弹性力学基础及有限元法

.,内蒙古科技大学机械工程学院刘学杰2015-05,动力学问题的有限元法，动态分析FEM&ANSYS-12,有限元法及实践-12FiniteElementMethod(FEM)&thePractice,.,Outline概要,1.Review回顾2.有限元法:动力学问题3.动态分析实例模态分析,.,Review回顾：,1学习报告：13组-王炎2静态分析小结1）平面问题：三节点单元、四节点单元2)空间问题3)案例,.,动力学方程：与静态有什么不同？,Elementalvolume,位移/displacementsu,v,w,应变/strains,应力/stress,Not-steadyloadsanymore,.,动力学方程：与静态有什么不同？,1.质量矩阵及阻尼矩阵,.,动力学方程质量矩阵及阻尼矩阵,.,特征值问题,.,纽马克法,动力响应和逐步积分法,.,纽马克法,.,综合纽马克法计算步骤,1）初始计算,（1）形成刚度矩阵K、质量矩阵M、组逆矩阵C,（2）获得初始值,（3）选择步长参数和，并计算下列有关常数,（4）形成“刚度”矩阵,（5）分解矩阵,.,2）对于每个时间步长进行下列计算,（1）计算时刻的“载荷”矢量,（2）解矩阵方程求时刻的位移,（3）计算时刻的加速度、速度,综合纽马克法计算步骤,.,Whatisamodalanalysis?,Amodalanalysisisusedtodeterminethenaturalfrequenciesandmodeshapesofastructure.Thenaturalfrequenciesandmodeshapesareimportantparametersinthedesignofastructurefordynamicloadingconditions.ThenaturalfrequenciesandmodeshapesarealsorequiredifyouwanttodoaspectrumanalysisoraHarmonicResponseAnalysisortransientanalysis.,.,Whatisamodalanalysis?,Theequationforastaticanalysis:Theequationforadynamicanalysis:Theequationforamodalanalysis:,.,Theprocedureforamodalanalysis,Theprocedureforamodalanalysisconsistsoffourmainsteps:Buildthemodel.Applyloadsandobtainthesolution.Expandthemodes.Reviewtheresults.,.,BuildtheModel,Whenbuildingyourmodel,rememberthesepoints:1.Onlylinearbehaviorisvalidinamodalanalysis.Ifyouspecifynonlinearelements,theyaretreatedaslinear.Forexample,ifyouincludeacontactelement,itsstiffnessarecalculatedbasedonitsinitialstatusandneverchange.2.Materialpropertiescanbelinear,isotropicororthotropic,andconstantortemperature-dependent.YoumustdefinebothYoungsmodulus(EX)(orstiffnessinsomeform)anddensity(DENS)(ormassinsomeform)foramodalanalysis.Nonlinearpropertiesareignored.Ifapplyingelementdamping,youmustdefinetherequiredrealconstantsforthespecificelementtype(COMBIN7,COMBIN14,COMBIN37,andsoon).,.,ApplyingLoadsandObtaintheSolution,DefineAnalysisTypeandOptionsOption1:NewAnalysisOption2:AnalysisType:ModalOption3:Mode-ExtractionMethod(Chooseoneoftheextractionmethodslistedbelow).1.BlockLanczosmethod(default)2.Subspacemethod3.PowerDynamicsmethod4.Reduced(Householder)method5.Unsymmetricmethod6.Dampedmethod7.QRDampedmethodFormostapplications,youwillusetheBlockLanczos,subspace,reduced,orPowerDynamicsmethod.Theunsymmetric,damped,andQRdampedmethodsaremeantforspecialapplications.,.,ApplyingLoadsandObtaintheSolution,Option4:NumberofModestoExtractOption5:NumberofModestoExpandOption6:Pre-stressEffectsCalculationApplyLoadsTheonlyloadsvalidinatypicalmodalanalysisarezero-valuedisplacementconstraints.(Ifyouinputanonzerodisplacementconstraint,theprogramassignsazero-valueconstrainttothatDOFinstead.)Otherloadscanbespecified,butareignoredSolve,.,ReviewtheResults,Resultsfromamodalanalysis(thatis,themodalexpansionpass)arewrittentothestructuralresultsfile,Jobname.RST.Resultsconsistof:Naturalfrequencies,ExpandedmodeshapesRelativestressandforcedistributions.YoucanreviewtheseresultsinPOST1,thegeneralpostprocessor.,.,CaseNo.10:Amodalanalysisofacantileverbeam(模态分析实例均匀直杆的纵向固有频率分析),图10-1所示为一根长度为L的等截面(0.01x0.01m2)直杆，杆长L=0.1m,一端固定，一端自由。已知杆材料的弹性模量E=21011N/m2，密度=7800kg/m3。要求计算直杆纵向振动的固有频率。,图10-1均匀直杆的固有频率分析,.,Analysisprocedure,1.ChangeJobname2.Definetheelementtype3.Definematerialproperties4.BuildtheelementmodelCreateBlockGeneratevolumemesh5.ApplyconstraintstothemodelApplieddisplacementboundarycondition6.ObtainsolutionSpecifyanalysistypeandoptionsSolve7.ReviewtheresultsListthenaturalfrequenciesAnimatethefivemodeshapes,.,Pleaselookatthedetailsintextofthiscasestudy。(请看教案中的具体操作）,.,Conclusion（总结）,Mainmenu(1)PREP7:ElementtypeMaterialpropertiesModeling:createVolumeMeshing(2)SolutionDefineanalysistypeApplyloadsSolve,Mainmenu:(3)POST1ResultsSummeryReadresultsUntilityMenu:(1)PlotCtrls:animite,.,Commandflow,/CLEAR/FILNAME,EXAMPLE10/PREP7ET,1,SOLID186MP,EX,1,2E11MP,PRXY,1,0.3MP,DENS,1,7800BLOCK,0,0.01,0,0.01,0,0.1LESIZE,1,3LESIZE,2,3LESIZE,9,15MSHAPE,0MSHKEY,1VMESH,1FINISH,/POST1SET,LISTSET,FIRST/VIEW,1,-1/REPLOTPLDIANMODE,10,0.5,0SET,NEXTPLDIANMODE,10,0.5,0FINISH,/SOLUANTYPE,MODALMODOPT,LANB,5MXPAND,5DA,1,UZDA,3,UYDA,5,UXSOLVESAVEFINISH,.,Hom