弹性力学基础及有限元法-12

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 displacements u 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 YoumustdefinebothYoung smodulus 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 stressEffectsCalculationApplyLoadsTheonly loads validinatypicalmodalanalysisarezero 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 2 1011N 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 BuildtheelementmodelCreateBlock Generatevolumemesh5 ApplyconstraintstothemodelApplieddisplacementboundarycondition6 ObtainsolutionSpecifyanalysistypeandoptions Solve7 ReviewtheresultsListthenaturalfrequenciesAnimatethefivemodeshapes Pleaselookatthedetailsintextofthiscasestudy 请看教案中的具体操作 Conclusion 总结 Mainmenu 1 PREP7 ElementtypeMaterialpropertiesModeling createVolume Meshing 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