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ANSYS Mechanical APDL Structural Analysis Guide.pdf

522 Pages · 2013 · 6.33 MB · English

  • ANSYS Mechanical APDL Structural Analysis Guide.pdf

    ANSYS Mechanical APDL Structural Analysis


    Guide


    ANSYS, Inc. Release 15.0


    Southpointe November 2013


    275 Technology Drive


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    Published in the U.S.A. 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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    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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