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ANSYS Mechanical APDL Verification Manual (1).pdf

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ANSYS Mechanical APDL Verification Manual ANSYS, Inc. Southpointe 275 Technology Drive Canonsburg, PA 15317 ansysinfo@ansys.com http://www.ansys.com (T) 724-746-3304 (F) 724-514-9494 Release 15.0 November 2013 ANSYS, Inc. is certified to ISO 9001:2008. 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 an
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  ANSYS Mechanical APDL Verification Manual Release 15.0ANSYS, Inc.November 2013Southpointe275 Technology DriveCanonsburg, PA 15317 ANSYS, Inc. iscertified to ISO9001:2008. ansysinfo@ansys.comhttp://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 anyand all ANSYS, Inc. brand, product, service and feature names, logos and slogans are registered trademarks ortrademarks of ANSYS, Inc. or its subsidiaries in the United States or other countries. ICEM CFD is a trademark usedby ANSYS, Inc. under license. CFX is a trademark of Sony Corporation in Japan. All other brand, product, serviceand 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 productsand documentation are furnished by ANSYS, Inc., its subsidiaries, or affiliates under a software license agreementthat contains provisions concerning non-disclosure, copying, length and nature of use, compliance with exportinglaws, warranties, disclaimers, limitations of liability, and remedies, and other provisions.The software productsand documentation may be used, disclosed, transferred, or copied only in accordance with the terms and conditionsof 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 softwareand 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 I.Verification Test Case Descriptions ..........................................................................................................1 1. Introduction ......................................................................................................................................31.1. Program Overview......................................................................................................................41.2. Program Verification...................................................................................................................41.3. Finding Test Cases of Interest......................................................................................................51.4. Accessing Test Case Inputs..........................................................................................................51.5.Verification Manual Versus Other Manuals...................................................................................51.6.Verification Manual Contents......................................................................................................51.7. Expected Results........................................................................................................................61.8.Test Case Selection and Method of Solution................................................................................61.9. Numerical Comparisons..............................................................................................................61.10. References................................................................................................................................71.11.Test Case Format.......................................................................................................................71.12. Symbols and Nomenclature......................................................................................................81.13. Memory Requirements and Run Times......................................................................................81.14. Abbreviation and Symbol List....................................................................................................81.15. Units Abbreviation List............................................................................................................101.16. Index by Element Number.......................................................................................................111.VM1: Statically Indeterminate Reaction Force Analysis........................................................................252.VM2: Beam Stresses and Deflections...................................................................................................273.VM3:Thermally Loaded Support Structure..........................................................................................294.VM4: Deflection of a Hinged Support.................................................................................................315.VM5: Laterally Loaded Tapered Support Structure...............................................................................336.VM6: Pinched Cylinder.......................................................................................................................357.VM7: Plastic Compression of a Pipe Assembly.....................................................................................378.VM8: Parametric Calculation of Point-to-Point Distances.....................................................................419.VM9: Large Lateral Deflection of Unequal Stiffness Springs.................................................................4310.VM10: Bending of a Tee-Shaped Beam..............................................................................................4511.VM11: Residual Stress Problem.........................................................................................................4712.VM12: Combined Bending and Torsion.............................................................................................4913.VM13: Cylindrical Shell Under Pressure.............................................................................................5114.VM14: Large Deflection Eccentric Compression of a Column.............................................................5315.VM15: Bending of a Circular Plate Using Axisymmetric Elements.......................................................5516.VM16: Bending of a Solid Beam (Plane Elements)..............................................................................5917.VM17: Snap-Through Buckling of a Hinged Shell...............................................................................6118.VM18: Out-of-Plane Bending of a Curved Bar....................................................................................6519.VM19: Random Vibration Analysis of a Deep Simply-Supported Beam...............................................6720.VM20: Cylindrical Membrane Under Pressure....................................................................................6921.VM21:Tie Rod with Lateral Loading..................................................................................................7122.VM22: Small Deflection of a Belleville Spring.....................................................................................7323.VM23:Thermal-structural Contact of Two Bodies..............................................................................7524.VM24: Plastic Hinge in a Rectangular Beam.......................................................................................7725.VM25: Stresses in a Long Cylinder.....................................................................................................7926.VM26: Large Deflection of a Cantilever.............................................................................................8327.VM27:Thermal Expansion to Close a Gap..........................................................................................8528.VM28:Transient Heat Transfer in an Infinite Slab................................................................................8729.VM29: Friction on a Support Block ....................................................................................................8930.VM30: Solid Model of Surface Fillet...................................................................................................9131.VM31: Cable Supporting Hanging Loads...........................................................................................9532.VM32:Thermal Stresses in a Long Cylinder........................................................................................97 iii Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates.  33.VM33:Transient Thermal Stress in a Cylinder.....................................................................................9934.VM34: Bending of a Tapered Plate (Beam).......................................................................................10335.VM35: Bimetallic Layered Cantilever Plate with Thermal Loading.....................................................10736.VM36: Limit Moment Analysis.........................................................................................................10937.VM37: Elongation of a Solid Bar......................................................................................................11138.VM38: Internal Pressure Loading of a Thick-Walled Cylinder.............................................................11539.VM39: Bending of a Circular Plate with a Center Hole......................................................................11740.VM40: Large Deflection and Rotation of a Beam Pinned at One End.................................................12141.VM41: Small Deflection of a Rigid Beam..........................................................................................12342.VM42: Barrel Vault Roof Under Self Weight......................................................................................12543.VM43: Bending of an Axisymmetric Thick Pipe................................................................................12744.VM44: Bending of an Axisymmetric Thin Pipe..................................................................................12945.VM45: Natural Frequency of a Spring-Mass System.........................................................................13146.VM46: 2-D End Notched Flexure Problem .......................................................................................13347.VM47:Torsional Frequency of a Suspended Disk .............................................................................13548.VM48: Natural Frequency of a Motor-Generator..............................................................................13749.VM49: Electrostatic Field Analysis of Quadpole Wires......................................................................13950.VM50: Fundamental Frequency of a Simply Supported Beam..........................................................14151.VM51: Electrostatic Forces Between Charged Spheres.....................................................................14352.VM52: Automobile Suspension System Vibration............................................................................14953.VM53:Vibration of a String Under Tension......................................................................................15154.VM54:Vibration of a Rotating Cantilever Blade................................................................................15355.VM55:Vibration of a Stretched Circular Membrane.........................................................................15556.VM56: Hyperelastic Thick Cylinder Under Internal Pressure..............................................................15757.VM57:Torsional Frequencies of a Drill Pipe......................................................................................16158.VM58: Centerline Temperature of a Heat Generating Wire...............................................................16359.VM59: Lateral Vibration of an Axially-loaded Bar..............................................................................16560.VM60: Natural Frequency of a Cross-ply Laminated Shell.................................................................16761.VM61: Longitudinal Vibration of a Free-free Rod..............................................................................16962.VM62:Vibration of a Wedge............................................................................................................17163.VM63: Static Hertz Contact Problem...............................................................................................17564.VM64:Thermal Expansion to Close a Gap at a Rigid Surface.............................................................17765.VM65:Transient Response of a Ball Impacting a Flexible Surface......................................................17966.VM66:Vibration of a Flat Plate........................................................................................................18167.VM67: Radial Vibrations of a Circular Ring.......................................................................................18368.VM68: PSD Response of a Two DOF Spring-mass System.................................................................18569.VM69: Seismic Response................................................................................................................18770.VM70: Seismic Response of a Beam Structure..................................................................................18971.VM71:Transient Response of a Spring-Mass-Damper System...........................................................19172.VM72: Logarithmic Decrement.......................................................................................................19573.VM73: Free Vibration with Coulomb Damping.................................................................................19974.VM74:Transient Response to an Impulsive Excitation......................................................................20375.VM75:Transient Response to a Step Excitation................................................................................20576.VM76: Harmonic Response of a Guitar String..................................................................................20777.VM77:Transient Response to a Constant Force................................................................................20978.VM78:Transverse Shear Stresses in a Cantilever Beam.....................................................................21179.VM79:Transient Response of a Bilinear Spring Assembly.................................................................21380.VM80: Plastic Response to a Suddenly Applied Constant Force........................................................21581.VM81:Transient Response of a Drop Container...............................................................................21982.VM82: Simply Supported Laminated Plate Under Pressure..............................................................22183.VM83: Impact of a Block on a Spring Scale......................................................................................22384.VM84: Displacement Propagation along a Bar with Free Ends..........................................................227 Release 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationof ANSYS, Inc. and its subsidiaries and affiliates. iv Mechanical APDL Verification Manual
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