工字梁有限元报告.docx

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1、FiniteElementRaport1.AnalyticalsolutionDisplacementcreatedbythebendingfEmoment:v(L)==10.92〃〃“3EI：Displacementcreatedbytheshearforce:F•Simplifiedtheory:(rn=cZ^)=>v(/)==0.24/7/7?/k、GSF•Beamtheory:(rvv=parabolique^=>v(/)==0.2mmKyGSSo,totaldisplacementisv(/)=10.92+0.24=1

2、1.26min=10.92+0.21=11.22/h/wThenormalstressis：•Simplifiedtheory:-H+h、xeb(—)4•Beamtheory:(rx=Y,cryax=±3MpaTheshearstressis：Simplifiedtheory:十阳""=9.2MpaBeamtheory:Sh-earstressversusY精品1.FiniteElementsolution精品1-Themodelingofthisbeamwitha3Dmodel:The3Dmodelwithahalfofdi

3、mension：Weaddthelimitconditionbyusingthesymmetry.WeobtainforthesymmetryplanXOYTz=0.Theleftextremityisfixed,sotheTx,Ty,Tz=0・Wecangetthemodelwithlimitcondition:Thuswecangettheresult・Thedisplacementisshownasfollow.61173IWIH精品Wecanseethatthedisplacementofthebeamin3Dischan

4、ged1inearly.Attheendofthebeamthedisplacementis1.092503E+01mm.Itisclosetotheanalyticalsolution,andtheerroris2.6%.ThenormalstressofcomponentX:

5、minalvertexes・Themaxis±1・433663E+02attheseterminalvertexes,andtheerroris9.1%.TheshearstressofcomponentXY:rvv精品•£h¥/I10*C01例対二(KOMLAY£t们8oiKca8ISCdl7maY»*r-622

6、011LEGENDResuld.StressTensor.Xf•ssn卜•I47*CfloL"怙九Frn片H&130-«1«fif4d42：・」osu①一SS21S精品精品Wecanseethattheshearstressofthebeamin3DisnearlyconstantinthemiddlepartofthebeaminthedirectionofX・WechoseseveralnodesinthedirectionYinthemiddlepart・Theprecedentfigureshowsarangeasaqua

7、draticfunctionofyalongtheweb,whichverifiesthebeamtheory.Therangeoftheshearstressisaround8-9Mpa,sowecanmakethesimplifiedmodelwhichhasconstantshearstressalongtheweb・Themaximumshearis9.570804E+00,theerrorwithbeamtheoryis1.8%.Comparingwiththeanalyticalsolution,wemakeatabl

8、etocritiquetheresults・DisplacementMax(mm)Normalstressmax(Mpa)Shearstress(Mpa)Finite1.092503E+011.435663E+029.570804E+00(max)