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 |  موضوع: كتاب Finite Element Modeling and Simulation with ANSYS Workbench السبت 24 أغسطس 2019, 12:28 am | |
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Finite Element Modeling and Simulation with ANSYS Workbench
Second Edition
Xiaolin Chen, Yijun Liu
و المحتوى كما يلي :
Contents
Preface xi
Authors . xiii
1. Introduction .1
1.1 Some Basic Concepts 1
1.1.1 Why FEA? .1
1.1.2 Finite Element Applications in Engineering 1
1.1.3 FEA with ANSYS Workbench 3
1.1.4 A Brief History of FEA 3
1.1.5 A General Procedure for FEA 4
1.2 An Example in FEA: Spring System .4
1.2.1 One Spring Element .5
1.2.2 A Spring System .6
1.2.2.1 Assembly of Element Equations: Direct Approach .6
1.2.2.2 Assembly of Element Equations: Energy Approach .8
1.2.3 Boundary and Load Conditions 9
1.2.4 Solution Verification 10
1.2.5 Example Problems . 10
1.3 Overview of ANSYS Workbench 13
1.3.1 The User Interface 13
1.3.2 The Toolbox . 14
1.3.3 The Project Schematic . 14
1.3.4 Working with Cells 16
1.3.5 The Menu Bar . 16
1.4 Summary 17
Problems 18
2. Bars and Trusses . 21
2.1 Introduction . 21
2.2 Review of the 1-D Elasticity Theory . 21
2.3 Modeling of Trusses .22
2.4 Formulation of the Bar Element 23
2.4.1 Stiffness Matrix: Direct Method 23
2.4.2 Stiffness Matrix: Energy Approach .25
2.4.3 Treatment of Distributed Load 27
2.4.4 Bar Element in 2-D and 3-D 28
2.4.4.1 2-D Case .28
2.4.4.2 3-D Case . 31
2.4.5 Element Stress 31
2.5 Examples with Bar Elements . 32
2.6 Case Study with ANSYS Workbench .40
2.7 Summary 59
2.8 Review of Learning Objectives .59
Problems 59vi Contents
3. Beams and Frames 65
3.1 Introduction .65
3.2 Review of the Beam Theory 65
3.2.1 Euler–Bernoulli Beam and Timoshenko Beam .65
3.2.2 Stress, Strain, Deflection, and Their Relations 67
3.3 Modeling of Beams and Frames .68
3.3.1 Cross Sections and Strong/Weak Axis .68
3.3.2 Support Conditions .69
3.3.3 Conversion of a Physical Model into a Line Model 70
3.4 Formulation of the Beam Element 70
3.4.1 Element Stiffness Equation: The Direct Approach .71
3.4.2 Element Stiffness Equation: The Energy Approach .72
3.4.3 Treatment of Distributed Loads . 74
3.4.4 Stiffness Matrix for a General Beam Element 75
3.5 Examples with Beam Elements . 76
3.6 Case Study with ANSYS Workbench .85
3.7 Summary 112
3.8 Review of Learning Objectives . 112
Problems 112
4. Two-Dimensional Elasticity . 117
4.1 Introduction . 117
4.2 Review of 2-D Elasticity Theory . 117
4.2.1 Plane Stress . 117
4.2.2 Plane Strain . 118
4.2.3 Stress–Strain (Constitutive) Equations . 119
4.2.4 Strain and Displacement Relations . 120
4.2.5 Equilibrium Equations 121
4.2.6 Boundary Conditions 121
4.2.7 Exact Elasticity Solution 121
4.3 Modeling of 2-D Elasticity Problems 122
4.4 Formulation of the Plane Stress/Strain Element 123
4.4.1 A General Formula for the Stiffness Matrix 124
4.4.2 Constant Strain Triangle (CST or T3) 124
4.4.3 Quadratic Triangular Element (LST or T6) 129
4.4.4 Linear Quadrilateral Element (Q4) 130
4.4.5 Quadratic Quadrilateral Element (Q8) 131
4.4.6 Transformation of Loads . 132
4.4.7 Stress Calculation 134
4.4.7.1 The von Mises Stress . 134
4.4.7.2 Averaged Stresses . 135
4.4.8 General Comments on the 2-D Elements . 136
4.5 Case Study with ANSYS Workbench . 137
4.6 Summary 155
4.7 Review of Learning Objectives . 155
Problems 156
5. Modeling and Solution Techniques . 161
5.1 Introduction . 161Contents vii
5.2 Symmetry . 161
5.2.1 An Example 162
5.3 Substructures (Superelements) . 163
5.4 Equation Solving . 164
5.4.1 Direct Methods (Gauss Elimination) 164
5.4.2 Iterative Methods . 164
5.4.3 An Example: Gauss Elimination 164
5.4.4 An Example: Iterative Method . 165
5.5 Nature of Finite Element Solutions 166
5.6 Convergence of FEA Solutions 167
5.7 Adaptivity (h-, p-, and hp-Methods) 167
5.8 Case Study with ANSYS Workbench . 168
5.9 Summary 182
5.10 Review of Learning Objectives . 183
Problems 183
6. Plate and Shell Analyses . 187
6.1 Introduction . 187
6.2 Review of Plate Theory 187
6.2.1 Force and Stress Relations in Plates 187
6.2.2 Thin Plate Theory (Kirchhoff Plate Theory) 189
6.2.2.1 Example: A Thin Plate . 191
6.2.3 Thick Plate Theory (Mindlin Plate Theory) . 192
6.2.4 Shell Theory 193
6.2.4.1 Shell Example: A Cylindrical Container . 193
6.3 Modeling of Plates and Shells . 194
6.4 Formulation of the Plate and Shell Elements 195
6.4.1 Kirchhoff Plate Elements 195
6.4.2 Mindlin Plate Elements . 196
6.4.3 Discrete Kirchhoff Elements 197
6.4.4 Flat Shell Elements . 197
6.4.5 Curved Shell Elements 198
6.5 Case Studies with ANSYS Workbench . 199
6.6 Summary 214
6.7 Review of Learning Objectives . 214
Problems 214
7. Three-Dimensional Elasticity 219
7.1 Introduction . 219
7.2 Review of Theory of Elasticity 219
7.2.1 Stress–Strain Relation .220
7.2.2 Displacement 221
7.2.3 Strain–Displacement Relation 221
7.2.4 Equilibrium Equations 221
7.2.5 Boundary Conditions 222
7.2.6 Stress Analysis .222
7.3 Modeling of 3-D Elastic Structures 222
7.3.1 Mesh Discretization .223
7.3.2 Boundary Conditions: Supports 223viii Contents
7.3.3 Boundary Conditions: Loads . 224
7.3.4 Assembly Analysis: Contacts . 224
7.4 Formulation of Solid Elements 225
7.4.1 General Formulation .225
7.4.2 Typical Solid Element Types 226
7.4.3 Formulation of a Linear Hexahedral Element Type .227
7.4.4 Treatment of Distributed Loads .230
7.5 Case Studies with ANSYS Workbench .230
7.6 Summary 255
7.7 Review of Learning Objectives .255
Problems 255
8. Structural Vibration and Dynamics . 261
8.1 Introduction . 261
8.2 Review of Basic Equations . 261
8.2.1 A Single DOF System 262
8.2.2 A Multi-DOF System .264
8.2.2.1 Mass Matrices .264
8.2.2.2 Damping 266
8.3 Formulation for Modal Analysis 267
8.3.1 Modal Equations 269
8.4 Formulation for Frequency Response Analysis . 271
8.4.1 Modal Method 271
8.4.2 Direct Method 272
8.5 Formulation for Transient Response Analysis 272
8.5.1 Direct Methods (Direct Integration Methods) . 273
8.5.2 Modal Method 274
8.6 Modeling Examples 275
8.6.1 Modal Analysis 275
8.6.2 Frequency Response Analysis . 276
8.6.3 Transient Response Analysis . 276
8.6.4 Cautions in Dynamic Analysis 276
8.7 Case Studies with ANSYS Workbench .277
8.8 Summary 293
8.9 Review of Learning Objectives . 294
Problems 294
9. Thermal Analysis . 301
9.1 Introduction . 301
9.2 Review of Basic Equations . 301
9.2.1 Thermal Analysis . 301
9.2.1.1 Finite Element Formulation for Heat Conduction .303
9.2.2 Thermal Stress Analysis .303
9.2.2.1 1-D Case .304
9.2.2.2 2-D Cases .305
9.2.2.3 3-D Case .305
9.2.2.4 Notes on FEA for Thermal Stress Analysis 305
9.3 Modeling of Thermal Problems 306
9.3.1 Thermal Analysis .306Contents ix
9.3.2 Thermal Stress Analysis .306
9.4 Case Studies with ANSYS Workbench .308
9.5 Summary 330
9.6 Review of Learning Objectives .330
Problems 330
10. Introduction to Fluid Analysis 337
10.1 Introduction . 337
10.2 Review of Basic Equations . 337
10.2.1 Describing Fluid Motion . 337
10.2.2 Types of Fluid Flow . 337
10.2.3 Navier–Stokes Equations 338
10.3 Modeling of Fluid Flow 339
10.3.1 Fluid Domain .339
10.3.2 Meshing .339
10.3.3 Boundary Conditions 339
10.3.4 Solution Visualization .340
10.4 Case Studies with ANSYS Workbench .341
10.5 Summary 368
10.6 Review of Learning Objectives .368
Problems 368
11. Design Optimization . 373
11.1 Introduction . 373
11.2 Topology Optimization 373
11.3 Parametric Optimization . 374
11.4 Design Space Exploration for Parametric Optimization . 374
11.4.1 Design of Experiments 375
11.4.2 Response Surface Optimization 377
11.5 Case Studies with ANSYS Workbench .377
11.6 Summary 415
11.7 Review of Learning Objectives . 415
Problems 415
12. Failure Analysis 419
12.1 Introduction . 419
12.2 Static Failure 419
12.2.1 Ductile Failure 419
12.2.1.1 Maximum Shear Stress Theory (Tresca Criterion) 419
12.2.1.2 Distortion Energy Theory (von Mises Criterion) .420
12.2.2 Brittle Failure 420
12.2.2.1 Maximum Normal Stress Theory 420
12.2.2.2 Mohr–Coulomb Theory 420
12.3 Fatigue Failure . 421
12.3.1 Soderberg Failure Criterion 422
12.3.2 Goodman Failure Criterion 422
12.3.3 Gerber Failure Criterion 423
12.4 Buckling Failure 424
12.5 Case Studies with ANSYS Workbench .425x Contents
12.6 Summary 436
12.7 Review of Learning Objectives .436
Problems 437
Appendix 1: Review of Matrix Algebra 441
Appendix 2: Photo Credits .447
References .449
Index .
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