NE/Nastran Verification Manual
Autodesk Inventor Nastran 2020Verification Manual
Verification Manual 2019 Autodesk, Inc. All rights reserved.Autodesk Inventor Nastran 2020Except as otherwise permitted by Autodesk, Inc., this publication, or parts thereof, may not be reproduced in any form, by anymethod, for any purpose.Certain materials included in this publication are reprinted with the permission of the copyright holder.TrademarksThe following are registered trademarks or trademarks of Autodesk, Inc., and/or its subsidiaries and/or affiliates in the USA and other countries:123D, 3ds Max, Alias, ATC, AutoCAD LT, AutoCAD, Autodesk, the Autodesk logo, Autodesk 123D, Autodesk Homestyler, Autodesk Inventor,Autodesk MapGuide, Autodesk Streamline, AutoLISP, AutoSketch, AutoSnap, AutoTrack, Backburner, Backdraft, Beast, BIM 360, Burn,Buzzsaw, CADmep, CAiCE, CAMduct, Civil 3D, Combustion, Communication Specification, Configurator 360, Constructware, Content Explorer,Creative Bridge, Dancing Baby (image), DesignCenter, DesignKids, DesignStudio, Discreet, DWF, DWG, DWG (design/logo), DWG Extreme,DWG TrueConvert, DWG TrueView, DWGX, DXF, Ecotect, Ember, ESTmep, Evolver, FABmep, Face Robot, FBX, Fempro, Fire, Flame, Flare,Flint, ForceEffect, FormIt, Freewheel, Fusion 360, Glue, Green Building Studio, Heidi, Homestyler, HumanIK, i-drop, ImageModeler, Incinerator,Inferno, InfraWorks, InfraWorks 360, Instructables, Instructables (stylized robot design/logo), Inventor, Inventor HSM, Inventor LT, Lustre, Maya,Maya LT, MIMI, Mockup 360, Moldflow Plastics Advisers, Moldflow Plastics Insight, Moldflow, Moondust, MotionBuilder, Movimento, MPA(design/logo), MPA, MPI (design/logo), MPX (design/logo), MPX, Mudbox, Navisworks, ObjectARX, ObjectDBX, Opticore, Pixlr, Pixlr-o-matic,Productstream, Publisher 360, RasterDWG, RealDWG, ReCap, ReCap 360, Remote, Revit LT, Revit, RiverCAD, Robot, Scaleform, Showcase,Showcase 360, SketchBook, Smoke, Socialcam, Softimage, Sparks, SteeringWheels, Stitcher, Stone, StormNET, TinkerBox, ToolClip,Topobase, Toxik, TrustedDWG, T-Splines, ViewCube, Visual LISP, Visual, VRED, Wire, Wiretap, WiretapCentral, XSI.NASTRAN is a registered trademark of the National Aeronautics Space Administration. All other brand names, product names or trademarksbelong to their respective holders.DisclaimerTHIS PUBLICATION AND THE INFORMATION CONTAINED HEREIN IS MADE AVAILABLE BY AUTODESK, INC. “AS IS.”AUTODESK, INC. DISCLAIMS ALL WARRANTIES, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TOANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE REGARDING THESEMATERIALS.Autodesk Inventor Nastran 2020ii
Verification ManualTABLE OF CONTENTS1. Introduction . 71.1 Model Files Location. 72. Linear Statics Verification Using Theoretical Solutions. 82.1 Nodal Loads on a Cantilever Beam . 92.2 Axial Distributed Load on a Linear Beam. 112.3 Distributed Loads on a Cantilever Beam. 132.4 Moment Load on a Cantilever Beam . 152.5 Thermal Strain, Displacement, and Stress on a Heated Beam . 172.6 Uniformly Distributed Load on a Linear Beam . 192.7 Membrane Loads on a Plate . 212.8 Thin Wall Cylinder in Pure Tension. 232.9 Thin Shell Beam Wall in Pure Bending . 252.10 Strain Energy of a Truss. 272.11 Flat Square Plate . 292.12 The Raasch Challenge Problem for Shell Elements . 312.13 Twisted Beam Static Load . 342.14 Plane Frame with Beam Span Loads . 362.15 Thermal Gradient Loads on a Beam . 382.16 Statically Indeterminate Reaction Force Analysis . 402.17 Beam Stresses and Deflection . 422.18 Laterally Loaded Tapered Support Structure Case 1. 442.19 Laterally Loaded Tapered Support Structure Case 2. 462.20 Bending of a Tee-Shaped Beam . 482.21 Bending of a Circular Plate . 502.22 Beam on Elastic Foundation. 522.23 Thick Walled Cylinder Plain Strain . 542.24 Scordelis-Lo Roof . 562.25 Out-of-Plane Bending of a Curved Bar . 582.26 Deflection of Hinged Support . 602.27 Thermal Stresses in a Plate . 622.28 Bending of a Tapered Plate. 642.29 Bending of a Tapered Beam . 662.30 Bending of a Curved Thick Beam. 682.31 Truss Reaction One . 702.32 Truss Reaction Two . 722.33 Fixed Ended Beam Un-symmetric Tapered Member . 742.34 Straight Cantilever Beam Using Solids . 762.35 Curved Beam Using Solids . 782.36 Cantilever Modeled with Variable Thickness Shells and Membranes . 802.37 Cantilever Modeled with Variable Thickness Solids . 822.38 Elongation of a Solid Bar . 842.39 Thin Shell Beam in Pure Bending . 862.40 Static Analysis of Thermal Loading . 88Autodesk Inventor Nastran 2020iii
Verification Manual2.41 Static Analysis of Pressure Loading . 903. Linear Statics Verification Using Standard NAFEMS Benchmarks . 923.1 Warped Element Test Cases . 933.1.1 Cylindrical Shell Patch . 933.1.2 Hemisphere-Point Loads . 963.2 Laminate Plate Element Test Cases . 983.2.1 Laminated Strip. 983.2.2 Wrapped Thick Cylinder . 1003.3 Shell Element Test Cases . 1023.3.1 Elliptic Membrane . 1023.3.2 Z-Section Cantilever . 1043.3.3 Skew Plate Under Normal Pressure. 1064. Normal Modes/Eigenvalue Verification Using Theoretical Solutions . 1084.1 Two Degree of Freedom Undamped Free Vibration – Principle Modes . 1094.2 Three Degree of Freedom Torsional System . 1114.3 Cantilever Plate Eigenvalue Problem . 1134.4 Bathe and Wilson Frame Eigenvalue Problem . 1154.5 Natural Frequency of a Cantilevered Mass . 1174.6 Fundamental Frequency of a Simply Supported Beam . 1194.7 Natural Frequencies of a Cantilever Beam. 1214.8 Vibration of a String Under Tension . 1234.9 Vibration of a Wedge . 1255. Normal Modes/Eigenvalue Verification Using Standard NAFEMS Benchmarks . 1275.1 Bar Element Test Cases . 1285.1.1 Pin-ended Cross – In-plane Vibration . 1285.1.2 Free Square Frame – In-plane Vibration . 1305.1.3 Cantilever with Off-center Point Masses . 1325.1.4 Deep Simply-Supported Beam . 1345.1.5 Pin-ended Double Cross – In-plane Vibration . 1365.1.6 Circular Ring – In-plane and Out-of-plane Vibration . 1385.2 Plate Element Test Cases . 1405.2.1 Thin Square Cantilevered Plate – Symmetric Modes . 1405.2.2 Thin Square Cantilevered Plate – Anti-symmetric Modes . 1435.2.3 Free Thin Square Plate . 1455.2.4 Simply – Supported Thin Square Plate . 1475.2.5 Simply – Supported Thin Annular Plate . 1495.2.6 Clamped Thin Rhombic Plate . 1515.2.7 Simply – Supported Thick Square Plate, Test A . 1535.2.8 Simply – Supported Thick Square Plate, Test B . 1555.2.9 Clamped Thick Rhombic Plate . 1575.2.10 Simply – Supported Thick Annular Plate . 1595.2.11 Cantilevered Square Membrane . 1615.2.12 Cantilevered Tapered Membrane. 1635.2.13 Free Annular Membrane. 1665.3 Axisymmetric Solid and Solid Element Test Cases . 1685.3.1 Simply – Supported “Solid” Square Plate . 1686. Verification Test Cases from the Société Francaise des Mechaniciens . 1716.1 Mechanical Structures – Linear Statics Analysis with Bar or Rod Elements . 1726.1.1 Short Beam on Two Articulated Supports . 1726.1.2 Clamped Beams Linked by a Rigid Element . 1746.1.3 Plane Bending Load on a Thin Arc. 1766.1.4 Articulated Plane Truss . 178Autodesk Inventor Nastran 2020iv
Verification Manual6.2 Mechanical Structures – Linear Statics Analysis with Plate Elements. 1806.2.1 Plane Shear and Bending Load on a Plate . 1806.2.2 Uniformly Distributed Load on a Circular Plate . 1826.2.3 Torque Loading on a Square Tube . 1846.2.4 Cylindrical Shell with Internal Pressure . 1866.2.5 Gravity Loading on a Thin Wall Cylinder . 1886.2.6 Pinched Cylindrical Shell . 1906.2.7 Infinite Plate with a Circular Hole . 1926.3 Mechanical Structures – Linear Statics Analysis with Solid Elements . 1946.3.1 Thick Plate Clamped at Edges . 1946.4 Mechanical Structures – Normal Modes/Eigenvalue Analysis . 1976.4.1 Cantilever Beam with a Variable Rectangular Section . 1976.4.2 Thin Circular Ring Clamped at Two Points . 1996.4.3 Vibration Modes of a Thin Pipe Elbow . 2016.4.4 Thin Square Plate (Clamped or Free) . 2046.4.5 Simply – Supported Rectangular Plate . 2076.4.6 Bending of a Symmetric Truss . 2096.4.7 Hovgaard’s Problem – Pipes with Flexible Elbows . 2116.4.8 Rectangular Plates . 2136.5 Stationary Thermal Tests – Steady-State Heat Transfer Analysis . 2156.5.1 L-Plate. 2157. Buckling Verification Using Theoretical Solutions . 2177.1 Buckling of a Thin Walled Cylinder . 2187.2 Buckling of a Bar with Hinged Ends . 2207.3 Buckling of a Bar with Hinged Ends Using Plates . 2227.4 Buckling of a Bar with Hinged Ends Using Solids . 2247.5 Buckling of a Rectangular Plate Under Concentrated Center Loads . 2267.6 Buckling of a Rectangular Plate Under End Uniform Load . 2288. Dynamics Verification Using Standard NAFEMS Benchmarks. 2308.1 Transient Forced Vibration Response – Deep Simply Supported Beam . 2318.2 Periodic Forced Vibration Response – Deep Simply Supported Beam . 2338.3 Modal Transient Forced Vibration Response – Simply Supported Plate . 2368.4 Harmonic Forced Vibration Response – Simply Supported Plate . 2388.5 Random Forced Vibration Response – Simply Supported Plate . 2408.6 Direct Transient Forced Vibration Response – Simply Supported Plate. 2428.7 Direct Frequency Response – Simply Supported Plate . 2459. Dynamics Verification Using Theoretical Solutions . 2489.1 Seismic Response of a Beam Structure . 2499.2 Cantilever Beam Subjected to Sine Plus Tip Load. 2519.3 Simply Supported Beam, Ramped Nodal Forcing Function, Transient Forced Vibration . 2549.4 Tower Structure Under a Harmonic Excitation Force . 2569.5 Simply Supported Beam Subjected to a Traveling Dynamic Load . 25910. Nonlinear Static Verification Using Theoretical Solutions . 26210.1 Nonlinear Cable Tension . 26310.2 Cable Supporting Hanging Loads . 26510.3 Ten Story Plane Frame . 26710.4 Straight Cantilever with Axial End Point Load . 26910.5 Residual Stress Problem . 27111. Nonlinear Static Verification Using Standard NAFEMS Benchmarks . 273Autodesk Inventor Nastran 2020v
Verification Manual11.1 Elastic Large Deformation Response of a Z-shaped Cantilever Under an End Load . 27411.2 Straight Cantilever with End Moment . 27611.3 Lee’s Frame Buckling Problem . 27812. Nonlinear Dynamic Verification Using Theoretical Solutions . 28012.1 Impact Load on a Rod by a Mass at a Constant Velocity . 28112.2 Impact of a Block on a Spring Scale . 284APPENDIX A – REFERENCES . 286Autodesk Inventor Nastran 2020vi
Verification ManualIntroduction1. IntroductionThis guide contains verification test cases for the Autodesk Inventor Nastran Finite Element Analysissolver. These test cases verify the functionality of Autodesk Inventor Nastran and encompass thedifferent analysis types using theoretical and benchmark solutions from well-known engineering testcases. Each test case contains all test data needed to reproduce the given results. This guide containstest cases for: Linear Statics verification using theoretical solutionsNormal Modes/Eigenvalue verification using theoretical solutionsNormal Modes/Eigenvalue verification using standard NAFEMS benchmarksVerification Test Cases from the Société Francaise des Mechaniciens1.1 Model Files LocationAll the Autodesk Inventor Nastran model files (.nas) used for these test cases are located in this folder:C:\Users\Public\Public Documents\Autodesk\Inventor Nastran 2020\Example Files\en-us\VerificationModelsAutodesk Inventor Nastran 20207
Verification ManualLinear Statics Verification Using Theoretical Solutions2. Linear Statics Verification Using Theoretical SolutionsThe purpose of these linear static test cases is to verify the functionality of Autodesk Inventor Nastranusing theoretical solutions of well-known engineering linear static problems. The test cases are basic inform and have closed-form theoretical solutions.The theoretical solutions given in these examples are from reputable engineering texts. For each case, aspecific reference is cited. All theoretical reference texts are listed in Appendix A.The finite element method is very broad in nature and is by no means exhausted by the verification testsprovided in this manual. These examples, rather, represent basic, common and well-known applicationsof the finite element method.For most cases, discrepancies between Autodesk Inventor Nastran computed and theoretical results areminor and can be considered negligible. To produce exact results, for most cases, a larger number ofelements would need to be used. Element quantity is chosen to achieve reasonable engineeringaccuracy in a reasonable amount of time.Autodesk Inventor Nastran 20208
Verification ManualNodal Loads on a Cantilever Beam2.1 Nodal Loads on a Cantilever BeamProblem DescriptionFigure 1 shows the cantilever beam with a load acting on the free end. A static analysis is performed onthe model. Beam deflection at the free end of the beam, and shear stress at the constrained end of thebeam are determined. All dimensions are in inches.Py480.xzFigure 1. Cantilever Beam with Nodal LoadAutodesk Inventor Nastran Analysis Model Filename vm2 1.nasModel DataFinite Element Modeling Mesh (4 x 1): 5 nodes, 4 bar elementsUnitsinch/pound/secondModel GeometryLength: L 480 inCross Sectional PropertiesArea: A 900 in2Square Cross Section (30 in x 30 in)Moment of Inertia: Iy Iz 67500 in4Material PropertiesYoung’s Modulus: E 30.0 E 6 psiBoundary ConditionsOne end of the beam is constrained in all translations and rotations. A load P 50,000 lb force in thenegative Y-direction is set at the free end of the beam.Autodesk Inventor Nastran 20209
Verification ManualNodal Loads on a Cantilever BeamSolution TypeStaticComparison of ResultsThe tabular results are given in Table 1.Table 1. or (%)Beam Constrained End Z Shear Force Stress (psi)5333.35333.30.0Beam Free End T2 Translation (in)0.9130*0.91300.0*Note: The original theoretical value of 0.9102 neglects the shear deformation. The value for sheardeformation is calculated below and added to the original theoretical value.Post ProcessingShear Deformation VLAGwhere: V Shear Load, L Length of the beam, A Shear area 0.8333 x cross section area, andG modulus of rigidityShear deformation 0.0028Adding the shear deformation to the theory, T2 Translation (Theory value shear deformation)T2 Translation (0.9102 0.0028) 0.9130 inReferences1. Beer and Johnston, Mechanics of Materials. New York: McGraw-Hill, Inc., 1992. p.716.Autodesk Inventor Nastran 202010
Verification ManualAxial Distributed Load on a Linear Beam2.2 Axial Distributed Load on a Linear BeamProblem DescriptionFigure 1 shows the model of the linear beam. A static analysis is performed using an axially distributedload. The beam axial stress at the constrained end (A), deflection at the free end (B), and the constraintforce at the constrained end of the beam are determined. All dimensions are in inches.ABy300xzFigure 1. Linear Beam with Axial Distributed LoadAutodesk Inventor Nastran Analysis Model Filename vm2 2.nasModel DataFinite Element Modeling Mesh (30 x 1): 31 nodes, 30 bar elementsUnitsinch/pound/secondModel GeometryLength: L 300 inCross Sectional PropertiesArea: A 9 in2Square Cross Section (3 in x 3 in)Moment of Inertia: I 6.75 in4Material PropertiesYoung’s Modulus: E 30.0 E 6 psiAutodesk Inventor Nastran 202011
Verification ManualAxial Distributed Load on a Linear BeamBoundary ConditionsOne end of the beam is constrained in all translations and rotations (point A). An axially distributed load(force per unit length) is set to 1,000 lb/in in the negative Y-direction for the 10-inch long element furthestfrom the constrained end (at point B). See Figure 2.MAByz300xFigure 2. Boundary ConditionsSolution TypeStaticComparison of ResultsThe tabular results are given in Table 1.Table 1. ResultsDescriptionBeam Constrained End Axial Stress (psi)Beam Free End T1 Translation (in)Beam T1 Constraint Force (lb)TheoryAutodeskInventorNastranError 0000.0References1. Beer and Johnston, Mechanics of Materials. New York: McGraw-Hill, Inc., 1992.Autodesk Inventor Nastran 202012
Verification ManualDistributed Loads on a Cantilever Beam2.3 Distributed Loads on a Cantilever BeamProblem DescriptionFigure 1 shows the model of a cantilever beam with a distributed load acting in the negative Y-direction.A static analysis is performed on the model. The beam torque stress at the constrained end of the beam(A), the deflection of the free end (B), and the total beam constraint force are determined. All dimensionsare in inches.PABy480xzFigure 1. Cantilever Beam with Distributed LoadAutodesk Inventor Nastran Analysis Model Filename vm2 3.nasModel DataFinite Element Modeling Mesh (8 x 1): 9 nodes, 8 bar elementsUnitsinch/pound/secondModel GeometryLength: L 480 inCross Sectional PropertiesArea: A 900 in2Square Cross Section (30 in x 30 in)Moment of Inertia: Iy Iz 67500 in4Material PropertiesYoung’s Modulus: E 30.0 E 6 psiAutodesk Inventor Nastran 202013
Verification ManualDistributed Loads on a Cantilever BeamBoundary ConditionsOne end of the beam is constrained in all translations and rotations. A distributed load P 250 lb/in inthe negative Y-direction is defined on all elements.Solution TypeStaticComparison of ResultsThe tabular results are given in Table 1.Table 1. ResultsDescriptionBeam Constrained End Torque Stress (psi)Beam Free End Total Tr
Verification Manual Introduction Autodesk Inventor Nastran 2020 7 1. Introduction This guide contains verification test cases for the Aut
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