英文彈性力學(xué)之緒論

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 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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(wàn)、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(chóng),Co閱ntin允uum崗Mech見(jiàn)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(qiáng)y,P刊rent各ice寬Hall孕Inc倉(cāng),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(shí)微觀斷裂工力學(xué)妄，被199館5捎，國(guó)防工暫業(yè)出版社葡，捕第派1蛙章鵲W.Y鄉(xiāng)ang護(hù)and赤W.B.柄Lee啄,Me才sopl蜓a(bǔ)sti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(tīng)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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an睜icia錦nan檔dge啞olog航ist童e度(雕1968知).T漏hec終riti裹c(diǎn)al額para項(xiàng)mete徹rsi府nfr薄actu逮rem才echa怠nics醉,su賊cha沿sth腦een拜ergy余rel剪ease昌rat眠e親G服,th綢est宣ress上int協(xié)ensi提t(yī)yf混acto釘r慈K弱,an灘dth付eJ-本inte小gral泥俯J拜are花nam耍eda凳fter國(guó)Gri煩ffit煩h,I撫rwin間and渡Ric濤e,r擇espe脫ctiv閥ely.皇AnotherimportantdevelopmentwhichnowformsthebasicsolutionstrategyinengineeringistheinventionoftheFiniteElementMethod(FEM).ThismethodwasoutlinedbythemathematicianRichardCourant(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