工字梁有限元报告

.FiniteElementRaport1.AnalyticalsolutionDisplacementcreatedbythebendingmoment:谢谢阅读v(L)FL310.92mm3EIzDisplacementcreatedbytheshearforce:谢谢阅读•Simplifiedtheory:ctev(l)F0.24mmxykGSy•Beamtheory:paraboliquev(l)F0.21mmxykGSySo,totaldisplacementisv(l)10.920.2411.26mm感谢阅读10.920.2111.22mmThenormalstressis：•Simplifiedtheory:F(Lx)Yaverage140.8MpaXeb(Hh)X4•Beamtheory:F(Lx)Y,max131MpaXIXzTheshearstressis：Simplifiedtheory:average9.2Mpa谢谢阅读xyBeamtheory:.2.FiniteElementsolution精品文档放心下载1．Themodelingofthisbeamwitha3Dmodel:精品文档放心下载The3Dmodelwithahalfofdimension:精品文档放心下载Weaddthelimitconditionbyusingthesymmetry.WeobtainforthesymmetryplanXOYTz=0.Theleftextremityisfixed,sotheTx,Ty,Tz=0.精品文档放心下载Wecangetthemodelwithlimitcondition:谢谢阅读Thuswecangettheresult. Thedisplacementisshownasfollow.精品文档放心下载.Wecanseethatthedisplacementofthebeamin3Dischangedlinearly.Attheendofthebeamthedisplacementis1.092503E+01mm.Itisclosetotheanalyticalsolution,andtheerroris2.6%.精品文档放心下载ThenormalstressofcomponentX:精品文档放心下载XFortheleftsection:X.WecanseethatthestressofcomponentXofthebeamin3Dischangedlinearlyintheleftsection.Itreachesthemaximumattheterminalvertexes.ThemaxXis1.435663E+02attheseterminalvertexes,andtheerroris9.1%.谢谢阅读TheshearstressofcomponentXY:xy精品文档放心下载Wecanseethattheshearstressofthebeamin3DisnearlyconstantinthemiddlepartofthebeaminthedirectionofX.WechoseseveralnodesinthedirectionYinthemiddlepart.Theprecedentfigureshowsarangeasaquadraticfunctionofyalong谢谢阅读.theweb,whichverifiesthebeamtheory.Therangeoftheshearstressisaround8-9Mpa,sowecanmakethesimplifiedmodelwhichhasconstantshearstressalongtheweb.Themaximumshearis9.570804E+00,theerrorwithbeamtheoryis1.8%.感谢阅读Comparingwiththeanalyticalsolution,wemakeatabletocritiquetheresults.谢谢阅读DisplacemeNormalShearstressntstress(Mpa)Max(mm)max(Mpa)Finite1.092503E+1.435663E+9.570804E+00(mElement0102ax)in3DAnalytical11.221319.4(max)solutionTheresultsof3Dfiniteelementmodelareclosetotheanalyticalsolutionofbeamtheorynomatterinthedisplacementandthestress.Sothe3Dmodelmakesagoodapproximationtotheanalyticalresults.谢谢阅读Weaugmenttwicethesizeoftheelementwiththesame3Dmodel.谢谢阅读Wecangettheresultofthenormalstress.感谢阅读Themaxnormalstressis183Mpa,whichisfarmorethantheprecedentmodelcomparedwiththeanalyticalsolution,butthedelayofthecalculationismuchlessthantheprecedentmodel.谢谢阅读.Soitisnotawisechoicetouse3Dmodel,becauseweshouldtrytofindabalanceoftheaccuracyandthedelay.谢谢阅读.2．Themodelingofthisbeamwitha2Dmodel:感谢阅读Weconstructthemodelwithmembraneandbeamelementsby5surfaces.Amongthesefivesurface,thewebsurfaceismodeledbyamembrane,andtheothersaremodeledbyshells.感谢阅读Fromthemodelwecangettheresults谢谢阅读Wecanseethatthedisplacementofthebeamin3Dischangedlinearly.Attheendofthebeamthedisplacementis1.0702785E+01mm.Itisclosetotheanalyticalsolution,andtheerroris4.6%.精品文档放心下载.Thenormalstressdoesn’treachethemaximumattheterminalvertexes,butattheleftsection.ThemaxXis7.5603534,andtheerrorcomparedwithbeamtheoryis32.6%谢谢阅读.Wecanseethattheshearstressofthebeamin2DmodelisnearlyconstantinthemiddlepartofthebeaminthedirectionofX.WechoseseveralnodesinthedirectionYinthemiddlepart.Theprecedentfigureshowsarangeasaquadraticfunctionofyalongtheweb.Themaxis-9.624660E+00mm,andtheerroris2.3%.谢谢阅读.Themodelingofthisbeamwithmembraneandbeamelements:谢谢阅读WeconstructthemodelwithmembraneandbeamelementsDisplay:1Dline谢谢阅读Display:3DFullSpanFromthemodelwecangettheresults精品文档放心下载Wecanseethatthedisplacementofthebeaminmodelofmembraneandbeamischangedlinearly.Attheendofthebeam感谢阅读.thedisplacementis9.814795E+00mm.Theerrorwiththeanalyticalsolutionreaches12.5%.谢谢阅读ThenormalstressofcomponentX:谢谢阅读XWecanseethatthenormalstressofcomponentXofthebeaminthismodelisalsochangedlinearlyintheleftsection.Itreachesthemaximumattheterminalvertexes.Themaxis1.093545E+02at感谢阅读Xtheseterminalvertexes.Theerrorreaches16.5%.精品文档放心下载.WechoseseveralnodesinthedirectionYinthemiddlepartofthemodel.Theprecedentfigureshowsarangeasaquadraticfunctionofyalongtheweb.Themaxis-6.271123E+00.Theerrorreaches33.3%.感谢阅读.4.Themodelingofthisbeamwitha1Dmodel:感谢阅读Weconstructthemodelin1Dmodel感谢阅读Thesectionofbeam:Display:3DFullScanFromthemodelwecangettheresults精品文档放心下载.Wecanseethatthedisplacementofthebeamin1Dischanged感谢阅读linearly. At the end of the beam the displacement is谢谢阅读1.1136911E+01mm.Theerrorwiththeanalyticalsolutionreaches谢谢阅读0.7%.Thenormalstress:Xreachesthemaximumattheterminalvertexes.Themaxis精品文档放心下载X X1.31282E+02attheseterminalvertexes,C/D/E/F.Theerrorreaches0.2%.谢谢阅读.5.Themodelingofthisbeamwithmembraneandrod精品文档放心下载elements:Weconstructthemodelwithmembraneandrodelements.Thesectionofthetworodsis960mm2.Themodelisshownasfollow.谢谢阅读Wecanseethatthedisplacementofthebeamin1Disalsochanged感谢阅读linearly. At the end of the beam the displacement is精品文档放心下载1.0735427E+01mm.Theerrorwiththeanalyticalsolutionreaches精品文档放心下载4.3%..WecanseethatthenormalstressofcomponentXofthebeaminthismodelisalsochangedlinearlyintheleftsection.Itreachesthemaximumattheterminalvertexes.ThemaxXis1.190676E+02mmattheseterminalvertexes.Theerrorreaches6.1%.谢谢阅读.WecanseethattheshearstressofthebeamwithmembraneandrodsisnearlyconstantinthemiddlepartofthebeaminthedirectionofX.WechoseseveralnodesinthedirectionYinthemiddlepart.Theprecedentfigureshowsarangeasaquadraticfunctionofyalongtheweb.Themaxis-9.084330E+00mm,theerroris3.4%.感谢阅读.3.Conclusion:Inthefollowingtable,welistthecomparisonofdifferentmodelswiththeanalyticalsolutionofbeamtheory.精品文档放心下载DifferenceErroroftheErrorofthewithErroroftheCalculation