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El. knyga: Boundary Element Methods in Manufacturing

(Professor, Department of Mechanical Engineering and Engineering Mechanics, Michigan Technological University), (Professor, Department of Theoretical and Applied Mechanics, Cornell University, USA)
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Manufacturing processes have existed, in some form, since the dawn of civilization. Modelling and numerical simulation of mechanics of such processes, however, are of fairly recent vintage; made possible, mainly by improved understanding of the fundamental mechanics and physics of these processes as well as by the availability of ever more powerful computers. Our capabilities of designing manufacturing processes, however, significantly lag behind our abilities in simulating such processes. In fact, research in the area of design of manufacturing processes is barely a decade old.

Analysis of manufacturing processes, and its integration into the design cycle of these processes, are the dual themes of this book. The boundary element method (BEM) is the computational method of choice. This versatile and powerful method has enjoyed extensive development during the last two decades and has been applied to virtually all areas of engieering mechanics (both linear and nonlinear) as well as in other areas.

The BEM infra-structure is presented in Chapters 2, 3, and 4. Chapters 2 and 3, respectively provide reviews of the fundamentals of nonlinear and thermal problems. Material and geometric nonlinearities are ubiquitous in manufacturing processes such as forming and machining while thermal issues play significant roles in casting and machining processes. Chapter 4 discusses design sensitivity analysis, and provides an avenue for utilizing insights gained from analysis toward design synthesis of manufacturing processes. Chapters 5 through 9 are devoted to detailed discussions of a broad range of manufacturing processes - forming, solidification, machining, and ceramic grinding.

The unique features of this book are its emphasis on numerical simulation as well as on design of manufacturing processes, and the use of the boundary element method as the computational method of choice.

Recenzijos

"This work can be used as a reference book in a graduate course in boundary element methods applied to manufacturing. Boundary Element Methods in Manufacturing, which is written by experts in the field and is full of original current research, should be of immense interest to researchers, engineers, scientists, and graduate and postgraduate students who are interested in computational solid mechanics and heat transfer as applied to manufacturing."--Applied Mechanics Review "This work can be used as a reference book in a graduate course in boundary element methods applied to manufacturing. Boundary Element Methods in Manufacturing, which is written by experts in the field and is full of original current research, should be of immense interest to researchers, engineers, scientists, and graduate and postgraduate students who are interested in computational solid mechanics and heat transfer as applied to manufacturing."--Applied Mechanics Review

1 Introduction
3(12)
1.1 Deformation Processes
3(2)
1.2 Material Removal Processes
5(2)
1.3 Phase Change Processes
7(1)
1.4 Salient Features of Manufacturing Processes and the Boundary Element Method
8(7)
2 Problems Involving Large Strains and Rotations
15(71)
2.1 Continuum Mechanics Fundamentals
15(19)
2.1.1 Kinematics in Cartesian Coordinates
15(4)
2.1.2 Kinetics in Cartesian Coordinates
19(5)
2.1.3 Kinematics and Kinetics in General Curvilinear Coordinates
24(4)
2.1.4 Objective Rates of Tensors
28(6)
2.2 Boundary Element Formulations
34(25)
2.2.1 Constitutive Assumptions
35(1)
2.2.2 Three-Dimensional BEM Formulation Velocities
36(6)
2.2.3 Stress Rates and Velocity Gradients on the Boundary
42(1)
2.2.4 Internal Stress Rates and Velocity Gradients
43(3)
2.2.5 Plane Strain
46(1)
2.2.6 Plane Stress
46(1)
2.2.7 Axisymmetric Problems
47(8)
2.2.8 Derivative Boundary Integral Equations (DBEM) for Plane Strain Problems
55(2)
2.2.9 Derivative Boundary Integral Equations (DBEM) for Plane Stress Problems
57(1)
2.2.10 Sharp Corners for Planar Problems
58(1)
2.3 Finite Element Formulations
59(4)
2.3.1 A Three-Dimensional FEM in the Updated Lagrangian Formulation
60(3)
2.4 Numerical Implementation and Results
63(23)
2.4.1 Viscoplastic Constitutive Models
63(3)
2.4.2 Planar Problems
66(9)
2.4.3 Axisymmetric Problems
75(11)
3 Thermal Problems
86(98)
3.1 Steady-State Conduction
86(8)
3.1.1 Direct Formulation
86(2)
3.1.2 Alternative Complex Variable Approach
88(2)
3.1.3 A Derivative BEM (DBEM) Formulation
90(4)
3.2 Steady-State Conduction-Convection
94(37)
3.2.1 Formulation
94(4)
3.2.2 Numerical Implementation
98(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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