彈性力學(xué)課件二三

9SolutionofSpatialProblems9.1Solutionintermsofdisplacements9.2Infiniteelasticlayerundergravityanduniformpressure9.6Concentratednormallodeonboundaryofasemi-infinitebody9.10Solutionintermsofstresses按劇應(yīng)裹力志求助解盤空奏間高問尊題9源.庸1轎0S蹦o牌l嘆u形t口i醋o(hù)住n以i蔬n哭t演e辰r蒸m農(nóng)s統(tǒng)o濾f氧s躺t恩r節(jié)e芬s誤s糞e釋s取應(yīng)力分量為基本未知量，從15個(gè)基本方程中消去位移分量和應(yīng)變分量，得出只包含6個(gè)應(yīng)力分量的方程Takethesixstresscomponentsasthebasicunknownfunction，formulateasystemofdifferentialequationsandboundaryconditionscontainingthestresscomponentsonly，solvefortheseunknownfunctionsandtherebyfindthestraincomponentsbythephysicalequationsandthenthedisplacementcomponentsbythegeometricalequations.平衡方程中只含應(yīng)力分量，應(yīng)保留從幾何方程和物理方程中導(dǎo)出補(bǔ)充方程Sincethedifferentialequationsofequilibriumdonotinvolvedisplacementsandstrains,itisnecessaryonlytoeliminatethedisplacementandstraincomponentsinthegeometricalandphysicalequationsT位h胞e僻g贊e掌o血m玩e麗t斬r舅i頃c苗a滾l猜e洋q載u舌a彩t蓮i艇o扎n想s好,即同理變形協(xié)調(diào)方程，也是一組相容方程推刻導(dǎo)納另浪一案組膜相脈容彩方刊程末：因?yàn)椋核裕和恚哼@本是屋另臣一違組鳳相暫容患方獄程通過以上相同的步驟，可以導(dǎo)出無數(shù)的相容方程，都是應(yīng)變分量應(yīng)該滿足的，但如果六個(gè)應(yīng)變分量滿足了上述兩組相容方程，就可以保證位移分量的存在，即可以由幾何方程求位移分量Bysimilarmanipulations,wecanderivemanyothercompatibilityequationswhichthestraincomponentsmustsatisfy.However,itcanbeprovedthatthetwoEqs.aresufficienttoensuretheexistenceofdisplacementcomponentscorrespondingtoagivensetofstraincomponents.將物理方程代入上述相容方程—消除應(yīng)變分量，得到只含應(yīng)力分量的相容方程：Substitutingthephysicalequationsintothecompatibilityequationsabove,weobtainthecompatibilityequationsintermsofstresscomponents.利輪用抄平饒衡嶼微售分痕方堆程款化圖簡(jiǎn)燙上急述腐六役個(gè)喉相耳容疤方駁程唯后圖得雹：B橫y乳u滋s老i賊n臨g蘆t矩h損e挪d卵i妻f執(zhí)f右e摧r夾e薦n間t四i立a誘l拘e撕q名u拌a淋t略i勉o梅n慢so聾f探e魂q苦u窗i胡l食i醫(yī)b貨r般i樹u副m牙,嫁w胳e旋c管a智n喉s備i慘m椒p匹l閣i孕f皺y鄉(xiāng)豐t吸h汗eE承q零s.上述六個(gè)方程就是密切爾相容方程TheMichell’scompatibilityequations.在皂體辯力雙為扣零強(qiáng)或陳常悼體騾力燭情非況臘下還，料相小容教方倉(cāng)程臂可達(dá)以掃簡(jiǎn)芽化裹為憐：扁（舉拉易密題方愛程痰）W獵h巡壽e宰n渣b勁o丑d接y加f低o肝r炎c偷e狂s董a動(dòng)r烘e肝c楊o到n兆s淡t燃a北n萌t擁o譜r覽e宮q存u忙a閃l覺t唇oz淋e跳r遇o畏,慰T協(xié)h脹eM箱i說c晶h葬e聞l區(qū)l虧’柄sc獻(xiàn)o嗚m他p初a勒t艘i胃b糾i點(diǎn)l充i英t餡y鋸e滑q籮u多a虜t榆i擱o設(shè)n勢(shì)s湊r析e燒d母u餡c訂e尋t黨o宴t價(jià)h泉eB胳e戰(zhàn)l碎t止r崇a祥m懶i戒’醋sc忍o鄙m肉p時(shí)a艇t悠i帖b申i腥l股i卵t灘y昌e卷q隙u接a厘t序i嗽o稿n堂s翻.T刷h繪u玩s歸引納膽：按屈應(yīng)綱力紐奉求往解牽空悠間臘問旅題嗚時(shí)僑，凍要智使號(hào)6燈個(gè)薯應(yīng)納力置分限量谷滿鳥足腸平丟衡剪微宏分撲方液程租和為上跡述積六劉個(gè)盡相婆容蛋方錫程玩，仆并見在原邊廈界港上勝滿唇足抹應(yīng)緞力花邊仁界崗條盲件若貞應(yīng)框力啞分夕量漁的糾表態(tài)達(dá)褲式買是x預(yù)、覆y治、蔑z的吼線楚性端函撕數(shù)毛，民則蔑相尺容且方主程作總猾能搶滿填足肥，陡對(duì)附單纏連包域道的碧應(yīng)量力馬邊杯界她問車題太，嬌若萌體筍力歡為惠常驅(qū)量策，齡則鳥能幕滿