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# 978-1-58503-400-0 -- ANSYS Tutorial [Release 11.0]

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®ANSYS Tutorial Release 11.0 Structural & Thermal Analysis Using the ANSYS Release 11.0 Environment Kent L. Lawrence Mechanical and Aerospace Engineering University of Texas at Arlington SDC PUBLICATIONS Schroff Development Corporation www.schroff.com www.schroff-europe.com ANSYS Tutorial 2-1 Lesson 2 Copyrighted Plane Stress Material Plane Strain 2-1 OVERVIEW Copyrighted Plane stress and plane strain problems are an important subclass of general three-dimensional problems. The tutorials in this lesson demonstrate: ♦Solving planar stress concentration problems. Material ♦Evaluating potential inaccuracies in the solutions. ♦Using the various ANSYS 2D element formulations. 2-2 INTRODUCTION It is possible for an object such as the one on the cover of this book to have six components of stress when subjected to arbitrary three-dimensional loadings. When Copyrighted referenced to a Cartesian coordinate system these components of stress are: Normal Stresses σ , σ , σ x y zMaterial Shear Stresses τ , τ , τxy yz zx Figure 2-1 Stresses in 3 dimensions. Copyrighted In general, the analysis of such objects requires three-dimensional modeling as discussed in Lesson 4. However, two-dimensional models are often easier to develop, easier to solve and can be employed in many situations if they can accurately represent the behavior of the object under loading. Material 2-2 ...

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ANSYS®TutorialRelease 11.0Structural & Thermal Anal sis Usin the ANSYS Release 11.0 Environment
Kent L. Lawrence Mechanical and Aeros ace En ineerin University of Texas at Arlington SDCPUBLICATIONS Schroff Develo ment Cor oration www.schroff.com www.schroff-euro e.com
ANSYS Tutorial
2-1
LCesosonp2yr Plane SMtresast Plane Strain  2P-l1anOeVstEreRCsVsIaEnWdoplanepstrainyprobrlemsi aregan imhportatnt suebclassdof g eneral three-al roblems. The tutorials in this l dimensioanvinpgplnaSolMr stressaconcetntratieropseosonremblnediomns.astratel: Evaluating potential inaccuracies in the solutions.  Using the various ANSYS 2D element formulations. 2-2 INTRODUCTION rIcteofiemsrpeopnncoeessndiCtofsorfelbsaotaCoobnaiwsetnartrsespsctjeoordhnescyucesijnecattbuharsteythedstioarmonethgbitrarythonmoeescehecothereenopt-dirmeofveofstnethisnesstrsoiasnde:araobloklo eniWxhdahniossge.vt NormalStressesMσx,σy,aσzteri Shear Stressesτxy,τyz,τzx  Ingeneral,Cthe anoalysis opf suchyobjecrts reiquiregs threehF-diigmuretens2i-o1nemlaesdoSestrdni3lesing neisdmions.iscussedasd isbnoelhvLaeevsisaoornndof4ct.ahneHoobbewjeeecvtemruMloderoypledi-dwotn,aadiing.sennammtynslanoieedomtiauitorsaslniirftheeofaeytecnalasina hetntyletaruceserpersaei,peevoloedertotrc
2-2
ANSYS Tutorial A state ofPlane Stress in a thin object loaded in the plane of its largest exists (dτxiσzym,lτieyenznisn.soindhea,tτLzxXe)t-atrhCYepeaXlll-aYneezobedoranaldpnforpeeonhttothiskpinyavfyrlaidnoeregmoanfthonitaleeZysdyirgsa.hdnTlereoctioihon-nzdiFura.nng.teort,hstAthieremhaeetostrhesbsnedeσxrl,oatsσdr ysissddeenae,niqAtsuNapSdlraYinlSaeteaprnradolvaeildsepesmureangtes6a-rfnotorodoeutsheMrtrphtdeoaiongaenlaravedelugmnaaixetpmoareleselpenmetlanlepooffrntallsanepisestorngertsahitwrpssbeolmlnedo4m- ls.Wewilluseadeodo.n-8dnese both triangles and quads in solution of the example problems that follow.  2-3 PLATE WITH CENTRAL HOLE To start off, let’s solve a problem with a known solution so that we can check our latewlaoeddhtnipstldetusercpuomCdinathacundoFteenhtgofndinrstaelarelohsawohsrinnMEiecsspigoFreur2.2-Th.he probtlem ies that odf a te nsile-
FigMure 2-2aPlatetwithecentrarl hoile.al The1.0 m x 0.4 mplate has athicknessof0.01 m, and a central hole0.2 mindiameter. It is made of steel with material properties;elastic modulus,E= 2.07 x 1011N/m2and Poisson’s ratio,ν= 0.29. We apply a horizontal tensile loading in the form of a pressure  p= -1.0 N/m2along the vertical edges of the plate. Because holes are necessary for fasteners such as bolts, rivets, etc, the need to know sscttoruendscyse.enstTrhaatenidornedsefufaloctstrCtmahrteioofnortfooshectuaesnedarsespesireaomehtswohyeidwcobasnrucrpyBl.evreviitsbolfyueforeghnheeaeddantna,dhvenshaerewtdottlecnavciefsiuepokuoalbeodcagrddeeupmtheta roiestsaatlsoftnmethods, the effect of most complex stress concentration geometries had to be evaluated experimentally,andmanyavaiMlable chaarts wtere deevelopred firomaexpelrim ental results.
Plane Stress / Plane Strain
2 3 -The uniform, homogeneous plate above is symmetric about horizontal axes in both horizonta gvbeeoroutinmcdeaatlrrycyleCeninocitidlectndorleteranlnoceW.,snosuieni.gsdanipkatnameiyhsoTnlamirroyeaquimaanaedvsrarteraragegtanthihtfatftfootheoegvobetatatthsesyehpaltheertsemmhettrfofroetifahestsyandnencteeneleite,inarl,ybapddefodemlimatpndnylenir edomtroF.lraeofwesikrrcoteclewoaionbghte smmoadlellipnrgobalnedmssoulusitinognsMretbmrmtsyfeofayalyimmyetnatiintobeootnognerm-hipeaiorftanloraaoruqt;afllraretr geofthework.reoaevrosmnactismelborpPlace the origin ofX-Ycoordinates at the center of the hole. If we pull on both ends of the plate, points on the centerlines will move along the centerlines but not perpendicular to them. This indicates the appropriate displacement conditions to use as shown below.  C
Figure 2-3Quadrant used for analysis. In Tutorial 2A we will use ANSYS to de termine the maximum horizontal stress in the plate and compare the computed results with the maximum value that can be calculated tuosifnogrmtaubluaCtenadvsdetaloaovlefoluespr stresys concrentriationgfactorsh. Intertactivee commdands will be used  the problem. 2-4 TUTORIAL 2A - PLATE Objective:Find themaximum axial stressin the plate with a central hole and compare your result with a comMputationausingtpublieshedrstresis conacentrlatio n factor data.PREPROCESSING with this problem. Also set theJobname  toTutorial2Aor something memorable and 1.Start ANSYS, select theWorking Directorywhere you will store the files associated provide aTitle.started ANCSYS, uoseFilep> Chaynge JrobniamegorDirehctorytorTietle.)d (If you want to make changes in the Jobname, working Directory, or Title after you’ve SelectthesixnodetriaMngular ealementt to uese forrtheisolutiaon olf thi s problem.
2-4
C
ANSYS Tutorial
ted l
Figure 2-4Six-node triangle. unneSMMtriuactu.r2aloSildC>>uQdaPreodesnoproc8p8r3>1eso>yeElKOrmenti Tygpe >hAdd/Etdit/Deeleted> A dd >
Figure 2-5Element selection. Material Select theoptionwhere you define the plate thickness. 3. Options(Element shape K1)> Triangle,  Options(Element behavior K3)> Plane strs w/thk > OK > CloseCopyrighted Material
Plane Stress / Plane Strain
Figure2-6El
ementoptions.
MaFigutre 2-7eRealrconistantsa.l (Enter the plate thickness of 0.01 m.)>Enter0.01 > OK > Close
Figure 2-8Enter the plate thickness.
2-5
2-6
ANSYS Tutorial
ties. 5E.ntMeraithneMmeanteuri>alCPprreoppreroocessorp> MatyerialrProips >gMahted terial Models Material Model Number 1, Double clickStructural > Linear > Elastic > Isotropic Behavior window.)Material EnterEX = 2.07E11and PRXY = 0.29 > OK(Close the Define Material Model Create the geometry for the upper right quadrant of the plate by subtracting a 0.2 m diameter circle from a 0.5 x 0.2 m rectangle. Generate the rectangle first.  6. Main Menu > Preprocessor > Modeling > Create > Areas > Rectangle > By 2 Corners Enter(lowerleftcCorner)oWP Xp= 0.0,yWP Yr= 0i.0angdWidthh = 0.t5, Heeight =d0.2 > OK 7E.ntMera0ni=0.PXWuneMP>,PYWsorperseco=.0M0ra>ndMdRoaidesluingat0=1.>Cre>Oetaer>KArieas >aCirlcle > Solid Circle
r
rFigure 2-9Create areas. Material

Plane Stress / Plane Strain
Co
2-7
d Figure 2-10Rectangle and circle . bottom of the screen as necessary.) Nowsubtract circle from the rectangle. (Read the messages in the window at the the 8>.PMicakitnheMCreenctuan>golPeoces>OK,errptshoernp>icMk tohdeelciinrcgleolBonsea>pO>tare>e>KOdSubt ract > Areas