9.5.3 Numerical Results for Grinding of Ceramic Composites......Page 477
9.6 Micro-Scale Features in Macro-Scale Problems......Page 486
9.6.1 Micro-Scale Fundamental Solutions......Page 491
9.6.2 Micro-Macro BEM Formulation......Page 498
9.6.3 Numerical Implementation for Hybrid Micro-Macro BEM......Page 501
9.6.4 Numerical Results for Hybrid Micro-Macro BEM......Page 502
C......Page 520
I......Page 521
P......Page 522
S......Page 523
U......Page 524
Z......Page 525
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