Boundary Element Methods in Manufacturing

, by Chandra, Abhijit; Mukherjee, Subrata

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ISBN: 9780195079210 | 0195079213
Cover: Hardcover
Copyright: 4/10/1997

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This book focuses on the analysis of manufacturing processes and the integration of this analysis into the design cycle. Uniquely, the boundary element method (BEM) is the computational model of choice. This versatile and powerful method has undergone extensive development during the past two decades and has been applied to virtually all areas of engineering mechanics as well as to other fields. Among topics covered are BEM infrastructure, design sensitivity analysis, and detailed discussions of a broad range of manufacturing processes including forming, solidification, machining, and ceramic grinding.

1 Introduction

(12)

1.1 Deformation Processes

(2)

1.2 Material Removal Processes

(2)

1.3 Phase Change Processes

(1)

1.4 Salient Features of Manufacturing Processes and the Boundary Element Method

(7)

2 Problems Involving Large Strains and Rotations

(71)

2.1 Continuum Mechanics Fundamentals

(19)

2.1.1 Kinematics in Cartesian Coordinates

(4)

2.1.2 Kinetics in Cartesian Coordinates

(5)

2.1.3 Kinematics and Kinetics in General Curvilinear Coordinates

(4)

2.1.4 Objective Rates of Tensors

(6)

2.2 Boundary Element Formulations

(25)

2.2.1 Constitutive Assumptions

(1)

2.2.2 Three-Dimensional BEM Formulation Velocities

(6)

2.2.3 Stress Rates and Velocity Gradients on the Boundary

(1)

2.2.4 Internal Stress Rates and Velocity Gradients

(3)

2.2.5 Plane Strain

(1)

2.2.6 Plane Stress

(1)

2.2.7 Axisymmetric Problems

(8)

2.2.8 Derivative Boundary Integral Equations (DBEM) for Plane Strain Problems

(2)

2.2.9 Derivative Boundary Integral Equations (DBEM) for Plane Stress Problems

(1)

2.2.10 Sharp Corners for Planar Problems

(1)

2.3 Finite Element Formulations

(4)

2.3.1 A Three-Dimensional FEM in the Updated Lagrangian Formulation

(3)

2.4 Numerical Implementation and Results

(23)

2.4.1 Viscoplastic Constitutive Models

(3)

2.4.2 Planar Problems

(9)

2.4.3 Axisymmetric Problems

(11)

3 Thermal Problems

(98)

3.1 Steady-State Conduction

(8)

3.1.1 Direct Formulation

(2)

3.1.2 Alternative Complex Variable Approach

(2)

3.1.3 A Derivative BEM (DBEM) Formulation

(4)

3.2 Steady-State Conduction-Convection

(37)

3.2.1 Formulation

(4)

3.2.2 Numerical Implementation

(4)

3.2.3 Evaluation of Singular Integrals

102

(1)

3.2.4 Numerical Results and Verification

103

(28)

3.3 Transient Conduction with Moving Boundaries and Phase Changes

131

(6)

3.3.1 Formulation

131

(6)

3.4 Transient Conduction-Convection

137

(14)

3.4.1 Formulation

137

(3)

3.4.2 Numerical Implementation

140

(5)

3.4.2.1 Discretization

140

(2)

3.4.2.2 Integration of Kernels in Time and Space

142

(3)

3.4.3 Example Problems and Numerical Results

145

(6)

3.5 Thermal Stresses and Thermomechanical Aspects

151

(33)

3.5.1 Constitutive Laws

152

(4)

3.5.2 Stationary Thermoplasticity in Nonhomogeneous Media

156

(12)

3.5.2.1 Special Case for Homogeneous Media

164

(4)

3.5.3 Nonstationary Thermoelasticity

168

(11)

3.5.3.1 Numerical Implementation

171

(8)

3.5.4 Nonstationary Thermoplasticity

179

(5)

4 Design Sensitivities and Optimization

184

(66)

4.1 Design Sensitivity Coefficients (DSCs)

184

(3)

4.1.1 The Finite Difference Approach (FDA)

185

(1)

4.1.2 The Adjoint Structure Approach (ASA)

185

(1)

4.1.3 The Direct Differentiation Approach (DDA)

185

(1)

4.1.4 Linear Elasticity

186

(1)

4.1.5 Nonlinear Problems in Solid Mechanics

186

(1)

4.2 DBEM Sensitivity Formulation

187

(18)

4.2.1 Boundary Integral Equations for Sensitivities

188

(2)

4.2.2 Boundary Condition Sensitivities

190

(1)

4.2.3 Sensitivities of Inelastic Constitutive Model Equations

191

(1)

4.2.4 Kinematic and Geometric Sensitivities

192

(2)

4.2.5 Stress Rates and Velocity Gradient Sensitivities on the Boundary

194

(1)

4.2.6 Sensitivities of Integral Equations at an Internal Point

195

(2)

4.2.7 Stress Rate Sensitivities at an Internal Point

197

(1)

4.2.8 Sensitivities of Corner and Compatibility Equations

197

(1)

4.2.9 Special Cases--Small-Strain Elasto-viscoplasticity and Linear Elasticity

198

(1)

4.2.10 Leibnitz Rule, Calculation of Geometric Sensitivities, and Related Issues

199

(6)

4.3 Numerical Implementation

205

(4)

4.3.1 Discretization of Equations

205

(1)

4.3.2 Solution Strategy

206

(3)

4.4 Numerical Results for Sample Problems

209

(18)

4.4.1 One-Dimensional Problems

209

(9)

4.4.2 A 2D Problem--Simple Shearing Motion

218

(4)

4.4.3 Axisymmetric Problems

222

(5)

4.5 Design Optimization

227

(4)

4.6 Optimization of Plates with Cutouts

231

(19)

4.6.1 Parametrization of Cutout Boundary

231

(1)

4.6.2 Obejctive Functions and Constraints

231

(1)

4.6.3 Elastic Shape Optimization

232

(3)

4.6.4 Elasto-viscoplastic Shape Optimization

235

(15)

5 Planar Forming Processes

250

(56)

5.1 Introduction

250

(2)

5.2 Interface Conditions in Planar Forming Problems

252

(5)

5.2.1 General Equations

253

(2)

5.2.2 Follower Load

255

(1)

5.2.3 Sheet Forming

255

(1)

5.2.4 Extrusion

256

(1)

5.2.5 Slab Rolling

256

(1)

5.3 Numerical Implementation for Planar Cases

257

(7)

5.3.1 Objective Stress Rates for Problems Involving Large Shear Strains

258

(6)

5.3.1.1 Relationship with the Dienes Rate

259

(1)

5.3.1.2 Relationship with Rolph and Bathe's Model

259

(1)

5.3.1.3 Elastoplasticity with Finite Rotations

260

(1)

5.3.1.4 Solution Strategy

261

(3)

5.4 Applications to Forming Problems

264

(26)

5.4.1 Plane Strain Extrusion

265

(5)

5.4.1.1 Numerical Results for Plane Strain Extrusion

266

(4)

5.4.2 Profile Rolling of Gears

270

(9)

5.4.2.1 Numerical Results for Profile Rolling

274

(5)

5.4.3 Plane Strain Slab Rolling

279

(7)

5.4.3.1 Numerical Results for Slab Rolling

281

(5)

5.4.4 Plane Strain Sheet Forming

286

(4)

5.4.4.1 Numerical Results for Plane Strain Sheet Forming

287

(3)

5.5 Concurrent Preform and Process Design for Formed Products

290

(16)

5.5.1 The Concept of Reverse Forming

292

(2)

5.5.2 Integrated Design Algorithm

294

(12)

5.5.2.1 Step 1: Reverse Froming along Minimum Plastic Work Path

294

(1)

5.5.2.2 Step 2: Feasibility Check for the Forward Forming Step

295

(1)

5.5.2.3 Step 3: Analysis of a Feasible Forward Forming Step

296

(1)

5.5.2.4 Step 4: Design Sensitivities of the Forward Forming Step

297

(1)

5.5.2.5 Step 5: Optimization of the Forward Forming Step

298

(3)

5.5.2.6 Issues Relating to Concurrent Product and Process Design

301

(5)

6 Axisymmetric Forming Processes

306

(21)

6.1 Introduction

306

(1)

6.2 Interface Conditions for Axisymmetric Forming Problems

307

(4)

6.2.1 Axisymmetric Ring Compression

308

(1)

6.2.2 Axisymmetric Extrusion

309

(2)

6.3 Numerical Implementation for Axisymmetric Cases

311

(6)

6.4 Applications to Axisymmetric Forming

317

(8)

6.4.1 Axisymmetric Upsetting and Ring Compression

317

(4)

6.4.2 Axisymmetric Extrusion

321

(4)

6.5 Design Sensitivity and Optimization Issues

325

(2)

7 Solidification Processes

327

(27)

7.1 Introduction

327

(2)

7.2 Direct Analysis of Solidification

329

(8)

7.2.1 Governing Differential Equations

329

(2)

7.2.2 Integral Formulation

331

(1)

7.2.3 Numerical Implementation

332

(2)

7.2.4 Evaluation of Integrals

334

(1)

7.2.5 Modeling of Corners

335

(1)

7.2.6 Matrix Formulation

335

(2)

7.3 An Inverse (Design) Solidification Problem

337

(5)

7.3.1 The Problem

337

(1)

7.3.2 Future Information and Spatial Regularization Methods

338

(2)

7.3.3 Calculation of the Sensitivity Coefficients

340

(2)

7.4 Numerical Examples

342

(12)

7.4.1 Dimensionless Parameters

342

(1)

7.4.2 The Direct Problem

342

(4)

7.4.3 The Design Problem

346

(8)

8 Machining Processes

354

(55)

8.1 Introduction

354

(4)

8.2 Boundary Element Formulation

358

(6)

8.2.1 Numerical Implementation

360

(3)

8.2.2 Verificaiton of the Conduction-Convection Algorithm

363

(1)

8.3 Modeling of Machining Processes

364

(10)

8.3.1 Mathematical Formulation

365

(5)

8.3.1.1 Within the Workpiece

366

(1)

8.3.1.2 Within the Chip

367

(1)

8.3.1.3 Within the Tool

368

(1)

8.3.1.4 Matching Boundary Conditions

369

(1)

8.3.2 Matching Scheme

370

(4)

8.4 Results from BEM Analyses

374

(6)

8.5 BEM Sensitivity Formulation

380

(9)

8.6 Sensitivities of Machining Processes

389

(5)

8.6.1 Matching Boundary Conditions for Sensitivity Calculations

390

(2)

8.6.2 Matching Scheme for the Sensitivity Problem

392

(2)

8.7 Results from BEM Sensitivity Analysis

394

(11)

8.8 Discussion and Conclusion

405

(4)

9 Integral Equations for Ceramic Grinding Processes

409

(94)

9.1 Introduction

409

(3)

9.2 Background of Strength Degradation in Ceramic Grinding

412

(2)

9.3 Indentation Fracture Mechanics Model for Monolithic Ceramics

414

(11)

9.3.1 An Integral Equation Formulation for Grinding of Monolithic Ceramics

415

(7)

9.3.2 Numerical Solution Procedure

422

(3)

9.4 Determination of Effective Elastic Properties

425

(17)

9.4.1 Numerical Results for Monolithic Ceramics

426

(16)

9.5 Grinding of Ceramic Composites

442

(27)

9.5.1 Fundamental Fields due to Point Loads and Point Dislocations

446

(6)

9.5.2 An Integral Equation Formulation for General Crack-Anticrack Systems

452

(8)

9.5.3 Numerical Results for Grinding of Ceramic Composites

460

(9)

9.6 Micro-Scale Features in Macro-Scale Problems

469

(34)

9.6.1 Micro-Scale Fundamental Solutions

474

(7)

9.6.2 Micro-Macro BEM Formulation

481

(3)

9.6.3 Numerical Implementation for Hybrid Micro-Macro BEM

484

(1)

9.6.4 Numerical Results for Hybrid Micro-Macro BEM

485

(18)

Index

503

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Boundary Element Methods in Manufacturing

Summary

Table of Contents

Supplemental Materials