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ElasticityABriefLectureNote(Incomplete)GuidelinesThelectureswillbegiveninChinese,buttheLectureNoteswillbewritteninEnglish(well,ratherinformalEnglish).ThebilingualapproachisanticipatedtooffersurprisingadvantagessuchasloweringthelanguagebarrierandgettingfamiliarwithEnglishvocabulariesthatwillbeindesperateuseintheyearstocome.Ialsoforeseethepotentialtoexpandthelecturenotestoaformallywritingtextbook.Thecontentsareselectedtohighlightthephysicalinsightsofelasticity,topromotethereadabilitybyfrequentlycitingthehistoriceventsandperspectives,enumeratingthenewapplicationsofelasticity,andaddressingthenewresearchthrustsofelasticityinthepast50years.Thelectureswillbegivenmainlyinatraditionalwayofchalksplusblackboard.ForacoursewithaperfectlogicsystemsuchasElasticity,Icannotfindabetterwayotherthantheoldtradition.Lettheimaginativemindsofthestudentsfollowthetraceofachalktiponblackboard.Besidelectures,thecourseshouldbecomplementedthroughintensivereadings.Twelvereferencesareappointed.Discussionsamongstudentsabouttheircontentsareencouraged.Thehomeworkwilltake20%oftheoverallscore,themid-termexamanother20%,whilethefinalexam(openbook)willtaketherest60%.Forthosestudentswhoareeagertoexploremorechallengingissuesofelasticity,atotalof10to15advancedproblemswillbeproposed.Astudentmaysolveanyoneoftheseproblems,writeintheformofareport,andsubmitittotheinstructor.Thesereportswillbegradedbytheinstructor,andthosescoredhigherthan90/100canbeusedassubstitutesfortheirfinalexams.Onlythereportsthatsolvetheproblemearliestamongtheentireclassorsolvetheprobleminauniqueapproacharequalifiedasthesubstitutesofthefinalexams.WhoCares?Elasticityisthemostimportantcourseinthefieldofsolidmechanics,andalsotopsthelistforthekeycoursesinabroaderareaofengineeringmechanics.Elasticitygoesalongwayinitsapplications,spanninglengthscalesfromnanometersforacarbonnanotubetokilometersofageologicalformation.Withoutthemasteryofelasticity,youareincompetentindoinganyseriousworksasaprofessionalinengineeringmechanics,evennotrankedasacapableengineer.Besideitscontents,elasticityisacoursethatexemplifiesthebeautyofmathematicalphysics.Manyconceptsandmethodsinmodernscienceandengineeringareoriginatedfromelasticity.However,elasticityisalsoaquitedifficultcoursetolearn,pleasebepreparedforit.Youdefinitelyneedtospend5timesasthelecturehourstograspthematerials.Withoutcompetitors,itwillbeTheCoursethatburdensyouthemostinthissemester.AsoneoftheelitecoursesinTsinghuaUniversity,weareplanningafeastofmaterialsthatwouldbeunparallelinthemostuniversitiesintheworld(theexceptionsareMITandEcolePolytechnique).SomeofthecontentspreparedinthislecturenotewillsurpassthecoverageofthetextbookbyMingwanLUandXuefuLUO.Pre-requestThestudentsarerequiredtohavefirstcoursesonCalculus,MathematicalPhysics(includingtheintroductiononComplexAnalysis,OperationalCalculus,andPDE)andStrengthofMaterials.WealsoassumeyouhaveapreliminaryknowledgeonContinuumMechanics,familiarwiththeconceptsofstress,strainandbalancelaws.Theknowledgeontheindicialnotationoftensorsisalsoassumed.Forthosestudentswhoarelackofthispreliminaryknowledge,wesuggestthemtoreadthefirstfourchaptersandtherelevantappendicesinthetextbookbyLuandLuo.ContentsIntroduction跌1.1筹 尝Hist前ory筐ofE椅last抗icit编y们1.2剥 研 栋Appl幅icat裹ions驻of弱Elas寺tici染ty叉2何.千 如Elas卧tici谨tyo延fSo寨lids广2.1昆 呆 良Defi挥niti皂ono连fEl吊asti傻city贸2.2值 堵 能Two怀Phys侍ical元Ori鹊gins市of岗Elas添tici休ty期2.3井 脉 芦Tens绞orD鄙escr菊ipti喝ono侮fEl透asti刚city偶2.4即 雄 捡Phys宇ical爬Fou屑ndat肠ion绑ofE旋last档icS胜ymme娃try掩3该.谜 厚Fiel粒dEq浇uati竟ons逃ofE凉last披icit差y-匀Diff测eren灰tial号For糟mula衬tion迟3.1寸 刃Bala等nce弟Equa迎tion逐sof爽Mom糊entu灰man俊dMo耳ment限3.2雅 常 采Comp葱atib现ilit咏yEq熄uati姓on盆3.3嘱 榜 锈Fiel集dEq驰uati疏ons亏ofD截ynam按icE顺last柏icit梳y切3.4您 瑞 锅Quas府i-st偿atic惯Fie仿ldE汽quat革ions攻3.5佩 载 找Cons厅trai疤nts疼3.6介 艰 告Boun脂dary勾Con甲diti稿ons裳3.7枣 叹 坛Form颤ulat目ion姓ofE础last厨icit疫y缴4.努 请 犬Pris年mati龙c钟Rods脚4.1塘 赢 省Form细ulat戚ion建for篮Pris孤mati默cRo换ds悉4.2搜 征 铸Unia敲xial材Ten差sion呈and马Pur岗eBe取ndin概g故4.3继 瓶 淘Corr宜ecti腐veS刊olut改ion田(Sai牢ntV授enan驼tDe艇cay)么4.4护 哪 夹Free仙Tor蝶sion延of禾Pris处mati宾cRo俱ds窃4.5啊 呜 铸Inve峰rse泉and馆Semi量-inv脆erse港Sol鸦utio调ns臭4.6班 捐 掀Form丝ulat纲ion蝇ofA舞nti-企plan软ePr沾oble章ms点5透.躬 剧Plan坛ePr枪oble根ms描–详The羞ory谢and百Meth楚ods域5.1岩 幼 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oblems,andexpandsbeyondimaginationtoformthebasicbuildingblocksofcomputationalmechanics.ThenewestapplicationsofFEMincludematerialsmicrostructures,biologicalstructuresandmedicalprocedures.Thetheoreticalaspectofelasticityhasalsobeenenrichedintherecentyears.Theclassicaldevelopmentofelasticityneverfullyconfrontedtheproblemoffiniteelasticstraining,inwhichmaterialfiberschangetheirlengthsbyotherthanverysmallamount.Thewidespreaduseofnaturalpolymericmaterials,suchasnaturalrubbersputtheanalysisoffinitedeformationelasticityinlargedemand.TheworksofBritish-bornengineerandappliedmathematicianRonaldS.Rivlin(1960)forfinitedeformationelasticityprovidedsolutionsfortension,torsion,bendingandinflectionatextremelylargedeformation.Healsoparticipatedinintroducingthetensorrepresentationtheorem(Rivlin-Ericksentheorem)forisotropicelasticity.Theso-calledtheMooney-Rivlintheorygivesafairdescriptionforthesubjectofrubberelasticity.Anotherimportantarenaforthedevelopmentofelasticityistargetedforanisotropicmaterials.Inthisarea,theworksofJ.D.Eshelby,S.G.LehnitskiiandA.N.Stroh(1959-1962)madearevolutionarychangeofthefield.ThetragiclifeofStrohandhisbrilliantcontributioninashortprofessionalperiodoftenyearswasprescribedintheeulogyinthecomprehensivebookofT.C.T.Ting(1996).Thescopeofthislecturenoteisunfortunatelynotabletocoverthissubject

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