ANSYS Mechanical APDL Coupled-Field Analysis Guide

288 Pages·2013·5.02 MB·English

ANSYS Mechanical APDL Coupled-Field
Analysis Guide
ANSYS, Inc. Release 15.0
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Table of Contents
1. Coupled-Field Analyses .......................................................................................................................... 1
1.1.Types of Coupled-Field Analysis........................................................................................................ 1
1.1.1. Direct Method ......................................................................................................................... 2
1.1.2. Load Transfer Methods............................................................................................................. 2
1.1.2.1. Load Transfer Coupled Analysis - Workbench: System Coupling......................................... 2
1.1.2.2. Load Transfer Coupled Analysis - ANSYS Multi-field solver................................................. 3
1.1.2.3. Load Transfer Coupled Analysis - Physics File.................................................................... 3
1.1.2.4. Load Transfer Coupled Analysis - Unidirectional Load Transfer.......................................... 4
1.1.3.When to Use Direct vs. Load Transfer......................................................................................... 4
1.1.4. Additional Analysis Methods.................................................................................................... 7
1.1.4.1. Reduced Order Modeling................................................................................................. 7
1.1.4.2. Coupled Physics Circuit Simulation.................................................................................. 8
1.2. System of Units................................................................................................................................. 8
1.3. About GUI Paths and Command Syntax........................................................................................... 13
2. Direct Coupled-Field Analysis............................................................................................................... 15
2.1. Lumped Electric Elements............................................................................................................... 17
2.2.Thermal-Electric Analysis................................................................................................................. 18
2.2.1. Elements Used in a Thermal-Electric Analysis.......................................................................... 18
2.2.2. Performing a Thermal-Electric Analysis................................................................................... 19
2.3. Piezoelectric Analysis...................................................................................................................... 20
2.3.1. Hints and Recommendations for Piezoelectric Analysis........................................................... 21
2.3.2. Material Properties for Piezoelectric Analysis........................................................................... 21
2.3.2.1. Permittivity Matrix (Dielectric Constants)........................................................................ 21
2.3.2.2. Piezoelectric Matrix....................................................................................................... 22
2.3.2.3. Elastic Coefficient Matrix................................................................................................ 23
2.4. Electroelastic Analysis..................................................................................................................... 24
2.4.1. Elements Used in an Electroelastic Analysis............................................................................. 24
2.4.2. Performing an Electroelastic Analysis...................................................................................... 24
2.5. Piezoresistive Analysis..................................................................................................................... 25
2.5.1. Material Properties................................................................................................................. 26
2.5.1.1. Electrical Resistivity....................................................................................................... 26
2.5.1.2. Elastic Coefficient Matrix................................................................................................ 26
2.5.1.3. Piezoresistive Matrix...................................................................................................... 27
2.6. Structural-Thermal Analysis............................................................................................................. 28
2.6.1. Elements Used in a Structural-Thermal Analysis...................................................................... 28
2.6.2. Performing a Structural-Thermal Analysis............................................................................... 28
2.7. Structural-Thermal-Electric Analyses............................................................................................... 31
2.7.1. Structural-Thermoelectric Analysis ......................................................................................... 31
2.7.2.Thermal-Piezoelectric Analysis................................................................................................ 32
2.8. Magneto-Structural Analysis........................................................................................................... 32
2.9. Electromechanical Analysis............................................................................................................. 33
2.9.1. Element Physics..................................................................................................................... 34
2.9.2. A Reduced Order Model......................................................................................................... 34
2.9.3. Static Analysis........................................................................................................................ 35
2.9.4. Modal Analysis....................................................................................................................... 37
2.9.5. Harmonic Analysis.................................................................................................................. 38
2.9.6.Transient Analysis................................................................................................................... 38
2.9.7. Electromechanical Circuit Simulation...................................................................................... 38
2.10. Pore-Fluid-Diffusion-Structural Analysis......................................................................................... 38
2.10.1. Pore-Fluid-Diffusion-Structural Applications ......................................................................... 39
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2.10.2. Coupled Pore-Pressure Element Support............................................................................... 39
2.10.3. Defining Porous Media......................................................................................................... 40
2.10.4. Performing a Pore-Fluid-Diffusion-Structural Analysis............................................................ 40
2.11. Structural-Diffusion Analysis ......................................................................................................... 41
2.11.1. Elements Used in a Structural-Diffusion Analysis................................................................... 41
2.11.2. Performing a Structural-Diffusion Analysis............................................................................ 42
2.12.Thermal-Diffusion Analysis............................................................................................................ 43
2.12.1. Elements Used in a Thermal-Diffusion Analysis...................................................................... 43
2.12.2. Performing a Thermal-Diffusion Analysis............................................................................... 43
2.13. Structural-Thermal-Diffusion Analysis............................................................................................ 44
2.13.1. Elements Used in a Structural-Thermal-Diffusion Analysis...................................................... 44
2.13.2. Performing a Structural-Thermal-Diffusion Analysis............................................................... 45
2.14. Example Coupled-Field Analyses................................................................................................... 45
2.14.1. Example:Thermoelectric Cooler Analysis............................................................................... 45
2.14.1.1. Problem Description.................................................................................................... 45
2.14.1.2. Expected Results ......................................................................................................... 47
2.14.1.3. Command Listing........................................................................................................ 48
2.14.2. Example:Thermoelectric Generator Analysis......................................................................... 50
2.14.2.1. Problem Description.................................................................................................... 50
2.14.2.2. Expected Results ......................................................................................................... 53
2.14.2.3. Command Listing........................................................................................................ 53
2.14.3. Example: Structural-Thermal Harmonic Analysis.................................................................... 56
2.14.3.1. Problem Description.................................................................................................... 56
2.14.3.2. Expected Results ......................................................................................................... 57
2.14.3.3. Command Listing........................................................................................................ 58
2.14.4. Example: Electro-Thermal Microactuator Analysis.................................................................. 60
2.14.4.1. Problem Description.................................................................................................... 60
2.14.4.2. Results ........................................................................................................................ 61
2.14.4.3. Command Listing........................................................................................................ 62
2.14.5. Example: Piezoelectric Analysis............................................................................................. 65
2.14.5.1. Problem Description.................................................................................................... 65
2.14.5.2. Problem Specifications ................................................................................................ 66
2.14.5.3. Results ........................................................................................................................ 66
2.14.5.4. Command Listing........................................................................................................ 67
2.14.6. Example: Piezoelectric Analysis with Coriolis Effect................................................................ 69
2.14.6.1. Problem Description.................................................................................................... 69
2.14.6.2. Problem Specifications ................................................................................................ 70
2.14.6.3. Results ........................................................................................................................ 71
2.14.6.4. Command Listing........................................................................................................ 71
2.14.7. Example: Electroelastic Analysis of a Dielectric Elastomer ...................................................... 74
2.14.7.1. Problem Description.................................................................................................... 74
2.14.7.2. Problem Specifications ................................................................................................ 74
2.14.7.3. Results ........................................................................................................................ 75
2.14.7.4. Command Listing........................................................................................................ 76
2.14.8. Example: Electroelastic Analysis of a MEMS Switch................................................................ 79
2.14.8.1. Problem Description.................................................................................................... 79
2.14.8.2. Problem Specifications ................................................................................................ 79
2.14.8.3. Results ........................................................................................................................ 80
2.14.8.4. Command Listing........................................................................................................ 80
2.14.9. Example: Piezoresistive Analysis............................................................................................ 82
2.14.9.1. Problem Description.................................................................................................... 82
2.14.9.2. Problem Specification.................................................................................................. 83
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2.14.9.3. Results ........................................................................................................................ 84
2.14.9.4. Command Listing........................................................................................................ 84
2.14.10. Example: Electromechanical Analysis.................................................................................. 86
2.14.10.1. Problem Description.................................................................................................. 87
2.14.10.2. Expected Results........................................................................................................ 87
2.14.10.2.1. Static Analysis................................................................................................... 87
2.14.10.2.2. Modal Analysis.................................................................................................. 87
2.14.10.2.3. Harmonic Analysis............................................................................................. 88
2.14.10.2.4. Displays............................................................................................................ 88
2.14.10.3. Building and Solving the Model................................................................................. 88
2.14.11. Example: Electromechanical Comb Finger Analysis.............................................................. 90
2.14.11.1. Problem Specifications............................................................................................... 90
2.14.11.2. Results....................................................................................................................... 90
2.14.11.3. Command Listing...................................................................................................... 91
2.14.12. Example: Force Calculation of Two Opposite Electrodes....................................................... 94
2.14.12.1. Problem Specifications............................................................................................... 94
2.14.12.2. Results....................................................................................................................... 94
2.14.12.3. Command Listing...................................................................................................... 95
2.14.13. Example: Structural-Diffusion Analysis................................................................................. 97
2.14.13.1. Problem Description.................................................................................................. 97
2.14.13.2. Problem Specifications............................................................................................... 97
2.14.13.3. Results....................................................................................................................... 98
2.14.13.4. Command Listing...................................................................................................... 98
2.14.14. Example:Thermal-Diffusion Analysis................................................................................... 99
2.14.14.1. Problem Description.................................................................................................. 99
2.14.14.2. Results..................................................................................................................... 101
2.14.14.3. Command Listing .................................................................................................... 103
2.14.15. Other Coupled-Field Analysis Examples............................................................................. 106
3.The ANSYS Multi-field (TM) Solver - MFS Single-Code Coupling........................................................ 107
3.1.The ANSYS Multi-field solver and Solution Algorithm..................................................................... 108
3.1.1. Load Transfer........................................................................................................................ 108
3.1.2. Mapping.............................................................................................................................. 113
3.1.2.1. Mapping Algorithms.................................................................................................... 113
3.1.2.2. Mapping Diagnostics................................................................................................... 115
3.1.2.3. Mapping Operations.................................................................................................... 117
3.1.3. Coupled Field Loads............................................................................................................. 117
3.1.4. Elements Supported............................................................................................................. 118
3.1.5. Solution Algorithm............................................................................................................... 119
3.2. ANSYS Multi-field solver Solution Procedure.................................................................................. 120
3.2.1. Set up Field Models.............................................................................................................. 120
3.2.2. Flag Field Interface Conditions.............................................................................................. 120
3.2.3. Set up Field Solutions........................................................................................................... 120
3.2.3.1. Define Fields and Capture Field Solutions..................................................................... 121
3.2.3.2. Set up Interface Load Transfers..................................................................................... 123
3.2.3.3. Set up Global Field Solution......................................................................................... 123
3.2.3.4. Set up Stagger Solution............................................................................................... 125
3.2.3.5. Set up Time and Frequency Controls............................................................................ 126
3.2.3.6. Set up Morphing (if Necessary).................................................................................... 128
3.2.3.7. Clear or List Settings.................................................................................................... 129
3.2.4. Obtain the solution.............................................................................................................. 130
3.2.5. Postprocess the Results........................................................................................................ 130
3.3. Sample Thermal-Stress Analysis of a Thick-walled Cylinder (Batch or Command Method)................ 130
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3.3.1. Problem Description............................................................................................................. 130
3.3.2. Results................................................................................................................................. 131
3.3.3. Command Listing................................................................................................................. 132
3.4. Sample Electrostatic Actuated Beam Analysis (Batch or Command Method)................................... 134
3.4.1. Problem Description............................................................................................................. 134
3.4.2. Results................................................................................................................................. 135
3.4.3. Command Listing................................................................................................................. 136
3.5. Sample Induction-Heating Analysis of a Circular Billet.................................................................... 138
3.5.1. Problem Description............................................................................................................. 138
3.5.2. Results................................................................................................................................. 140
3.5.3. Command Listing................................................................................................................. 141
4. Multi-field Analysis Using Code Coupling........................................................................................... 145
4.1. How MFX Works............................................................................................................................ 147
4.1.1. Synchronization Points and Load Transfer............................................................................. 147
4.1.2. Load Interpolation................................................................................................................ 147
4.1.3. Elements and Load Types Supported.................................................................................... 150
4.1.4. Solution Process................................................................................................................... 150
4.2. MFX Solution Procedure................................................................................................................ 151
4.2.1. Set Up ANSYS and CFX Models............................................................................................. 151
4.2.2. Flag Field Interface Conditions.............................................................................................. 151
4.2.3. Set Up Master Input.............................................................................................................. 151
4.2.3.1. Set Up Global MFX Controls......................................................................................... 152
4.2.3.2. Set Up Interface Load Transfer...................................................................................... 154
4.2.3.3. Set Up Time Controls................................................................................................... 155
4.2.3.4. Set Up Mapping Operations......................................................................................... 155
4.2.3.5. Set Up Stagger Solution............................................................................................... 156
4.2.3.6. List or Clear Settings.................................................................................................... 158
4.2.4. Obtain the Solution.............................................................................................................. 159
4.2.5. Multi-field Commands.......................................................................................................... 159
4.2.6. Postprocess the Results........................................................................................................ 160
4.3. Starting and Stopping an MFX Analysis......................................................................................... 160
4.3.1. Starting an MFX Analysis via the Command Line................................................................... 160
4.3.2. Stopping an MFX Run Manually............................................................................................ 161
4.4. Example Simulation of a Piezoelectric Actuated Micro-Pump......................................................... 161
4.4.1. Problem Description............................................................................................................. 161
4.4.2. Setup Tasks.......................................................................................................................... 163
4.4.2.1. Set Up the Piezoelectric and Fluid Inputs...................................................................... 163
4.4.2.2. Set Up the MFX Launcher Controls............................................................................... 164
4.4.2.3. Set Up the MFX Groups................................................................................................ 165
4.4.2.4. Set Up the MFX Time Controls and Load Transfer.......................................................... 165
4.4.2.5. Set Up MFX Advanced Options.................................................................................... 165
4.4.2.6. Set up the CFX Model and Create the CFX Definition File.............................................. 166
4.4.3. Run the Example.................................................................................................................. 168
4.4.4.View the Results................................................................................................................... 168
5. Load Transfer Coupled Physics Analysis............................................................................................. 171
5.1.What Is a Physics Environment?..................................................................................................... 172
5.2. General Analysis Procedures.......................................................................................................... 173
5.3.Transferring Loads Between Physics............................................................................................... 175
5.3.1. Compatible Element Types................................................................................................... 175
5.3.2.Types of Results Files You May Use........................................................................................ 177
5.4. Performing a Load Transfer Coupled Physics Analysis with Multiple Physics Environments.............. 177
5.4.1. Mesh Updating.................................................................................................................... 178
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5.4.2. Restarting an Analysis Using Multiple Physics Environments ................................................. 181
5.5. Example Thermal-Stress Analysis Using Separate Databases........................................................... 182
5.5.1.The Problem Described........................................................................................................ 182
5.6. Example Thermal-Stress Analysis Using Multiple Physics Environments.......................................... 184
5.7. Example Induction-heating Analysis Using Physics Environments.................................................. 186
5.7.1.The Problem Described........................................................................................................ 187
5.7.2.The Procedure...................................................................................................................... 187
5.7.2.1. Step 1: Develop Attribute Relationship......................................................................... 188
5.7.2.2. Step2: Build the Model................................................................................................. 188
5.7.2.3. Step 3: Create Electromagnetic Physics Environment.................................................... 189
5.7.2.4. Step 4: Create Thermal Physics Environment................................................................. 189
5.7.2.5. Step 5:Write Thermal Physics Environment................................................................... 190
5.7.2.6. Step 6: Prepare DO Loop.............................................................................................. 190
5.7.2.7. Step 7: Repeat Prior Step.............................................................................................. 191
5.7.2.8. Step 8: Postprocess Results........................................................................................... 191
5.7.2.9. Command Input Listing............................................................................................... 191
5.7.2.10. Results....................................................................................................................... 193
6. Unidirectional Load Transfer............................................................................................................... 195
6.1.The Unidirectional Load Transfer Method: Mechanical APDL to CFX................................................ 195
6.2. Sample Unidirectional Load Transfer Analysis: Mechanical APDL to CFX.......................................... 196
6.2.1. Command Listings............................................................................................................... 197
6.2.1.1. Solve Solid Analysis and Write Profile File...................................................................... 197
6.2.1.2. Generate and Write Fluid Region Mesh......................................................................... 198
6.2.1.3. Generate and Write Solid Region Mesh......................................................................... 199
6.2.2. CFX Procedure ..................................................................................................................... 200
6.3.The Unidirectional Load Transfer Method: CFX to Mechanical APDL................................................ 201
6.4. Unidirectional Pressure Mapping: CFD to Mechanical APDL............................................................ 202
7. Coupled Physics Circuit Simulation.................................................................................................... 205
7.1. Electromagnetic-Circuit Simulation............................................................................................... 205
7.1.1. 2-D Circuit Coupled Stranded Coil......................................................................................... 206
7.1.2. 2-D Circuit Coupled Massive Conductor................................................................................ 207
7.1.3. 3-D Circuit Coupled Stranded Coil......................................................................................... 208
7.1.4. 3-D Circuit Coupled Massive Conductor................................................................................ 208
7.1.5. 3-D Circuit Coupled Solid Source Conductor......................................................................... 210
7.1.6.Taking Advantage of Symmetry............................................................................................ 211
7.1.7. Series Connected Conductors............................................................................................... 212
7.2. Electromechanical-Circuit Simulation............................................................................................ 213
7.3. Piezoelectric-Circuit Simulation..................................................................................................... 215
7.4. Sample Electromechanical-Circuit Analysis.................................................................................... 218
7.4.1. Problem Description............................................................................................................. 218
7.4.2. Results................................................................................................................................. 219
7.4.3. Command Listing................................................................................................................. 220
7.5. Sample Piezoelectric-Circuit Analysis (Batch or Command Method)................................................ 221
7.5.1. Problem Description............................................................................................................. 221
7.5.2. Problem Specifications......................................................................................................... 222
7.5.3. Equivalent Electric Circuits (Reduced Order Model)............................................................... 222
7.5.4. Results................................................................................................................................. 224
7.5.5. Command Listing................................................................................................................. 225
8. Reduced Order Modeling.................................................................................................................... 229
8.1. Model Preparation........................................................................................................................ 230
8.1.1. Build the Solid Model........................................................................................................... 231
8.1.2. Mesh the Model................................................................................................................... 231
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8.1.3. Create Structural Physics File................................................................................................ 231
8.1.4. Create Electrostatic Physics File............................................................................................. 232
8.1.5. Save Model Database........................................................................................................... 232
8.2. Generation Pass............................................................................................................................ 232
8.2.1. Specify Generation Pass Jobname......................................................................................... 234
8.2.2. Assign ROM Features............................................................................................................ 234
8.2.3. Assign Names for Conductor Pairs........................................................................................ 234
8.2.4. Specify ROM Master Nodes................................................................................................... 234
8.2.5. Run Static Analysis for Test Load and Extract Neutral Plane Displacements............................. 235
8.2.6. Run Static Analysis for Element Loads and Extract Neutral Plane Displacements..................... 235
8.2.7. Perform Modal Analysis and Extract Neutral Plane Eigenvectors............................................ 236
8.2.8. Select Modes for ROM.......................................................................................................... 236
8.2.9. Modify Modes for ROM......................................................................................................... 236
8.2.10. List Mode Specifications..................................................................................................... 237
8.2.11. Save ROM Database............................................................................................................ 237
8.2.12. Run Sample Point Generation............................................................................................. 237
8.2.13. Specify Polynomial Order.................................................................................................... 238
8.2.14. Define ROM Response Surface............................................................................................ 238
8.2.15. Perform Fitting Procedure................................................................................................... 238
8.2.16. Plot Response Surface........................................................................................................ 239
8.2.17. List Status of Response Surface........................................................................................... 239
8.2.18. Export ROM Model to External System Simulator................................................................. 239
8.3. Use Pass........................................................................................................................................ 240
8.3.1. Clear Database..................................................................................................................... 241
8.3.2. Define a Jobname................................................................................................................ 241
8.3.3. Resume ROM Database........................................................................................................ 241
8.3.4. Define Element Type............................................................................................................ 241
8.3.5. Define Nodes....................................................................................................................... 242
8.3.6. Activate ROM Database........................................................................................................ 242
8.3.7. Define Node Connectivity..................................................................................................... 242
8.3.8. Define Other Model Entities.................................................................................................. 242
8.3.9. Using Gap Elements with ROM144........................................................................................ 243
8.3.10. Apply Loads....................................................................................................................... 244
8.3.11. Specify Solution Options.................................................................................................... 244
8.3.12. Run ROM Use Pass.............................................................................................................. 244
8.3.13. Review Results ................................................................................................................... 245
8.4. Expansion Pass ............................................................................................................................. 245
8.4.1. Clear Database..................................................................................................................... 246
8.4.2. Define a Jobname................................................................................................................ 246
8.4.3. Resume ROM ....................................................................................................................... 246
8.4.4. Resume Model Database...................................................................................................... 246
8.4.5. Activate ROM Database........................................................................................................ 246
8.4.6. Perform Expansion Pass........................................................................................................ 247
8.4.7. Review Results..................................................................................................................... 247
8.5. Sample Miniature Clamped-Clamped Beam Analysis (Batch or Command Method)........................ 247
8.5.1. Problem Description............................................................................................................. 247
8.5.2. Program Listings.................................................................................................................. 248
8.6. Sample Micro Mirror Analysis (Batch or Command Method)........................................................... 253
8.6.1. Problem Description............................................................................................................. 253
8.6.2. Program Listings.................................................................................................................. 254
Index........................................................................................................................................................ 271
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List of Figures
2.1. Extracting Capacitance......................................................................................................................... 34
2.2. Reduced Order Model........................................................................................................................... 35
2.3. Micromirror Model................................................................................................................................ 35
2.4. Electromechanical Hysteresis................................................................................................................ 36
2.5. Static Stability Characteristics................................................................................................................ 37
2.6.Thermoelectric Cooler........................................................................................................................... 46
2.7. Finite Element Model............................................................................................................................ 47
2.8.Temperature Distribution...................................................................................................................... 48
2.9.Thermoelectric Generator..................................................................................................................... 50
2.10.Temperature Dependent Material Properties....................................................................................... 52
2.11. Clamped-clamped Beam..................................................................................................................... 56
2.12. Frequency Dependence of Thermoelastic Damping in a Silicon Beam.................................................. 57
2.13.Temperature Distribution in the Beam................................................................................................. 58
2.14. Microactuator Model .......................................................................................................................... 61
2.15. Microactuator Displacements.............................................................................................................. 61
2.16. Microactuator Temperatures............................................................................................................... 62
2.17. Piezoelectric Bimorph Beam................................................................................................................ 65
2.18. Finite Element Model of Quartz Tuning Fork........................................................................................ 69
2.19.Voltage Load for In-Plane Vibration...................................................................................................... 70
2.20. In-Plane and Out-of-Plane Vibrations................................................................................................... 71
2.21. Elastomer Deformation....................................................................................................................... 75
2.22. Applied Sinusoidal Voltage.................................................................................................................. 76
2.23. Longitudinal Displacement of Elastomer............................................................................................. 76
2.24. Finite Element Model.......................................................................................................................... 79
2.25. Mid-Span Beam Deflection.................................................................................................................. 80
2.26. Four-Terminal Sensor.......................................................................................................................... 83
2.27. Finite Element Model.......................................................................................................................... 84
2.28. Electrostatic Parallel Plate Drive Connected to a Silicon Beam.............................................................. 87
2.29. Elements of MEMS Example Problem................................................................................................... 88
2.30. Lowest Eigenvalue Mode Shape for MEMS Example Problem............................................................... 88
2.31. Mid Span Beam Deflection for MEMS Example Problem....................................................................... 88
2.32. Potential Distribution on Deformed Comb Drive.................................................................................. 91
2.33. Potential Distribution of Overlapping Electrodes................................................................................. 94
2.34. Bimorph Beam Problem Sketch........................................................................................................... 97
2.35. Bimorph Beam Deformation................................................................................................................ 98
2.36. Finite Element Model of the Potato Slice............................................................................................ 100
2.37. Internal Temperature (˚C) vs Time (s) for Three Analyses..................................................................... 102
3
2.38. Internal Concentration (g/mm ) vs Time (s) for Three Analyses............................................................ 102
2.39. Moisture Mass of Entire Potato Slice (g) vs Time (s) for Three Analyses................................................. 103
3.1. Profile Preserving Interpolation........................................................................................................... 109
3.2. Globally Conservative Interpolation..................................................................................................... 109
3.3. Profile Preserving Interpolation - Load Imbalances............................................................................... 110
3.4. Globally Conservative Interpolation - Load Balance.............................................................................. 110
3.5. Profile Preserving Interpolation - Coarse Mesh on the Sending Side..................................................... 111
3.6. Profile Preserving Interpolation - Coarse Mesh on the Receiver Side..................................................... 111
3.7. Globally Conservative Interpolation - Fine Mesh on Sending Side......................................................... 112
3.8. Globally Conservative Interpolation - Fine Mesh on Receiver Side......................................................... 112
3.9.Three Lower Order Elements............................................................................................................... 112
3.10. Six Lower Order Elements.................................................................................................................. 113
3.11. Fluid-Solid Interaction Load Transfer.................................................................................................. 113
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3.12. Node Mapped to Minimize Gap......................................................................................................... 114
3.13. Node Mapped to Closest Node.......................................................................................................... 114
3.14. Node in Box 3 with Three Elements.................................................................................................... 115
3.15. Nine boxes and Node in Empty Box................................................................................................... 115
3.16. Relative Gap for MFTOL..................................................................................................................... 116
3.17. Improperly Mapped Nodes................................................................................................................ 116
3.18. ANSYS Multi-field solver Algorithm.................................................................................................... 119
3.19.Time Steps........................................................................................................................................ 128
3.20.Thermal and Structural Model Mesh ................................................................................................. 131
3.21.Temperature Profile and Axial Stress.................................................................................................. 132
3.22. Structural and Electrostatic Field Mesh.............................................................................................. 135
3.23. Beam Displacement for 120 Volt Load................................................................................................ 135
3.24. Electrostatic Field.............................................................................................................................. 136
3.25. Mid-span Beam Deflection vs Voltage................................................................................................ 136
3.26. Axisymmetric 1-D Slice of the Induction Heating Domain................................................................... 139
3.27. Nominal Electromagnetic Physics Boundary Conditions..................................................................... 139
3.28. Nominal Thermal Physics Boundary Conditions.................................................................................. 139
3.29. ANSYS Multi-field solver Flow Chart for Induction Heating................................................................. 139
3.30. Centerline and Surface Temperature.................................................................................................. 140
3.31.Temperature Profile at 3 Seconds....................................................................................................... 140
4.1. MFX Method Data Communication..................................................................................................... 147
4.2. Conservative Interpolation.................................................................................................................. 149
4.3. ANSYS Multi-field solver Process.......................................................................................................... 150
4.4. ANSYS and CFX Fields Solved Simultaneously...................................................................................... 153
4.5. ANSYS and CFX Fields Solved Sequentially, ANSYS First........................................................................ 153
4.6. Piezoelectric Micropump Description.................................................................................................. 162
4.7. Model Dimensions.............................................................................................................................. 163
4.8. Model Boundary Conditions................................................................................................................ 163
4.9.Vertical Displacement of the Silicon Membrane's Center Point.............................................................. 169
4.10. von Mises Stress Distribution............................................................................................................. 169
4.11. Air Streamline Velocity...................................................................................................................... 170
5.1. Data Flow for a Load Transfer Coupled-Field Analysis Using Separate Databases................................... 173
5.2. Data Flow for a Load Transfer Coupled Physics Analysis Using Multiple Physics Environments............... 174
5.3. Beam Above Ground Plane.................................................................................................................. 179
5.4. Area Model of Beam and Air Region.................................................................................................... 180
5.5. Area Model of Beam and Multiple Air Regions..................................................................................... 181
5.6. Stress Profile Across Material Discontinuity.......................................................................................... 186
5.7. Radial Stress Displayed on Geometry................................................................................................... 186
5.8. Axisymmetric 1-D Slice of the Induction Heating Domain.................................................................... 187
5.9. Solution Flow Diagram........................................................................................................................ 188
5.10. Nominal Electromagnetic Physics Boundary Conditions..................................................................... 189
5.11. Nominal Thermal Physics Boundary Conditions.................................................................................. 190
5.12.Temperature Response of Solid Cylinder Billet.................................................................................... 193
7.1. 2-D Circuit Coupled Stranded Coil....................................................................................................... 207
7.2. 2-D Circuit Coupled Massive Conductor............................................................................................... 207
7.3. 3-D Circuit Coupled Stranded Coil....................................................................................................... 208
7.4. 3-D Circuit Coupled Massive Conductor............................................................................................... 209
7.5. 3-D Circuit Coupled Solid Source Conductor........................................................................................ 210
7.6. Circuit for Go and Return Conductors.................................................................................................. 212
7.7. Series Wound Stranded Conductor...................................................................................................... 213
7.8. CIRCU94 Components......................................................................................................................... 216
7.9. Electrical Circuit Connections.............................................................................................................. 217
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