浮式平台一-结构强度分析基本原理

第二章结构强度设计

StructuralStrengthDesignandAnalysis

第一节结构强度分析根本原理

闫发锁

引言

1.船舶结构设计的过程？

2.浮式平台结构的设计与船舶结构的设计具有哪些相似和不同？

浮式平台与船舶的结构设计过程一致，细节不同。

结构根本设计结构分析结构荷载结构总布置确定的前提下，根据设计标准与设计经验分析反响Outline6hourscourseworkBasicsofstructuralplatingandshellApplicationofplatingandshellinoffshorestructuresLoadingandstressesStructuralfiniteelementanalysisFEAresultsdesignapplicationTableofContentsStrengthDesignFundamentals板壳结构的受力特点板壳结构中的应力分布和计算方法浮式结构常用的应力及特点设计标准和应用静水压的局部和整体作用整体力对板壳结构强度的影响TableofContents(cont)结构的有限元分析StructuralDesignLoadingConditions分析结果的应用和结构设计1StressFundamentals2StructureBending,shearandtorsioncolumn,beam,section3plateandshellbending4能量原理5柱，梁板壳的局部和整体屈曲6

FEA原理StrengthDesignFundamentals

StressVectorDefinition

应力的矢量定义Stress-StrainRelationship应力-应变关系EquivalentStressandPrincipalStresses等效应力和主应力StressVectorsMaterialRelationshipforLinearMaterialThestressisrelatedtostrain: {s}=[D]{eel}

where:stressvector{s}hasthefollowingcomponents

{s}=[sxsyszsxysyzsxz]T

[D]istheelasticityorelasticstiffnessmatrixorstress-strainmatrix

{eel}istheelasticstrainvector

{eel}={e}–{eth}MaterialRelationshipforLinearMaterialThetotalstrainvector{e}canbeexpressedas:

{e}=[ex

eyezexexyeyzexz] {eth}isthethermalstrainvector

{eel}arethestrainsthatcausestresses

TheFlexibilityorComplianceMatrixWheretypicaltermsare:Ex=Young’smodulusinthexdirectionnxy=majorPoisson’srationyx=minorPoisson’sratioGxy=shearmodulusinthexyplaneTheFlexibilityorComplianceMatrixThe[D]-1matrixispresumedtobesymmetric:nyx/Ey=nxy/Exnzx/Ez=nxz/Exnzy/Ez=nyz/Eynxy,nyz,nxz,nyx,nzy,andnzxarenotindependentquantities,Poisson’sRatioTheuseofPoisson’sratiosfororthotropicmaterialssometimescauseconfusion,sothatcareshouldbetakenintheiruse.AssumingthatExislargerthanEy,nxyislargerthannyx.Hence,nxyiscommonlyreferredtoasthe“majorPoisson’sratio〞,becauseitislargerthannyx,whichiscommonlyreferredtoasthe“minorPoisson’sratio〞.Fororthotropicmaterials,weneedtoinquireofthesourceofthematerialpropertydataastowhichtypeofinputisappropriate.Forisotropicmaterials,itmakesnodifferencewhichtypeofinputisused: Ex=Ey=Ez, nxy=nyx=nxzStress-StrainRelationsex=axDT+sx/Ex–nxysy/Ex-nxzsz/Ex

ey=ayDT-nxysx/Ex+sy/Ey-nyzsz/Eyez=azDT-nxzsx/Ex–nyzsy/Ey+sz/Ezexy=sxy/Gxyeyz=syz/Gyzexz=sxz/GxzWherethetypicaltermsare:ex=directstraininthexdirectionsx=directstressinthexdirectionexy=shearstrainonthex-yplanesxy=shearstressonthex-yplaneIsotropicMaterialForisotropicmaterialandnotemperaturechanges,therelationcanbegreatlysimplified:

DT=0 E=Ex=Ey=Eznxy=nxz=nxy Gxy=Gxz=Gyzex=(sx–nsy–nsz)/Eey=(sy-nsx-nsz)/Eez=(sz-nsx–nsy)/Eexy=sxy/Geyz=syz/Gexz=sxz/GEquivalentStressTheEquivalentStressisalsocalledvonMisesstressse=(sx2+sy2-sxsy+3sxy2)1/2Wheresx,sy,

andsxyrepresentthecomponentstressesintheXandYdirections,andcomponentshearstress,respectively.PrincipalStressesPrincipalstresscalculationsareperformedtohelpidentifyareasofthestructuresubjectedtohighcyclicloads.Theseareasarethengivenspecialattentionforreasonsoffatigue. S1=(sx+sy)/2+{[(sx-sy)/2]2+sxy2}1/2 S2=(sx+sy)/2-{[(sx-sy)/2]2+sxy2}1/2UseofVariousStressesEquivalentstressisusedmostlyinanalysisGlobalstructurecontrolloadcasesselectionGlobalstresscheckStructuralstresslevelcheckComplicatejointstresscheckComponentstressesCheckstressmagnitudeinparticulardirectionUsedforstabilitycheckUsedmostlyinnormalsectionNotapplicableincomplicatecornerortransitionsUseofVariousStresses(cont.)PrincipalstressesFatigueanalysisComplicatejointstresscheckCornerortransitionstabilitycheckStressVectorsStressflowcheckLoadpassHelptounderstandthecomplicatejointsDeformationHelptounderstandstructuralbehaviorSatisfythecode/designbasisrequirementsMaterialCoordinateSystemsThefundamentalassumptionsofplatetheory1.Thematerialiselastic,homogeneous,andisotropic.2.Theplateisinitiallyflat.3.Thedeflectionofmidplaneissmallcomparedwiththethicknessoftheplate..4.Thestraightlines,initiallynormaltothemiddleplanebeforebending,remainstraightandnormaltothemiddlesurfaceduringthedeformation5.Thestressnormaltothemiddleplane,σz,issmallandmaybeneglected6.Sincethedisplacementsofaplatearesmall,itisassumedthatthemiddlesurfaceremainsunstrainedafterbending.Thefundamentalequationsofelasticitytheory

CompatibilityequationsEquilibriumequationsConstitutiveequationsGeometryequationsGoverningdifferentialequationsofplateelementGoverningdifferentialequationsbythedeflectionsBytheforcesBoundaryconditions1Clamped,orbuilt-in,orfixededgey=02Simplysupportededgex=a3Freeedgey=bVariationalprinciplesofsolidmechanicsBoundaryBoundaryconditionsTotalpotentialenergyofadeformedelasticbodyandtheloadsactingonit=U+

ThestrainenergyTheworkdoneexternalforcesInternalVariationalprinciples(a)ThePrincipleofConservationofEnergy(b)ThePrincipleofVirtualWork(c)ThePrincipleofMinimumPotentialEnergySolutionofRectangularPlatesCylindricalbendingofaplate(桶形弯曲，likeabeam〕Purebendingofplates〔纯弯曲，Onlymoments〕NAVIER’SMethod(Doubleseriessolution,四边简支)SolutionofRectangularPlates(cont.)TrytofindthesolutionsofrectangularplateswithdifferentboundaryconditionsandloadsSubjectedtoapatchloadofintensityp0=constSubjectedtoaconcentr