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 |  موضوع: كتاب Finite Element Modeling and Simulation with ANSYS Workbench الخميس 16 نوفمبر 2017, 10:42 pm | |
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Finite Element Modeling and Simulation with ANSYS Workbench
Xiaolin Chen, Yijun Liu
ويتناول الموضوعات الأتية :
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 Verifcation 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 52
2.8 Review of Learning Objectives . 52
Problems 52vi Contents
3. Beams and Frames 57
3.1 Introduction .57
3.2 Review of the Beam Theory 57
3.2.1 Euler–Bernoulli Beam and Timoshenko Beam .57
3.2.2 Stress, Strain, De?ection, and Their Relations 59
3.3 Modeling of Beams and Frames .60
3.3.1 Cross Sections and Strong/Weak Axis .60
3.3.2 Support Conditions . 61
3.3.3 Conversion of a Physical Model into a Line Model 62
3.4 Formulation of the Beam Element 62
3.4.1 Element Stiffness Equation: The Direct Approach .63
3.4.2 Element Stiffness Equation: The Energy Approach .64
3.4.3 Treatment of Distributed Loads .66
3.4.4 Stiffness Matrix for a General Beam Element 67
3.5 Examples with Beam Elements .68
3.6 Case Study with ANSYS Workbench .77
3.7 Summary 96
3.8 Review of Learning Objectives .96
Problems 96
4. Two-Dimensional Elasticity . 101
4.1 Introduction . 101
4.2 Review of 2-D Elasticity Theory . 101
4.2.1 Plane Stress . 101
4.2.2 Plane Strain . 102
4.2.3 Stress–Strain (Constitutive) Equations . 103
4.2.4 Strain and Displacement Relations . 104
4.2.5 Equilibrium Equations 105
4.2.6 Boundary Conditions 105
4.2.7 Exact Elasticity Solution 105
4.3 Modeling of 2-D Elasticity Problems 106
4.4 Formulation of the Plane Stress/Strain Element 107
4.4.1 A General Formula for the Stiffness Matrix 108
4.4.2 Constant Strain Triangle (CST or T3) 108
4.4.3 Quadratic Triangular Element (LST or T6) 113
4.4.4 Linear Quadrilateral Element (Q4) 114
4.4.5 Quadratic Quadrilateral Element (Q8) 115
4.4.6 Transformation of Loads . 116
4.4.7 Stress Calculation 118
4.4.7.1 The von Mises Stress . 118
4.4.7.2 Averaged Stresses . 119
4.4.8 General Comments on the 2-D Elements . 120
4.5 Case Study with ANSYS Workbench . 121
4.6 Summary 138
4.7 Review of Learning Objectives . 138
Problems 138Contents vii
5. Modeling and Solution Techniques . 143
5.1 Introduction . 143
5.2 Symmetry . 143
5.2.1 An Example 144
5.3 Substructures (Superelements) . 145
5.4 Equation Solving . 146
5.4.1 Direct Methods (Gauss Elimination) 146
5.4.2 Iterative Methods . 146
5.4.3 An Example: Gauss Elimination 146
5.4.4 An Example: Iterative Method . 147
5.5 Nature of Finite Element Solutions 148
5.6 Convergence of FEA Solutions 149
5.7 Adaptivity (h-, p-, and hp-Methods) 149
5.8 Case Study with ANSYS Workbench . 150
5.9 Summary 161
5.10 Review of Learning Objectives . 162
Problems 162
6. Plate and Shell Analyses . 165
6.1 Introduction . 165
6.2 Review of Plate Theory 165
6.2.1 Force and Stress Relations in Plates 165
6.2.2 Thin Plate Theory (Kirchhoff Plate Theory) 167
6.2.2.1 Example: A Thin Plate . 169
6.2.3 Thick Plate Theory (Mindlin Plate Theory) . 170
6.2.4 Shell Theory 171
6.2.4.1 Shell Example: A Cylindrical Container . 171
6.3 Modeling of Plates and Shells . 172
6.4 Formulation of the Plate and Shell Elements 173
6.4.1 Kirchhoff Plate Elements 173
6.4.2 Mindlin Plate Elements . 174
6.4.3 Discrete Kirchhoff Elements 175
6.4.4 Flat Shell Elements . 175
6.4.5 Curved Shell Elements 176
6.5 Case Studies with ANSYS Workbench . 177
6.6 Summary 185
6.7 Review of Learning Objectives . 185
Problems 185
7. Three-Dimensional Elasticity 189
7.1 Introduction . 189
7.2 Review of Theory of Elasticity 189
7.2.1 Stress–Strain Relation . 190
7.2.2 Displacement 191
7.2.3 Strain–Displacement Relation 191
7.2.4 Equilibrium Equations 191
7.2.5 Boundary Conditions 192viii Contents
7.2.6 Stress Analysis . 192
7.3 Modeling of 3-D Elastic Structures 192
7.3.1 Mesh Discretization . 193
7.3.2 Boundary Conditions: Supports 193
7.3.3 Boundary Conditions: Loads . 194
7.3.4 Assembly Analysis: Contacts . 194
7.4 Formulation of Solid Elements 195
7.4.1 General Formulation . 195
7.4.2 Typical Solid Element Types 196
7.4.3 Formulation of a Linear Hexahedral Element Type . 197
7.4.4 Treatment of Distributed Loads .200
7.5 Case Studies with ANSYS Workbench .200
7.6 Summary 220
7.7 Review of Learning Objectives .220
Problems 220
8. Structural Vibration and Dynamics .225
8.1 Introduction .225
8.2 Review of Basic Equations .225
8.2.1 A Single DOF System 226
8.2.2 A Multi-DOF System .228
8.2.2.1 Mass Matrices .228
8.2.2.2 Damping 230
8.3 Formulation for Modal Analysis 231
8.3.1 Modal Equations 233
8.4 Formulation for Frequency Response Analysis .235
8.4.1 Modal Method 235
8.4.2 Direct Method 236
8.5 Formulation for Transient Response Analysis 236
8.5.1 Direct Methods (Direct Integration Methods) . 237
8.5.2 Modal Method 238
8.6 Modeling Examples 239
8.6.1 Modal Analysis 239
8.6.2 Frequency Response Analysis . 240
8.6.3 Transient Response Analysis . 240
8.6.4 Cautions in Dynamic Analysis 240
8.7 Case Studies with ANSYS Workbench . 241
8.8 Summary 260
8.9 Review of Learning Objectives .260
Problems 260
9. Thermal Analysis . 267
9.1 Introduction . 267
9.2 Review of Basic Equations . 267
9.2.1 Thermal Analysis . 267
9.2.1.1 Finite Element Formulation for Heat Conduction . 269
9.2.2 Thermal Stress Analysis . 269
9.2.2.1 1-D Case . 270
9.2.2.2 2-D Cases . 271Contents ix
9.2.2.3 3-D Case . 271
9.2.2.4 Notes on FEA for Thermal Stress Analysis 271
9.3 Modeling of Thermal Problems 272
9.3.1 Thermal Analysis .272
9.3.2 Thermal Stress Analysis .272
9.4 Case Studies with ANSYS Workbench . 274
9.5 Summary 292
9.6 Review of Learning Objectives . 292
Problems 293
10. Introduction to Fluid Analysis 299
10.1 Introduction .299
10.2 Review of Basic Equations .299
10.2.1 Describing Fluid Motion .299
10.2.2 Types of Fluid Flow .299
10.2.3 Navier–Stokes Equations 300
10.3 Modeling of Fluid Flow 301
10.3.1 Fluid Domain . 301
10.3.2 Meshing . 301
10.3.3 Boundary Conditions 301
10.3.4 Solution Visualization .302
10.4 Case Studies with ANSYS Workbench .303
10.5 Summary 325
10.6 Review of Learning Objectives . 325
Problems 326
11. Design Optimization . 331
11.1 Introduction . 331
11.2 Topology Optimization 331
11.3 Parametric Optimization . 332
11.4 Design Space Exploration for Parametric Optimization . 332
11.4.1 Design of Experiments 333
11.4.2 Response Surface Optimization 335
11.5 Case Studies with ANSYS Workbench .335
11.6 Summary 355
11.7 Review of Learning Objectives .355
Problems 356
12. Failure Analysis 361
12.1 Introduction . 361
12.2 Static Failure 361
12.2.1 Ductile Failure 361
12.2.1.1 Maximum Shear Stress Theory (Tresca Criterion) 361
12.2.1.2 Distortion Energy Theory (von Mises Criterion) . 362
12.2.2 Brittle Failure 362
12.2.2.1 Maximum Normal Stress Theory 362
12.2.2.2 Mohr–Coulomb Theory 362
12.3 Fatigue Failure .363x Contents
12.3.1 Soderberg Failure Criterion 364
12.3.2 Goodman Failure Criterion 364
12.3.3 Gerber Failure Criterion 365
12.4 Buckling Failure 366
12.5 Case Studies with ANSYS Workbench . 367
12.6 Summary 376
12.7 Review of Learning Objectives .377
Problems 377
Appendix 1: Review of Matrix Algebra 381
Appendix 2: Photo Credits . 387
References .
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