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1、KatholiekeUniversiteitLeuvenFacultyofEngineeringDepartmentofMetallurgyandMaterialScienceReportofFiniteElementsAnalyticBeamproblemGroupMember:LiChenXuJingcanZhangQingchengAssistant:KaiLiuDate11/01/2012Content1.Presentationoftheassignment12.Analyticalsolution13.DiscussionoftheFEmodel23.
2、1.FEmodel232Elementtype333Elementmesh334Boundaryconditions54.PresentationoftheFEresults55.ComparetheFEresultswiththeanalyticalsolution106.Verificationcalculations116.1・Equilibriumatnodes116.2Globalequilibriumofthestructure116.3Equilibriumatelements116.4Stressdiscontinuities126.5Calcul
3、ationofnodalforces127.Evaluationoftheelementmesh138.Thecleanedlogfile141.PresentationoftheassignmentAsshowninFigure1,theproblemcanbetreatedasacantileverbeamwithtwoforcesatitstwotipsapproximately.Thegravityofthebeamisignored.Tobeconscientious,thecrosssectionofthecantileverbeamisrftarec
4、tangularbutlikeaUshapedsteelchannel.Alsothatthewindowslocatedinsidethesidewallwon'tbeaccountedintoduringtheanalyticalcalculationbecauseofthenarrowlimitationoftheequationofdeflectioncurveused.(L=5m,B=4m,H=13m,h=2m,w=lm,b=2m,a=lm,t=0.3m,E=35*109N/m2,v=l/6,P=2000N)Figure1:schematicanalys
5、isoftheassignment2.AnalyticalsolutionUsingthefollowingformula,thedeflectionofthebeamatthetipandtheonealongthe'H'directioncanbefiguredouttocomparewiththefiniteelementresults.ThediagrammaticpresentationoftheformulaisshowninFigure2andFigure3.Momentofinertia:I=ab3/12,a=5,b=4,ai=4.4,bi=3.7
6、f(deflection)=-Pl3/3EI,f(x)=-Px2(引・x)/6EIdeflectionalongthe'H'direction,1=13,P=2000I=5*(43)/12-4.4*(3.73)/12=8.0939m4fmax=-2000*(133)/(3*35*109*8.0939>-0.10034*10-4mFigure2:schemeofmomentofinertia.Figure3:schemeofdeflection3・DiscussionoftheFEmodel3.1.FEmodelUsingtheFiniteElementAnalyt
7、icmethodtoexplainthisproblem,itcanbesimplifiedintohalfoftheoriginshapewithoneforceaddedtothetipwhichisschemedinFigure4becauseofthesymmetry.Theinitialbeamshouldbecutintotwopartsthroughtheplanewhichisperpendiculartothelowerpartofthebeamacrossthemiddlelinebetweenthetwotipsbearingforce.Fi
8、gure4
