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ANSYS Mechanical APDL Structural Analysis Guide PDF

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ANSYS Mechanical APDL Structural Analysis Guide ANSYS, Inc. Release 15.0 Southpointe November 2013 275 Technology Drive Canonsburg, PA 15317 ANSYS, Inc. is [email protected] certified to ISO 9001:2008. http://www.ansys.com (T) 724-746-3304 (F) 724-514-9494 Copyright and Trademark Information © 2013 SAS IP, Inc. All rights reserved. Unauthorized use, distribution or duplication is prohibited. ANSYS, ANSYS Workbench, Ansoft, AUTODYN, EKM, Engineering Knowledge Manager, CFX, FLUENT, HFSS and any and all ANSYS, Inc. brand, product, service and feature names, logos and slogans are registered trademarks or trademarks of ANSYS, Inc. or its subsidiaries in the United States or other countries. ICEM CFD is a trademark used by ANSYS, Inc. under license. CFX is a trademark of Sony Corporation in Japan. All other brand, product, service and feature names or trademarks are the property of their respective owners. Disclaimer Notice THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFID- ENTIAL AND PROPRIETARY PRODUCTS OF ANSYS, INC., ITS SUBSIDIARIES, OR LICENSORS.The software products and documentation are furnished by ANSYS, Inc., its subsidiaries, or affiliates under a software license agreement that contains provisions concerning non-disclosure, copying, length and nature of use, compliance with exporting laws, warranties, disclaimers, limitations of liability, and remedies, and other provisions.The software products and documentation may be used, disclosed, transferred, or copied only in accordance with the terms and conditions of that software license agreement. ANSYS, Inc. is certified to ISO 9001:2008. U.S. Government Rights For U.S. Government users, except as specifically granted by the ANSYS, Inc. software license agreement, the use, duplication, or disclosure by the United States Government is subject to restrictions stated in the ANSYS, Inc. software license agreement and FAR 12.212 (for non-DOD licenses). Third-Party Software See the legal information in the product help files for the complete Legal Notice for ANSYS proprietary software and third-party software. If you are unable to access the Legal Notice, please contact ANSYS, Inc. 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 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates. iii Structural Analysis Guide 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 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information iv of ANSYS, Inc. and its subsidiaries and affiliates. Structural Analysis Guide 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 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates. v Structural Analysis Guide 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 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information vi of ANSYS, Inc. and its subsidiaries and affiliates. Structural Analysis Guide 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 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates. vii Structural Analysis Guide 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 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information viii of ANSYS, Inc. and its subsidiaries and affiliates. Structural Analysis Guide 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 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates. ix 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 Release 15.0 - © SAS IP, Inc. 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