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MIT 2 002 - Structures­ Linear Analysis

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cover.pdfpreface.pdftoc.pdflec01.pdflec02.pdflec03.pdflec04.pdflec05.pdflec06.pdflec07.pdflec08.pdflec09.pdflec10.pdflec11.pdflec12.pdf_____tt~---Massachusetts InstituteofTechnologyMITVideoCOurseVideoCourseStudyGuideFiniteElementProceduresforSolidsandStructures-LinearAnalysisKlaus-JOrgenBatheProfessorofMechanical Engineering,MITPublishedbyMITCenterforAdvanced Engineering studyReorderNo672-2100PREFACETheanalysisof complexstaticanddynamicproblemsin-volvesinessencethreestages: selectionofa mathematicalmodel, analysisofthemodel,andinterpretationoftheresults.Duringrecentyearsthefinite elementmethodimplementedonthedigitalcomputerhasbeenusedsuccessfullyinmodelingverycomplexproblemsinvariousareasofengineeringandhassignificantlyincreasedthepossibilitiesfor safeandcost-effectivedesign. However,theefficientuseofthemethodisonlypossibleifthebasicassumptionsoftheproceduresemployedareknown,andthemethodcanbeexercisedconfidentlyonthecomputer.Theobjectiveinthiscourseistosummarizemodernandeffectivefinite elementproceduresforthelinearanalysesofstaticanddynamicproblems. Thematerialdiscussedinthelecturesincludesthebasicfinite elementformulations em-ployed,theeffectiveimplementationof theseformulationsincomputerprograms,andrecommendationsontheactualuseofthemethodsinengineeringpractice.Thecourseisintendedforpracticingengineersandscientistswhowanttosolveprob-lemsusingmodemandefficientfinite elementmethods.Finiteelementproceduresforthenonlinearanalysisofstructuresarepresentedinthefollow-up course, FiniteElementProceduresfor SolidsandStructures- NonlinearAnalysis.Inthis studyguideshortdescriptionsofthelecturesandtheviewgraphsusedinthelecturepresentationsaregiven.Belowtheshortdescriptionofeachlecture,referenceismadetotheaccompanyingtextbookforthecourse: FiniteElementProceduresinEngineeringAnalysis, byK.J. Bathe, Prentice-Hall, Inc., 1982.Thetextbooksectionsandexamples, listedbelowtheshortdescriptionofeachlecture, provideimportantreadingandstudymaterialtothecourse.ContentsLecturesl.Some basicconceptsofengineeringanalysis1-12.Analysis of continuous systems; differentialandvariational formulations2-13.Formulation of the displacement-based finite elementmethod_3-14.Generalizedcoordinatefinite element models4-15.Implementation of methods incomputerprograms;examples SAp, ADINA5-16.Formulationandcalculation of isoparametric models6-17.Formulation of structural elements7-18.Numerical integrations, modeling considerations8-19.Solution of finite element equilibriumequations in static analysis9-110.Solution of finite element equilibriumequations in dynamic analysis10-11l.Mode superposition analysis; time history11-112.Solution methods for calculations offrequenciesandmodeshapes12-1SOMEBASICCONCEPTSOFENGINEERINGANALYSISLECTURE 146 MINUTESI-ISolIebasicccnaceplsofeugiDeeriDgualysisLECTURE 1 Introduction tothecourse. objective oflecturesSomebasicconceptsofengineeringanalysis.discreteandcontinuoussystems.problemtypes:steady-state.propagationandeigen-valueproblemsAnalysisofdiscretesystems:exampleanalysisofaspringsystemBasicsolutionrequirementsUseandexplanationofthemoderndirectstiff-nessmethodVariationalformulationTEXTBOOK: Sections:3.1and3.2.1. 3.2.2. 3.2.3. 3.2.4Examples: 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7. 3.8. 3.9.3.10. 3.11. 3.12. 3.13. 3.141-2Somebasicconcepts01engineeringaulysisINTRODUCTION TO LINEARANALYSIS OF SOLIDSANDSTRUCTURES• The finite element methodisnowwidely used for analysisofstructuralengineering problems.•'ncivil, aeronautical, mechanical,ocean, mining, nuclear, biomechani-cal,... engineering• Sincethefirst applications twodecades ago,- we now see applicationsin linear, nonlinear, staticand dynamic analysis.- various computer programsare available andinsignificantuseMyobjectiveinthis setoflecturesis:•tointroducetoyou finiteelement methods forthelinear analysisofsolidsand structures.["Iinear" meaning infinitesi-mally small displacements andlinear elastic materialproeer-ties (Hooke's law applies)j•toconsider-theformulationofthefiniteelement equilibrium equations-thecalculationoffiniteelement matrices- methods for solutionofthegoverning equations- computer implementations.todiscuss modern and effectivetechniques, and their practicalusage.1·3SomebasicconceptsofengineeringanalysisREMARKS• Emphasisisgiventophysicalexplanationsratherthanmathe-matical derivations• Techniques discussed arethoseemployedinthecomputerpro-gramsSAPandADINASAP==Structural Analysis ProgramADINA=AutomaticDynamicIncremental Nonlinear Analysis• These few lectures represent a verybrief andcompactintroductiontothefieldoffiniteelementanalysis•Weshall followquitecloselycertain sectionsinthebookFinite Element Proceduresin Engineering Analysis,Prentice-Hall, Inc.(by K.J. Bathe).Finite Element Solution ProcessPhysical problemEstablish finiteelement...- -~modelofphysicalproblem1I:I,-__S_ol_v_e_th_e_m_o_d_el__I~~- - -iL-_I_n_te_r.;..p_re_t_t_h_e_re_s_u_lt_S_....JRevise (refine)themodel?1-4SolIebasicconceptsofengiDeeringanalysis10ft15ftI12at15°,.Analysisofcooling tower.K~~~~~-~,-Fault\\(norestraint assumed)Altered' gritE=toEc.,Analysisofdam.1·5SomebasicconceptsofengineeringanalysisB.t-WoE~~;;C=-------_........FFiniteelementmesh fortireinflation analysis.1·6SolDebasicconceptsofengineeringanalysisSegmentofa spherical coverofalaser vacuum target chamber.l,WppPINCHED CYLINDRICALSHELLOD;:...,...----.---~~~~~~CEtW-50P-100-150•16x16MESH-200-DISPLACEMENT DISTRIBUTION ALONGDCOFPINCHED CYLINDRICAL SHELL•16x16MESH-0.2Mil""=0.1~CBENDING MOMENT DISTRIBUTION ALONG DC OFPINCHED CYLINDRICAL SHELL1-7SoBlebasicconcepts01engineeringanalysisIFiniteelement idealizationofwindtunnelfordynamic analysisSOME BASIC CONCEPTSOF ENGINEERINGANALYSISTheanalysisofanengineeringsystemrequires:- idealizationofsystem- formulation of equili-briumequations- solution ofequations- interpretation ofresults1·8SYSTEMSSomebasicconceptsofengineeringanalysisDISCRETEresponseisdescribedbyvariablesatafinitenumberofpointssetofalge-braic--equationsCONTINUOUSresponseisdescribed byvariablesatan infinitenumberofpointssetofdiffer-entialequationsPROBLEM TYPES ARE• STEADY-STATE(statics)• PROPAGATION (dynamics)• EIGENVALUEFor discrete and continuoussystemsAnalysisofcomplex continu-ous system requires solutionofdifferential equations usingnumerical proceduresreductionofcontinuoussystemtodiscrete formpowerful mechanism:thefinite elementmethods,implementedondigitalcomputersANALYSIS OF DISCRETESYSTEMSSteps involved:- system idealizationinto elements-


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