工字梁有限元报告材料

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1、FiniteElementRaport1.AnalyticalsolutionDisplacementcreatedbythebendingmoment:Displacementcreatedbytheshearforce:·Simplifiedtheory:·Beamtheory:So,totaldisplacementisThenormalstressis：·Simplifiedtheory:·Beamtheory:,Theshearstressis：·Simplifiedtheory:·Beamtheory:2

2、.FiniteElementsolution1．Themodelingofthisbeamwitha3Dmodel:The3Dmodelwithahalfofdimension:Weaddthelimitconditionbyusingthesymmetry.WeobtainforthesymmetryplanXOYTz=0.Theleftextremityisfixed,sotheTx,Ty,Tz=0.Wecangetthemodelwithlimitcondition:Thuswecangettheresult.

3、Thedisplacementisshownasfollow.Wecanseethatthedisplacementofthebeamin3Dischangedlinearly.Attheendofthebeamthedisplacementis1.092503E+01mm.Itisclosetotheanalyticalsolution,andtheerroris2.6%.ThenormalstressofcomponentX:Fortheleftsection:Wecanseethatthestressofcom

4、ponentXofthebeamin3Dischangedlinearlyintheleftsection.Itreachesthemaximumattheterminalvertexes.Themaxis1.435663E+02attheseterminalvertexes,andtheerroris9.1%.TheshearstressofcomponentXY:Wecanseethattheshearstressofthebeamin3Disnearlyconstantinthemiddlepartoftheb

5、eaminthedirectionofX.WechoseseveralnodesinthedirectionYinthemiddlepart.Theprecedentfigureshowsarangeasaquadraticfunctionofyalongtheweb,whichverifiesthebeamtheory.Therangeoftheshearstressisaround8-9Mpa,sowecanmakethesimplifiedmodelwhichhasconstantshearstressalon

6、gtheweb.Themaximumshearis9.570804E+00,theerrorwithbeamtheoryis1.8%.Comparingwiththeanalyticalsolution,wemakeatabletocritiquetheresults.DisplacementMax(mm)Normalstressmax(Mpa)Shearstress(Mpa)FiniteElementin3D1.092503E+011.435663E+029.570804E+00(max)Analyticalsol

7、ution11.221319.4(max)Theresultsof3Dfiniteelementmodelareclosetotheanalyticalsolutionofbeamtheorynomatterinthedisplacementandthestress.Sothe3Dmodelmakesagoodapproximationtotheanalyticalresults.Weaugmenttwicethesizeoftheelementwiththesame3Dmodel.Wecangettheresult

8、ofthenormalstress.Themaxnormalstressis183Mpa,whichisfarmorethantheprecedentmodelcomparedwiththeanalyticalsolution,butthedelayofthecalculationismuchlessthantheprecedentmodel.