搜索
,,(,100084):,,,,,,,0018,WRCBulletin2970.8:;;;;:O34;TQ051:A:1001-4837(2004)01-0018-06LocalStressAnalysisofCylindricalShellsduetoBranchPipeMomentsXUEMing-de,LIDong-feng,HUANGKe-zhi(TheDepartmentofEngineeringMechanics,TsinghuaUniversity,Beijin100084,China)Abstract:Cylindricalshellsattachedbranchpipesareofcommonoccurrenceinpressurevesselandpipingin2dustry.Thehigheststressconcentrationoftenoccursinthevicinityofjunctionduetothepressureandexternalmoments,whichistheoriginpositionofmanycatastrophicaccidents.Atheoreticalsolution,whichcanbeap2plicableuptodiameterratio,0018,isintroducedinthispaper.ThepresentedresultsareingoodagreementwiththoseobtainedbyexperimentsandbyFEM.ThedimensionlessresultantforcesandmomentsobtainedbythepresentedmethodareinagreementwithWRCBulletin297.Thecurvesconcerningstressconcentrationfac2torsintheintersectingcylindricalshellswithdiameterratio0018basedonthetheoreticalsolutionsarepre2sented.Keywords:pressurevessel;stressanalysis;cylindricalshellattachedbranchpipe;thinshelltheoreticalsolu2tion;stressconcentration11,,,,,,2050,Bijlaard[12],,BijlaardWRCBulletin107[3],81©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[4]Donnell,MershonWRCBulletin297[5]d/D015d/DT5,12080,Afshari[6]Kov[7],Moffat[89],BS806,r/R1,D/T70,r/Rt/T1,2080,Morley[1014],,2090,(d/D018)[13,14],JB473295[15],[16,17],21Mxb,MybMzb()((a)),,(),1,(b)(c),(b),(c)((b),),(c)[16,17],2(a)(b)(c)(b),(),:=L/RMxb:T=0,u=0,un=0,M=0(1)MybMxb:=0,S=0,Q3=0,=0(2)2Mxb(a);(b),;(c)(b)(c),(a)(b),x=0,y=0(),()(,,,),,1(b):,,,()(,91211134©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.)(4)(4),,1(n=n2l,=+l=(x+L)/R)=0=/2G(1)N(m)G(1)N(m)G(2)N(m)G(2)N(m)G(3)N(n)G(4)N(n)N=2sin(2k)sin(m)-cos(2k)-cos(m)cos(n)sin(n)MzbN=3cos(2k+1)cos(m)sin(2k+1)sin(m)cos(n)sin(n)MybN=4sin(2k+1)sin(m)-cos(2k+1)-cos(m)sin(n)-cos(n)Mxb3MxbBijlaard(a)Mxbqz();(b)Mxbqn(Bijlaard);(c)()MxbMybMzb,Bijlaard[1,2]3Mxb,Bijlaard:2c(3(c))qz(3(a))qy,Timoshenko[18]Bijlaard[1,2](3(b)),:qz[1,2],qy[1,2]BijlaardqnMxb(Myb)Fy,qMzbFz,,Bijlaard[1,2]:=m=e(4,N)n=0UmnG(1)N(m)G(4)N(n)(3)=m=e(4,N)n=1VmnG(2)N(m)G(3)N(n)(4)n=m=e(4,N)n=1WmnG(1)N(m)G(3)N(n)(5)(3-5)Umn,Vmn,WmnTimoshenko[18]m=2k+e(2,N)(k=0,1,2111),G(1)N-G(4)N,e(2,N)e(2,N)(N,N=1x=0,y=0,[1617]Bijlaard:Morley[19],-=un+i42ETRª(un,ªAiry):=k=e(4,N)n=e(1,N)CnFkn()G(1)N(m)(6)Cn=Cn1+iCn2,e(1,N)2,Fkn()Bessel,Hankel:Fkn=(-1)k(1-12m0)[Jm-n(-i)+e(3,N)J-m-n(-i)]Hn()(7)42=[12(1-v2)]1/2R/T,=(12-i2)1/2,mn=0,mn1,m=n,e(3,N)2(6)[16,17],(MxbMyb)Mzb:T^=Mzn2r2,T^=T^=0,u^=2(1+v)EtMzn2r,u^=u^=0(8)02CPVTVol21.No12004©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.^=-Mybr2cos,T^=T^=0,u^=Myb2Etr2sin,u^=MybEtrcos,u^=-MybEtr(v+22)cos(9)Mxb:T^=Mxbr2sin,T^=T^=0,u^=-Mxb2Etr2cos,u^=MxbEtrsin,u^=-MxbEtr(v+22)sin(10),[1617]2e(j,N)e(1,N)e(2,N)e(3,N)e(4,N)N=210-11N=301-10N=41110=k=e(4,N)4l=1Dklgml()G(1)N(m)(11)Dkl(6)Cn,,gml()[16],[16,17]:=0cos=arcsin(0sin)(12):={20cos2+[arcsin(0sin)]2]1/2(13a)=arcsin{arcsin(0sin)[20cos2+[arcsin(0sin)]2]-1/2}(13b):()=10(1-20sin2)1/2=(0,)(14)3311ORNL-1(0=015,D/T=d/t=100)[20]ORNL-1[20](ANSYS,20,206353),(:0=Mxb/(r2t)0=Myb/(r2t)0=Mzb/(2r2t))46Mzb([20]),MxbMyb,312WRCBulletin107[3]297[5]WRCBulletin107[3]297[5],78,=d/DT,WRCBulletin297,WRCBulletin2974Myb=04,,0=d/D018,12211134©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=d/DT8,d/Dt/T2Mxb=90,MybMzb0909(ac):d/R=018,d/Rt/T2Tresca,t/T,MxbMyb0=M/(r2trTtR),Mzb0=M/(2r2t)5Mxb=905(1),d/D018=d/DT8,(2),,,WRCBulletin297,d/D018,8,d/Dt/T26Mzb=607Mxb=9022CPVTVol21.No12004©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=0(3)WRCBulletin107,297(a)MxbKxbt/T(b)MybKybt/T(c)MzbKzbt/T9BijlaardSteele,:1);2);3),,:[1]BijlaardPP.1StressesfromLocalLoadinginCylindrialPres2sureVessels[J].TransASME,1955,77:805-812.[2]BijlaardPP..StressesfromRadialLoadsandExternalMo2mentsinCylindricalPressureVessels,WeldingResearchSupplement,Dec.1955,608-s-617-s.[3]WichmanKR,HopperAG,MershonJL..LocalStressesinSphericalandCylindricalShellsduetoExternalLoadings[J].WeldingResearchCouncilBulletin107,1965.[4]SteeleCR,SteeleML..StressAnalysisofNozzleinCylin2dricalVesselswithExternalLoad[J].ASMEJPresVesTech,1983,105:191-200.[5]MershonJL,MokhtarianK,RanjanGV,etal.LocalStressesinCylindricalShellsDuetoExternalLoadingsonNozzleSulementtoWRCBulletinNo107[J].WRCBulletin297,1984.[6]AfshariP,WideraGEO,NatarajanR,etal.AnalysisofShellIntersections[R].Proceedings7thIntConfofPresVesTech,Dusseldurf,Germany,1992.378.[7]KovesWJ,SangerRJ..EvalutionofPressureDesignCrite2riaforNozzles[R].Proc8thIntConfonPresVes.Technolo2gy,Vol2:DesignandAnalysis,ASME,1996.271-279.[8]MoffatDG..ExperimentalStressAnalysisofFourFabricatedEqualDiameterBranchPipeIntersectionsSubjectedtoMo2mentLoadingsandtheImplicationsonBranchJunctionsDe2sign[R].ProcInstMechEngrs,1985,(33)32211134©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.