Verification.pdf

NX Nastran Veri ﬁ cation Manual

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2 NX Nastran Veri ﬁ cation Manual

Contents

Part I: Introduction

Overview of the Veri ﬁ cationManual..................................... 1-1

RunningtheTestCases ............................................... 2-1

Part II: Linear Statics Veri ﬁ cation Using Theoretical Solutions

Overview of Linear Statics Veri ﬁ cationUsingTheoreticalSolutions ........... 3-1

UnderstandingtheTestCaseFormat ....................................... 3-1

UnderstandingComparisonswithTheoreticalSolutions ......................... 3-2

References .......................................................... 3-2

TestCases.......................................................... 4-1

PointLoadonaCantileverBeam .......................................... 4-1

AxialDistributedLoadonaLinearBeam .................................... 4-3

DistributedLoadsonaCantileverBeam..................................... 4-5

MomentLoadonaCantileverBeam........................................ 4-7

Edge Pressure on Beam Element - Torque Loading ............................. 4-9

Thermal Strain, Displacement, and Stress onHeatedBeam ...................... 4-11

Uniformly Distributed Load on Linear Beam ................................. 4-13

Membrane Loads on a Linear Quadrilateral ThinShellElement ................... 4-15

AxialLoadingonRodElement ........................................... 4-17

Stress on a Beam as It Expands and Closes a Gap ............................. 4-19

ThinWallCylinderinPureTension ....................................... 4-21

ThinShellBeamWallinPureBending ..................................... 4-23

StrainEnergyofaTruss ............................................... 4-25

Part III: Linear Statics Veri ﬁ cation Using Standard NAFEMS Benchmarks

Overview of Linear Statics Veri ﬁ cation Using Standard NAFEMS Benchmarks . . . 5-1

UnderstandingtheTestCaseFormat ....................................... 5-1

Reference .......................................................... 5-1

TestCases.......................................................... 6-1

EllipticMembrane .................................................... 6-1

CylindricalShellPatchTest.............................................. 6-6

Hemisphere-PointLoads ............................................... 6-10

Z-SectionCantilever .................................................. 6-13

SkewPlateNormalPressure ............................................ 6-15

AxisymmetricCylinder/Sphere—Pressure .................................. 6-17

AxisymmetricShellPressure ............................................ 6-21

ThickPlatePressure .................................................. 6-25

SolidCylinder/Taper/Sphere—Temperature................................. 6-30

NX Nastran Veri ﬁ cation Manual

Contents

Part IV: Normal Mode Dynamics Veri ﬁ cation

Overview of Normal Mode Dynamics Veri ﬁ cation Using Theoretical Solutions . . . 7-1

UnderstandingtheTestCaseFormat ....................................... 7-1

UnderstandingComparisonswithTheoreticalSolutions.......................... 7-2

Reference ........................................................... 7-2

TestCases.......................................................... 8-1

NaturalFrequencyofCircularRingwithAxisymmetricModel ..................... 8-1

UndampedFreeVibration—SingleDegreeofFreedom .......................... 8-3

TwoDegreesofFreedomUndampedFreeVibration—PrincipleModes............... 8-5

ThreeDegreesofFreedomTorsionalSystem .................................. 8-7

TwoDegreesofFreedomVehicleSuspensionSystem ............................ 8-8

TwoDegreesofFreedomVehicleSuspensionSystem ........................... 8-10

CantileverBeamUndampedFreeVibrations................................. 8-12

NaturalFrequencyofaCantileveredMass .................................. 8-14

Part V: Normal Mode Dynamics Veri ﬁ cation Using Standard NAFEMS Benchmarks

Overview of Normal Mode Dynamics Veri ﬁ cation Using Standard NAFEMS

Benchmarks........................................................ 9-1

UnderstandingtheTestCaseFormat ....................................... 9-1

Reference ........................................................... 9-1

BeamElementTestCases ............................................ 10-1

Pin-endedCross—In-planeVibration ..................................... 10-1

Pin-endedDoubleCross-In-planeVibration ................................. 10-4

FreeSquareFrame-In-planeVibration .................................... 10-7

Cantilever with Off-center Point Masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-9

DeepSimply-SupportedBeam .......................................... 10-11

CircularRing—In-planeandOut-of-planeVibration.......................... 10-14

CantileveredBeam .................................................. 10-16

ShellElementTestCases............................................. 11-1

ThinSquareCantileveredPlate—SymmetricModes........................... 11-1

ThinSquareCantileveredPlate—Anti-symmetricModes ....................... 11-4

FreeThinSquarePlate ................................................ 11-7

SimplySupportedThinSquarePlate ..................................... 11-10

Simply Supported Thin Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-13

ClampedThinRhombicPlate........................................... 11-16

CantileveredThinSquarePlatewithDistortedMesh.......................... 11-19

SimplySupportedThickSquarePlate,TestA ............................... 11-24

SimplySupportedThickSquarePlate,TestB ............................... 11-27

ClampedThickRhombicPlate .......................................... 11-30

Simply Supported Thick Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-33

CantileveredSquareMembrane ......................................... 11-36

CantileveredTaperedMembrane ........................................ 11-39

Free Annular Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11-42

CantileveredThinSquarePlate ......................................... 11-45

NX Nastran Veri ﬁ cation Manual

Contents

AxisymmetricSolidandSolidElementTestCases ......................... 12-1

FreeCylinder—AxisymmetricVibration ................................... 12-1

ThickHollowSphere—UniformRadialVibration ............................. 12-4

Simply Supported Annular Plate — Axisymmetric Vibration . . . . . . . . . . . . . . . . . . . . . . 12-7

DeepSimplySupported"Solid"Beam ..................................... 12-10

SimplySupported"Solid"SquarePlate .................................... 12-13

Simply Supported "Solid" Annular Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12-16

CantileveredSolidBeam .............................................. 12-19

Part VI: Veri ﬁ cation Test Cases from the Societe Francaise des Mecaniciens

Overview of Veri ﬁ cation Test Cases Provided by the Societe Francaise des

Mecaniciens ....................................................... 13-1

UnderstandingtheTestCaseFormat ...................................... 13-1

Reference .......................................................... 13-2

Mechanical Structures — Linear Statics Analysis with Beam or Rod Elements . . 14-1

ShortBeamonTwoArticulatedSupports ................................... 14-1

ClampedBeamsLinkedbyaRigidElement ................................. 14-3

TransverseBendingofaCurvedPipe ...................................... 14-5

PlaneBendingLoadonaThinArch ....................................... 14-8

GridPointLoadonanArticulatedCONRODTruss ........................... 14-11

ArticulatedPlaneTruss............................................... 14-14

BeamonanElasticFoundation ......................................... 14-18

Mechanical Structures — Linear Statics Analysis with Shell Elements . . . . . . . . . 15-1

PlaneShearandBendingLoadonaPlate................................... 15-1

InﬁnitePlatewithaCircularHole ........................................ 15-4

UniformlyDistributedLoadonaCircularPlate............................... 15-7

TorqueLoadingonaSquareTube........................................ 15-10

CylindricalShellwithInternalPressure ................................... 15-13

UniformAxialLoadonaThinWallCylinder ................................ 15-17

HydrostaticPressureonaThinWallCylinder ............................... 15-21

GravityLoadingonaThinWallCylinder .................................. 15-25

PinchedCylindricalShell.............................................. 15-29

SphericalShellwithaHole ............................................ 15-32

BendingLoadonaCylindricalShell ...................................... 15-35

Uniformly Distributed Load on a Simply-Supported Rectangular Plate . . . . . . . . . . . . . 15-38

UniformlyDistributedLoadonaSimply-SupportedRhomboidPlate ............... 15-42

ShearLoadingonaPlate.............................................. 15-45

Mechanical Structures — Linear Statics AnalysiswithSolidElements......... 16-1

SolidCylinderinPureTension........................................... 16-1

InternalPressureonaThick-WalledSphericalContainer........................ 16-7

Internal Pressure on a Thick-Walled InﬁniteCylinder ......................... 16-11

PrismaticRodinPureBending ......................................... 16-15

ThickPlateClampedatEdges .......................................... 16-19

MechanicalStructures—NormalModeDynamicsAnalysis ................. 17-1

LumpedMass-SpringSystem............................................ 17-1

ShortBeamonSimpleSupports ......................................... 17-4

NX Nastran Veri ﬁ cation Manual

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