ANSYS Mechanical APDL Structural Analysis Guide

522 Pages·2013·6.33 MB·English

ANSYS Mechanical APDL Structural Analysis
Guide
ANSYS, Inc. Release 15.0
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Table of Contents
1. Overview of Structural Analyses............................................................................................................. 1
1.1.Types of Structural Analysis............................................................................................................... 1
1.2. Elements Used in Structural Analyses................................................................................................ 2
1.3. Material Model Interface................................................................................................................... 2
1.4. Damping.......................................................................................................................................... 2
1.4.1. Alpha and Beta Damping (Rayleigh Damping).......................................................................... 5
1.4.2. Material-Dependent Alpha and Beta Damping (Rayleigh Damping)........................................... 6
1.4.3. Constant Global Damping Ratio............................................................................................... 6
1.4.4. Constant Structural Damping Coefficient.................................................................................. 6
1.4.5. Mode-Dependent Damping Ratio............................................................................................. 7
1.4.6.Viscoelastic Material Damping.................................................................................................. 7
1.4.7. Element Damping.................................................................................................................... 7
1.5. Solution Method............................................................................................................................... 7
2. Structural Static Analysis........................................................................................................................ 9
2.1. Linear vs. Nonlinear Static Analyses................................................................................................... 9
2.2. Performing a Static Analysis.............................................................................................................. 9
2.2.1. Build the Model...................................................................................................................... 10
2.2.1.1. Points to Remember...................................................................................................... 10
2.2.2. Set Solution Controls.............................................................................................................. 10
2.2.2.1. Access the Solution Controls Dialog Box......................................................................... 11
2.2.2.2. Using the Basic Tab........................................................................................................ 11
2.2.2.3.The Transient Tab........................................................................................................... 12
2.2.2.4. Using the Sol'n Options Tab........................................................................................... 12
2.2.2.5. Using the Nonlinear Tab................................................................................................. 12
2.2.2.6. Using the Advanced NL Tab........................................................................................... 13
2.2.3. Set Additional Solution Options.............................................................................................. 13
2.2.3.1. Stress Stiffening Effects.................................................................................................. 13
2.2.3.2. Newton-Raphson Option............................................................................................... 14
2.2.3.3. Prestress Effects Calculation........................................................................................... 14
2.2.3.4. Mass Matrix Formulation................................................................................................ 14
2.2.3.5. Reference Temperature.................................................................................................. 14
2.2.3.6. Mode Number............................................................................................................... 15
2.2.3.7. Creep Criteria................................................................................................................ 15
2.2.3.8. Printed Output.............................................................................................................. 15
2.2.3.9. Extrapolation of Results................................................................................................. 15
2.2.4. Apply the Loads..................................................................................................................... 15
2.2.4.1. Load Types.................................................................................................................... 15
2.2.4.1.1. Displacements (UX, UY, UZ, ROTX, ROTY, ROTZ)....................................................... 15
2.2.4.1.2.Velocities (VELX,VELY,VELZ, OMGX, OMGY, OMGZ)................................................. 15
2.2.4.1.3. Forces (FX, FY, FZ) and Moments (MX, MY, MZ)........................................................ 16
2.2.4.1.4. Pressures (PRES).................................................................................................... 16
2.2.4.1.5.Temperatures (TEMP)............................................................................................ 16
2.2.4.1.6. Fluences (FLUE)..................................................................................................... 16
2.2.4.1.7. Gravity, Spinning, Etc............................................................................................. 16
2.2.4.2. Apply Loads to the Model.............................................................................................. 16
2.2.4.2.1. Applying Loads Using TABLE Type Array Parameters............................................... 17
2.2.4.3. Calculating Inertia Relief................................................................................................ 17
2.2.4.3.1. Inertia Relief Output.............................................................................................. 18
2.2.4.3.2. Using a Macro to Perform Inertia Relief Calculations............................................... 18
2.2.5. Solve the Analysis.................................................................................................................. 18
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2.2.6. Review the Results................................................................................................................. 19
2.2.6.1. Postprocessors .............................................................................................................. 19
2.2.6.2. Points to Remember...................................................................................................... 19
2.2.6.3. Reviewing Results Data.................................................................................................. 19
2.2.6.4.Typical Postprocessing Operations................................................................................. 20
2.3. A Sample Static Analysis (GUI Method)............................................................................................ 22
2.3.1. Problem Description.............................................................................................................. 22
2.3.2. Problem Specifications........................................................................................................... 22
2.3.3. Problem Sketch...................................................................................................................... 22
2.3.3.1. Set the Analysis Title...................................................................................................... 23
2.3.3.2. Set the System of Units.................................................................................................. 23
2.3.3.3. Define Parameters......................................................................................................... 23
2.3.3.4. Define the Element Types.............................................................................................. 24
2.3.3.5. Define Material Properties............................................................................................. 24
2.3.3.6. Create Hexagonal Area as Cross-Section......................................................................... 24
2.3.3.7. Create Keypoints Along a Path....................................................................................... 25
2.3.3.8. Create Lines Along a Path.............................................................................................. 25
2.3.3.9. Create Line from Shank to Handle.................................................................................. 26
2.3.3.10. Cut Hex Section........................................................................................................... 26
2.3.3.11. Set Meshing Density.................................................................................................... 27
2.3.3.12. Set Element Type for Area Mesh................................................................................... 27
2.3.3.13. Generate Area Mesh.................................................................................................... 27
2.3.3.14. Drag the 2-D Mesh to Produce 3-D Elements................................................................ 27
2.3.3.15. Select BOTAREA Component and Delete 2-D Elements................................................. 28
2.3.3.16. Apply Displacement Boundary Condition at End of Wrench.......................................... 28
2.3.3.17. Display Boundary Conditions....................................................................................... 29
2.3.3.18. Apply Pressure on Handle............................................................................................ 29
2.3.3.19.Write the First Load Step.............................................................................................. 31
2.3.3.20. Define Downward Pressure.......................................................................................... 31
2.3.3.21.Write Second Load Step............................................................................................... 32
2.3.3.22. Solve from Load Step Files........................................................................................... 32
2.3.3.23. Read First Load Step and Review Results...................................................................... 32
2.3.3.24. Read the Next Load Step and Review Results................................................................ 33
2.3.3.25. Zoom in on Cross-Section............................................................................................ 34
2.3.3.26. Exit ANSYS................................................................................................................... 34
2.4. A Sample Static Analysis (Command or Batch Method).................................................................... 34
2.5.Where to Find Other Examples........................................................................................................ 37
3. Modal Analysis...................................................................................................................................... 39
3.1. Uses for Modal Analysis................................................................................................................... 39
3.2. Understanding the Modal Analysis Process...................................................................................... 39
3.3. Building the Model for a Modal Analysis.......................................................................................... 40
3.4. Applying Loads and Obtaining the Solution.................................................................................... 40
3.4.1. Enter the Solution Processor................................................................................................... 40
3.4.2. Define Analysis Type and Options........................................................................................... 40
3.4.2.1. Option: New Analysis (ANTYPE)..................................................................................... 41
3.4.2.2. Option: Analysis Type: Modal (ANTYPE).......................................................................... 41
3.4.2.3. Option: Mode-Extraction Method (MODOPT)................................................................. 41
3.4.2.4. Option: Number of Modes to Extract (MODOPT)............................................................ 43
3.4.2.5. Option: Number of Modes to Expand (MXPAND)............................................................ 43
3.4.2.6. Option: Results File Output (OUTRES)............................................................................ 44
3.4.2.7. Option: Mass Matrix Formulation (LUMPM).................................................................... 44
3.4.2.8. Option: Prestress Effects Calculation (PSTRES)................................................................ 44
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3.4.2.9. Option: Residual Vector Calculation (RESVEC)................................................................ 44
3.4.2.10. Additional Modal Analysis Options............................................................................... 44
3.4.3. Apply Loads........................................................................................................................... 44
3.4.3.1. Applying Loads Using Commands.................................................................................. 45
3.4.3.2. Applying Loads Using the GUI........................................................................................ 45
3.4.3.3. Listing Loads................................................................................................................. 46
3.4.4. Specify Load Step Options...................................................................................................... 46
3.4.5. Solve...................................................................................................................................... 46
3.4.5.1. Output.......................................................................................................................... 47
3.4.6. Participation Factor Table Output........................................................................................... 47
3.4.7. Exit the Solution Processor..................................................................................................... 47
3.5. Reviewing the Results..................................................................................................................... 47
3.5.1. Points to Remember............................................................................................................... 47
3.5.2. Reviewing Results Data.......................................................................................................... 48
3.5.3. Option: Listing All Frequencies................................................................................................ 48
3.5.4. Option: Display Deformed Shape............................................................................................ 48
3.5.5. Option: Line Element Results.................................................................................................. 48
3.5.6. Option: Contour Displays........................................................................................................ 48
3.5.7. Option:Tabular Listings.......................................................................................................... 49
3.5.8. Other Capabilities.................................................................................................................. 49
3.6. Applying Prestress Effects in a Modal Analysis.................................................................................. 49
3.6.1. Performing a Prestressed Modal Analysis from a Linear Base Analysis...................................... 49
3.6.2. Performing a Prestressed Modal Analysis from a Large-Deflection Base Analysis...................... 50
3.7. Modal Analysis Examples................................................................................................................ 50
3.7.1. An Example Modal Analysis (GUI Method)............................................................................... 51
3.7.1.1. Problem Description...................................................................................................... 51
3.7.1.2. Problem Specifications.................................................................................................. 51
3.7.1.3. Problem Sketch............................................................................................................. 51
3.7.2. An Example Modal Analysis (Command or Batch Method)....................................................... 51
3.7.3. Brake Squeal (Prestressed Modal) Analysis ............................................................................. 53
3.7.3.1. Full Nonlinear Perturbed Modal Analysis........................................................................ 54
3.7.3.2. Partial Nonlinear Perturbed Modal Analysis.................................................................... 55
3.7.3.3. Linear Non-prestressed Modal Analysis.......................................................................... 57
3.7.4. Reuse of Jobname.MODESYM in QRDAMP eigensolver ......................................................... 58
3.7.5. Calculate the Complex Mode Contribution Coefficients (CMCC)............................................... 59
3.7.6.Where to Find Other Modal Analysis Examples........................................................................ 60
3.8. Comparing Mode-Extraction Methods............................................................................................. 61
3.8.1. Block Lanczos Method............................................................................................................ 62
3.8.2. PCG Lanczos Method.............................................................................................................. 62
3.8.3. Supernode (SNODE) Method.................................................................................................. 63
3.8.4. Subspace Method.................................................................................................................. 64
3.8.5. Unsymmetric Method............................................................................................................ 64
3.8.6. Damped Method.................................................................................................................... 64
3.8.6.1. Damped Method--Real and Imaginary Parts of the Eigenvalue........................................ 64
3.8.6.2. Damped Method-Real and Imaginary Parts of the Eigenvector........................................ 65
3.8.7. QR Damped Method.............................................................................................................. 65
3.8.8. Storage of Complex Results.................................................................................................... 65
3.9. Modal Analysis Tools for Subsequent Mode Superposition Analysis.................................................. 66
3.9.1. Using the Residual-Vector Method to Improve Accuracy......................................................... 66
3.9.1.1. Understanding the Residual Vector Method................................................................... 66
3.9.1.2. Using the Residual Vector Method................................................................................. 67
3.9.2. Reusing Eigenmodes.............................................................................................................. 68
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3.9.2.1. Spectrum Analysis (ANTYPE,SPECTRUM)....................................................................... 68
3.9.2.2. Modal Transient Analysis/Harmonic Analysis.................................................................. 68
3.9.2.3. QR Damp Complex Modes Extraction............................................................................. 68
3.9.3. Generating and Using Multiple Loads in Mode-Superposition Analyses................................... 68
3.9.3.1. Understanding the Multiple Loads Method.................................................................... 68
3.9.3.2. Using the Multiple Loads Method.................................................................................. 69
3.9.4. Restarting a Modal Analysis.................................................................................................... 69
3.9.5. Enforced Motion Method for Mode-Superposition Transient and Harmonic Analyses............... 70
3.9.5.1. Understanding the Enforced Motion Method................................................................. 70
3.9.5.2. Using the Enforced Motion Method............................................................................... 70
3.9.5.3. Sample Input for Enforced Motion Mode-Superposition Analysis.................................... 70
3.9.6. Using Mode Selection............................................................................................................ 71
3.9.6.1. Mode Selection Based on a User Defined Array............................................................... 72
3.9.6.2. Mode Selection Based on Modal Effective Mass.............................................................. 73
3.9.6.3. Mode Selection Based on the Mode Coefficients............................................................ 74
3.9.6.4. Mode Selection Based on DDAM Procedure................................................................... 75
4. Harmonic Analysis ................................................................................................................................ 77
4.1. Uses for Harmonic Analysis............................................................................................................. 77
4.2. Commands Used in a Harmonic Analysis......................................................................................... 78
4.3.Two Solution Methods.................................................................................................................... 78
4.3.1.The Full Method..................................................................................................................... 78
4.3.2.The Mode-Superposition Method........................................................................................... 79
4.3.3. Restrictions Common to Both Methods................................................................................... 79
4.4. Performing a Harmonic Analysis...................................................................................................... 79
4.4.1. Full Harmonic Analysis........................................................................................................... 79
4.4.2. Build the Model...................................................................................................................... 79
4.4.2.1. Modeling Hints.............................................................................................................. 80
4.4.3. Apply Loads and Obtain the Solution...................................................................................... 80
4.4.3.1. Enter the ANSYS Solution Processor............................................................................... 80
4.4.3.2. Define the Analysis Type and Options............................................................................ 80
4.4.3.3. Apply Loads on the Model............................................................................................. 82
4.4.3.3.1. Applying Loads Using Commands......................................................................... 84
4.4.3.3.2. Applying Loads and Listing Loads Using the GUI.................................................... 85
4.4.3.4. Specify Load Step Options............................................................................................. 85
4.4.3.4.1. General Options.................................................................................................... 86
4.4.3.4.2. Dynamics Options ................................................................................................ 86
4.4.3.4.3. Output Controls.................................................................................................... 87
4.4.3.5. Save a Backup Copy of the Database to a Named File...................................................... 87
4.4.3.6. Start Solution Calculations............................................................................................. 87
4.4.3.7. Repeat for Additional Load Steps................................................................................... 88
4.4.3.8. Leave SOLUTION............................................................................................................ 88
4.4.4. Review the Results................................................................................................................. 88
4.4.4.1. Postprocessors .............................................................................................................. 88
4.4.4.2. Points to Remember...................................................................................................... 88
4.4.4.3. Using POST26................................................................................................................ 88
4.4.4.4. Using POST1.................................................................................................................. 89
4.5. Sample Harmonic Analysis (GUI Method)......................................................................................... 90
4.5.1. Problem Description.............................................................................................................. 90
4.5.2. Problem Specifications........................................................................................................... 90
4.5.3. Problem Diagram................................................................................................................... 91
4.5.3.1. Set the Analysis Title...................................................................................................... 91
4.5.3.2. Define the Element Types.............................................................................................. 91
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4.5.3.3. Define the Real Constants.............................................................................................. 91
4.5.3.4. Create the Nodes........................................................................................................... 92
4.5.3.5. Create the Spring Elements............................................................................................ 92
4.5.3.6. Create the Mass Elements.............................................................................................. 93
4.5.3.7. Specify the Analysis Type, MDOF, and Load Step Specifications........................................ 93
4.5.3.8. Define Loads and Boundary Conditions.......................................................................... 94
4.5.3.9. Solve the Model............................................................................................................ 94
4.5.3.10. Review the Results....................................................................................................... 94
4.5.3.11. Exit ANSYS................................................................................................................... 96
4.6. Example Harmonic Analysis (Command or Batch Method)............................................................... 96
4.7.Where to Find Other Examples........................................................................................................ 96
4.8. Mode-Superposition Harmonic Analysis.......................................................................................... 97
4.8.1. Obtain the Modal Solution..................................................................................................... 97
4.8.2. Obtain the Mode-Superposition Harmonic Solution................................................................ 98
4.8.3. Expand the Mode-Superposition Solution............................................................................. 100
4.8.3.1. Points to Remember.................................................................................................... 101
4.8.3.2. Expanding the Modes.................................................................................................. 101
4.8.4. Review the Results of the Expanded Solution........................................................................ 103
4.8.5. Sample Input ....................................................................................................................... 103
4.9. Additional Harmonic Analysis Details............................................................................................ 104
4.9.1. Prestressed Harmonic Analysis.............................................................................................. 104
4.9.1.1. Prestressed Full Harmonic Analysis............................................................................... 104
4.9.1.2. Prestressed Mode-Superposition Harmonic Analysis..................................................... 105
5.Transient Dynamic Analysis................................................................................................................ 107
5.1. Preparing for a Transient Dynamic Analysis.................................................................................... 107
5.2.Two Solution Methods.................................................................................................................. 108
5.2.1. Full Method.......................................................................................................................... 108
5.2.2. Mode-Superposition Method ............................................................................................... 109
5.3. Performing a Full Transient Dynamic Analysis................................................................................ 109
5.3.1. Build the Model.................................................................................................................... 110
5.3.1.1. Points to Remember.................................................................................................... 110
5.3.2. Establish Initial Conditions.................................................................................................... 110
5.3.3. Set Solution Controls............................................................................................................ 113
5.3.3.1. Access the Solution Controls Dialog Box....................................................................... 113
5.3.3.2. Using the Basic Tab...................................................................................................... 113
5.3.3.3. Using the Transient Tab................................................................................................ 114
5.3.3.4. Using the Remaining Solution Controls Tabs................................................................. 115
5.3.3.4.1. Set Additional Solution Options.......................................................................... 115
5.3.3.4.1.1. Prestress Effects.......................................................................................... 116
5.3.3.4.1.2. Damping Option........................................................................................ 116
5.3.3.4.1.3. Mass Matrix Formulation............................................................................ 116
5.3.4. Apply the Loads................................................................................................................... 117
5.3.5. Save the Load Configuration for the Current Load Step......................................................... 117
5.3.6. Repeat Steps 3-6 for Each Load Step..................................................................................... 117
5.3.7. Save a Backup Copy of the Database..................................................................................... 118
5.3.8. Start the Transient Solution.................................................................................................. 118
5.3.9. Exit the Solution Processor................................................................................................... 118
5.3.10. Review the Results.............................................................................................................. 118
5.3.10.1. Postprocessors........................................................................................................... 118
5.3.10.2. Points to Remember.................................................................................................. 118
5.3.10.3. Using POST26............................................................................................................ 118
5.3.10.4. Other Capabilities...................................................................................................... 119
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5.3.10.5. Using POST1.............................................................................................................. 119
5.3.11. Sample Input for a Full Transient Dynamic Analysis.............................................................. 119
5.4. Performing a Mode-Superposition Transient Dynamic Analysis...................................................... 120
5.4.1. Build the Model.................................................................................................................... 121
5.4.2. Obtain the Modal Solution................................................................................................... 121
5.4.3. Obtain the Mode-Superposition Transient Solution............................................................... 122
5.4.3.1. Obtaining the Solution................................................................................................ 122
5.4.4. Expand the Mode-Superposition Solution............................................................................. 126
5.4.4.1. Points to Remember.................................................................................................... 126
5.4.4.2. Expanding the Solution............................................................................................... 126
5.4.4.3. Reviewing the Results of the Expanded Solution.......................................................... 128
5.4.5. Review the Results............................................................................................................... 128
5.4.6. Sample Input for a Mode-Superposition Transient Dynamic Analysis..................................... 128
5.5. Performing a Prestressed Transient Dynamic Analysis.................................................................... 129
5.5.1. Prestressed Full Transient Dynamic Analysis.......................................................................... 129
5.5.2. Prestressed Mode-Superposition Transient Dynamic Analysis................................................ 130
5.6.Transient Dynamic Analysis Options.............................................................................................. 130
5.6.1. Guidelines for Integration Time Step..................................................................................... 130
5.6.2. Automatic Time Stepping..................................................................................................... 132
5.7.Where to Find Other Examples...................................................................................................... 133
6. Spectrum Analysis............................................................................................................................... 135
6.1. Understanding Spectrum Analysis................................................................................................. 135
6.1.1. Response Spectrum ............................................................................................................. 135
6.1.1.1. Single-Point Response Spectrum (SPRS)....................................................................... 136
6.1.1.2. Multi-Point Response Spectrum (MPRS)........................................................................ 136
6.1.2. Dynamic Design Analysis Method (DDAM)............................................................................ 136
6.1.3. Power Spectral Density......................................................................................................... 136
6.1.4. Deterministic vs. Probabilistic Analyses................................................................................. 137
6.2. Single-Point Response Spectrum (SPRS) Analysis Process............................................................... 137
6.2.1. Step 1: Build the Model......................................................................................................... 137
6.2.1.1. Hints and Recommendations....................................................................................... 137
6.2.2. Step 2: Obtain the Modal Solution......................................................................................... 137
6.2.3. Step 3: Obtain the Spectrum Solution................................................................................... 138
6.2.4. Step 4: Review the Results..................................................................................................... 143
6.2.5. Running Multiple Spectrum Analyses.................................................................................... 145
6.3. Example Spectrum Analysis (GUI Method)..................................................................................... 146
6.3.1. Problem Description............................................................................................................. 146
6.3.2. Problem Specifications......................................................................................................... 146
6.3.3. Problem Sketch.................................................................................................................... 147
6.3.4. Procedure ............................................................................................................................ 147
6.3.4.1. Set the Analysis Title.................................................................................................... 147
6.3.4.2. Define the Element Type.............................................................................................. 147
6.3.4.3. Define the Cross-Section Area...................................................................................... 148
6.3.4.4. Define Material Properties........................................................................................... 148
6.3.4.5. Define Keypoints and Line........................................................................................... 148
6.3.4.6. Set Global Element Density and Mesh Line................................................................... 149
6.3.4.7. Set Boundary Conditions............................................................................................. 149
6.3.4.8. Specify Analysis Type and Options............................................................................... 150
6.3.4.9. Solve the Modal Analysis.............................................................................................. 150
6.3.4.10. Set Up the Spectrum Analysis..................................................................................... 150
6.3.4.11. Define Spectrum Value vs. Frequency Table................................................................ 150
6.3.4.12. Select Mode Combination Method............................................................................. 151
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6.3.4.13. Solve Spectrum Analysis............................................................................................ 151
6.3.4.14. Postprocessing: Print Out Nodal, Element, and Reaction Solutions............................... 151
6.3.4.15. Exit Mechanical APDL................................................................................................ 151
6.4. Example Spectrum Analysis (Command or Batch Method)............................................................. 152
6.4.1. Single Point Response Spectrum Analysis on a Beam Structure.............................................. 152
6.4.2. Single Point Response Spectrum Analysis on a Piping Structure with Excitation along X,Y, and
Z Directions.................................................................................................................................. 153
6.4.3. Single Point Response Spectrum Analysis on a Piping Structure with Excitation along X,Y, and
Z Directions Separately by Reusing the Existing Mode File............................................................. 155
6.5.Where to Find Other Examples...................................................................................................... 158
6.6. Performing a Random Vibration (PSD) Analysis.............................................................................. 159
6.6.1. Obtain the PSD Solution....................................................................................................... 159
6.6.2. Combine the Modes............................................................................................................. 163
6.6.3. Review the Results............................................................................................................... 164
6.6.3.1. Reviewing the Results in POST1................................................................................... 165
6.6.3.1.1. Read the Desired Set of Results into the Database................................................ 165
6.6.3.1.2. Display the Results.............................................................................................. 166
6.6.3.2. Calculating Response PSDs in POST26.......................................................................... 166
6.6.3.3. Calculating Covariance in POST26................................................................................ 167
6.6.4. Sample Input ....................................................................................................................... 167
6.7. DDAM Spectrum Analysis Process................................................................................................. 168
6.7.1. Step 3: Obtain the Spectrum Solution................................................................................... 169
6.7.2. Step 4: Review the Results..................................................................................................... 172
6.7.3. Sample Input ....................................................................................................................... 172
6.8. Performing a Multi-Point Response Spectrum (MPRS) Analysis....................................................... 173
6.8.1. Step 4: Obtain the Spectrum Solution................................................................................... 173
6.8.2. Step 5: Combine the Modes.................................................................................................. 176
6.8.3. Step 6: Review the Results..................................................................................................... 176
6.9. Example Multi-Point Response Spectrum (MPRS) Analysis (Command or Batch Method)................. 177
6.9.1. Problem Description............................................................................................................. 177
6.9.2. Problem Specifications......................................................................................................... 177
6.9.3. Problem Sketch.................................................................................................................... 177
6.9.4. Command Listing................................................................................................................. 177
7. Buckling Analysis................................................................................................................................ 179
7.1.Types of Buckling Analyses............................................................................................................ 179
7.1.1. Nonlinear Buckling Analysis.................................................................................................. 179
7.1.2. Eigenvalue Buckling Analysis................................................................................................ 179
7.2. Commands Used in a Buckling Analysis......................................................................................... 180
7.3. Performing a Nonlinear Buckling Analysis...................................................................................... 180
7.3.1. Applying Load Increments.................................................................................................... 180
7.3.2. Automatic Time Stepping..................................................................................................... 180
7.3.3. Unconverged Solution.......................................................................................................... 181
7.3.4. Hints and Tips for Performing a Nonlinear Buckling Analysis.................................................. 181
7.4. Performing a Post-Buckling Analysis.............................................................................................. 181
7.5. Procedure for Eigenvalue Buckling Analysis................................................................................... 182
7.5.1. Build the Model.................................................................................................................... 182
7.5.1.1. Points to Remember.................................................................................................... 182
7.5.2. Obtain the Static Solution..................................................................................................... 182
7.5.3. Obtain the Eigenvalue Buckling Solution.............................................................................. 183
7.5.4. Review the Results............................................................................................................... 186
7.6. Sample Buckling Analysis (GUI Method)......................................................................................... 186
7.6.1. Problem Description............................................................................................................. 186
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Structural Analysis Guide
7.6.2. Problem Specifications......................................................................................................... 186
7.6.3. Problem Sketch.................................................................................................................... 187
7.6.3.1. Set the Analysis Title.................................................................................................... 187
7.6.3.2. Define the Element Type.............................................................................................. 187
7.6.3.3. Define the Real Constants and Material Properties........................................................ 188
7.6.3.4. Define Nodes and Elements......................................................................................... 188
7.6.3.5. Define the Boundary Conditions.................................................................................. 189
7.6.3.6. Solve the Static Analysis............................................................................................... 190
7.6.3.7. Solve the Buckling Analysis.......................................................................................... 190
7.6.3.8. Review the Results....................................................................................................... 191
7.6.3.9. Exit ANSYS................................................................................................................... 191
7.7. Sample Buckling Analysis (Command or Batch Method)................................................................. 191
7.8.Where to Find Other Examples...................................................................................................... 192
8. Nonlinear Structural Analysis............................................................................................................. 193
8.1. Causes of Nonlinear Behavior........................................................................................................ 194
8.1.1. Changing Status (Including Contact)..................................................................................... 194
8.1.2. Geometric Nonlinearities...................................................................................................... 194
8.1.3. Material Nonlinearities ......................................................................................................... 195
8.2. Understanding Nonlinear Analyses................................................................................................ 195
8.2.1. Conservative vs. Nonconservative Behavior; Path Dependency.............................................. 197
8.2.2. Substeps.............................................................................................................................. 198
8.2.3. Load Direction in a Large-Deflection Analysis........................................................................ 198
8.2.4. Rotations in a Large-Deflection Analysis................................................................................ 199
8.2.5. Nonlinear Transient Analyses................................................................................................ 200
8.3. Using Geometric Nonlinearities..................................................................................................... 200
8.3.1. Stress-Strain......................................................................................................................... 200
8.3.1.1. Large Deflections with Small Strain.............................................................................. 200
8.3.2. Stress Stiffening ................................................................................................................... 200
8.4. Modeling Material Nonlinearities................................................................................................... 201
8.4.1. Nonlinear Materials.............................................................................................................. 201
8.4.1.1. Plasticity...................................................................................................................... 202
8.4.1.2. Hyperelasticity Material Model..................................................................................... 202
8.4.1.2.1. Mooney-Rivlin Hyperelastic Option (TB,HYPER,,,,MOONEY).................................. 203
8.4.1.2.2. Ogden Hyperelastic Option (TB,HYPER,,,,OGDEN)................................................. 203
8.4.1.2.3. Neo-Hookean Hyperelastic Option (TB,HYPER,,,,NEO)........................................... 204
8.4.1.2.4. Polynomial Form Hyperelastic Option (TB,HYPER,,,,POLY)..................................... 204
8.4.1.2.5. Arruda-Boyce Hyperelastic Option (TB,HYPER,,,,BOYCE)........................................ 204
8.4.1.2.6. Gent Hyperelastic Option (TB,HYPER,,,,GENT)....................................................... 205
8.4.1.2.7.Yeoh Hyperelastic Option (TB,HYPER,,,,YEOH)....................................................... 205
8.4.1.2.8. Blatz-Ko Foam Hyperelastic Option (TB,HYPER,,,,BLATZ)....................................... 205
8.4.1.2.9. Ogden Compressible Foam Hyperelastic Option (TB,HYPER,,,,FOAM).................... 205
8.4.1.2.10. Response Function Hyperelastic Option (TB,HYPER,,,,RESPONSE)........................ 206
8.4.1.2.11. User-Defined Hyperelastic Option (TB,HYPER,,,,USER)......................................... 208
8.4.1.3. Bergstrom-Boyce Hyperviscoelastic Material Model...................................................... 208
8.4.1.4. Mullins Effect Material Model....................................................................................... 209
8.4.1.5. Anisotropic Hyperelasticity Material Model.................................................................. 210
8.4.1.6. Creep Material Model.................................................................................................. 210
8.4.1.6.1. Implicit Creep Procedure..................................................................................... 211
8.4.1.6.2. Explicit Creep Procedure..................................................................................... 213
8.4.1.7. Shape Memory Alloy Material Model............................................................................ 213
8.4.1.8.Viscoplasticity.............................................................................................................. 213
8.4.1.9.Viscoelasticity.............................................................................................................. 215
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