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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籌 嘗Hist前ory筐ofE椅last抗icit編y們1.2剝 研 棟Appl幅icat裹ions駐of弱Elas寺tici染ty叉2何.千 如Elas臥tici謹(jǐn)tyo延fSo寨lids廣2.1昆 呆 良Defi揮niti皂ono連fEl吊asti傻city貿(mào)2.2值 堵 能Two懷Phys侍ical元Ori鵲gins市of崗Elas添tici休ty期2.3井 脈 蘆Tens絞orD鄙escr菊ipti喝ono侮fEl透asti剛city偶2.4即 雄 撿Phys宇ical爬Fou屑ndat腸ion綁ofE旋last檔icS勝ymme娃try掩3該.謎 厚Fiel粒dEq澆uati竟ons逃ofE涼last披icit差y-勻Diff測eren灰tial號For糟mula襯tion遲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蔥atib現(xiàn)ilit詠yEq熄uati姓on盆3.3囑 榜 銹Fiel集dEq馳uati疏ons虧ofD截ynam按icE順last柏icit梳y切3.4您 瑞 鍋Quas府i-st償atic慣Fie仿ldE汽quat革ions攻3.5佩 載 找Cons廳trai疤nts疼3.6介 艱 告Boun脂dary勾Con甲diti稿ons裳3.7棗 嘆 壇Form顫ulat目ion姓ofE礎(chǔ)last廚icit疫y繳4.努 請 犬Pris年mati龍c鐘Rods腳4.1塘 贏 省Form細(xì)ulat戚ion建for籃Pris孤mati默cRo換ds悉4.2搜 征 鑄Unia敲xial材Ten差sion呈and馬Pur崗eBe取ndin概g故4.3繼 瓶 淘Corr宜ecti腐veS刊olut改ion田(Sai牢ntV授enan駝tDe艇cay)么4.4護 哪 夾Free仙Tor蝶sion延of禾Pris處mati賓cRo俱ds竊4.5啊 嗚 鑄Inve峰rse泉and館Semi量-inv脆erse港Sol鴉utio調(diào)ns臭4.6班 捐 掀Form絲ulat綱ion蠅ofA舞nti-企plan軟ePr沾oble章ms點5透.躬 劇Plan壇ePr槍oble根ms描–詳The羞ory謝and百Meth楚ods域5.1巖 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華Disl冰ocat侵ion紙Loop羨s哥Revi塊ew在Refe榴renc漢es立陸明萬、蝦羅學(xué)富《父彈性理論敘基礎(chǔ)》,駝清華大學(xué)殿出版社墓,溫1990努J.R燕.Ba因rber斧,El技asti執(zhí)city蕩,Kl僚uwer怖Aca復(fù)demi梁cPu萌blis刪her,驢Bos鋸ton,役199百2直S.P.微Tim樓oshe倘nko父and檢J.N.嫌Goo蠢dier擁,Th淺eory連of逗Elas壇tici勇ty,筐3聯(lián)rd撈Edi蝕tion呈,Mc水Graw肢-Hil晚l,1膨969洲H.L百ove,要AT洲r(nóng)eat青ise慣ont騰heM擊athe仔mati述cal首Theo芒ryo竭fEl嶄asti茶city弊,4t掌hDo浙ver家Edit稍ion,墾194膊4俗A.E寧.腹Gree激nan榜dW.塌Zer組na,鋼Theo棟reti侄cal丘Elas擋tici虎ty,蘭Oxfo接rdU阻nive圾rsit臣yPr施ess,旨196辟8恐N.I衰.Mu艘skhe封lish授vi框l鉛li,堪Some債Bas誼icP親robl成ems脊inM剖athe飽mati如cal姓Theo坡ryo陳fEl良asti黑city窗,No嫌ordh戴off跟Int.奴,19海77錦M.E磚.Gu攻rtin蟲,Co閱ntin允uum崗Mech見anic區(qū)s,A捕cade姨mic廢Pres煤s,1要981幕J.E擱.Ma殿rsde夜nan碼dT.皂J.狂R.H馬ughe封s,M姓athe術(shù)mati腹cal喪Foun迎dati紡ons廟ofE籠last掌icit強y,P刊rent各ice寬Hall孕Inc倉,19短83矮武際可先,榮力學(xué)史佩,香重慶熱大學(xué)周出版社昌,肌1999證楊衛(wèi),宏時微觀斷裂工力學(xué)妄,被199館5捎,國防工暫業(yè)出版社葡,捕第派1蛙章鵲W.Y鄉(xiāng)ang護and赤W.B.柄Lee啄,Me才sopl蜓asti雨city師and性Its恢App階lica騾tion耳s,1馳993,狼Spr妄inge嚇r-Ve基rlag肢T.C奇.T.瞎Tin勉g,A聽niso泛trop慧icE形last壇icit響y:T珠heor潔yan慎dAp批plic預(yù)atio洞ns,盛1996嚴(yán),Ox寬ford墓Uni洲vers白ity枯Pres扣s.衡Intr花oduc備tion旬1.1貪 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(1943)andwasdevelopedindependently,andputtopracticaluseoncomputers,from50sto60s,bytheaeronauticalengineersM.J.Taylor,RayW.CloughandothersinUnitedStates,thecivilengineersJ.H.ArgyrisandO.C.ZienkiewiczinBritain,andthemathematicianFENGKanginChina.Themethodoriginatesinsolvingelasticityproblems,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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