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APPLIEDELASTICITY華中科技大學(xué)力學(xué)系

1Introduction1.1CONTENTSOFTHEORYOFELASTICITY1.2SOMEIMPORTANTCONCEPTSINTHEORYOFELASTICITY1.3BASICASSUMPTIONS1.1CONTENTSOFTHEORYOFELASTICITYPurposeThetheoryofelasticity,oftencalledelasticityforshort,isthebranchofsolidmechanics.Purposeistoanalysethestressesanddisplacementofstructuralormachineelementswithintheelasticrangeandtherebytocheckthesufficiencyoftheirstrength,stiffnessandstability.Althoughthispurposeisthesameasthatofstudyingmechanicsofmaterialsandstructuralmechanics,thesethreebranchesofsolidmechanicsdodifferfromoneanotherbothintheobjectsstudiedandinthemethodsofanalysisused.Mechanicsofmaterialsdealsessentiallywiththestressesanddisplacementsofastructuralormachineelementintheshapeofabar,straightorcurved,whichissubjectedtotension,compression,shear,bending,ortorsion.Structuralmechanics,onthebasisofmechanicsofmaterials,dealswiththestressesanddisplacementsofastructureofabarsystem,suchasatrussorarigidframe.DifferentTheobjectsstudiedAstothestructuralelementswhicharenotintheformofabar,suchasblocks,plates,shells,dams

andfoundations,theyareanalysedonlyinthetheoryofelasticity.ThemethodsofanalysisusedAbarshapeelementsubjectedtoexternalloads:MechanicsofmaterialsandelasticityElasticity:doesnotneedthoseassumptions.Thustheresultsobtainedaremoreaccurateandmaybeusedtochecktheapproximateresultsobtainedinmechanicsofmaterials.Mechanicsofmaterials:someassumptionsareusuallymadeonthestrainconditionorthestressdistribution.Theseassumptionssimplifythemathematicalderivationtoacertainextent,butofteninevitablyreducethedegreeofaccuracyoftheresultsobtained.Inme予ch響an版ic積s頁of福m旦at雅er臂ia蓮ls,做it膊i剃s雄as呀su做me晴d談th動(dòng)ata榆pl譯an主e槽se侵ct外io質(zhì)n竟of碑t緞he鏟b宗ea默m退re虧ma淘in蒙s階pl覽an似e蹤蝶af望te梯r施be窩nd悔in褲g.窗Th釘is企a今ss脆um雄pt便io制n企le錦ad膽s蚊to樂t慎he意l屈in扎ea灘r子di勿st絞ri知bu流ti憐on鋤o銜f紫be上nd祖in部g宣st解re頑ss燙es草.nnFo美r陸ex駛am掘pl面e,鬼t拐he駁p手ro出bl餐em偏o傍f酒be改nd騰in鉤g甩of曬a僵s通tr員ai壁gh嫌t蓋be極am川u姜nd要er樹t煌ra兩ns聽ve胸rs銀e啊lo盞ad喝s:Inth弟e父th填eo共ry灑o克f南el肅as矛ti粒ci命ty,息ho輛we酬ve因r,敵o久ne鬼c怖an冶s道ol租ve反t崖he榜p闊ro覺bl培em敘w巖it繳ho駕ut拐t磨hi爛s美as定su匯mp澤ti健on增a雅nd句p泰ro駱ve普t袋ha吧t較if堤t糞he幣d沒ep拿th撲o約f木th康e任be陽am擴(kuò)i注s柔no誰t壁mu連ch附s銜ma槍ll射er陽t殿ha儀n雄th直e化sp亮an雖l回en禾gt奶h,宋t斥he庸s潔tr察es塵s菊di境st招ri信bu堵ti嫩on攻w儉il宣l更be姓f惡ar抱f首ro爆m摘li顛ne損ar蜘v槽ar貸ia初ti五on控,襖an核d布th叨e焰ma揀xi艇mu劃m仇te處ns乘il短e夕st擴(kuò)re哀ss僵i盟s災(zāi)se雅ri銷ou們sl慈y猴un繪de臺(tái)rv迫al吉ue仿d賊inme閉ch慣an刷ic茅s賺of征m仍at雨er丘ia皮lsMut素ua斷l(xiāng)米in逮fi永lt謊ra景ti秩onTh創(chuàng)e盼ut償il挪iz雄at族io較n郵of節(jié)v桑ar斜io乞us職m枕et居ho笨ds茶o洪f牛an脆al椒ys冷is惜i怒n餡st俱ru鮮ct蔑ur探al損m防ec門ha鍵ni充cs漂g灶re甲at全ly辰s睬tr瘋en廊gt起he壩ne盈d箭th作e郊th遷eo尋ry牌o游f菊el劇as輩ti愈ci假ty似a籠nd危e鎖na繡bl綁ed段e雖ng崖in場(chǎng)ee脈rs刻t邪o席ob沙ta初in自t尼he風(fēng)s蛇ol洋ut魔io超ns詠o洽f繩ma復(fù)ny謎c巖om者pl拒ic脅at欠ed駱p聚ro草bl巧em功s割in莊e卡la廊st謠ic憤it懼y.Fo來r槐ex制am槍pl過e,增u司si吹ng羽t環(huán)he丸f塊in嫂it蒸e支el糟em賞en吳t辟me襲th偽od找,兩we謙c鍬an困s哥ol揉ve蟻a碰p謙ro奇bl臘em偏i古n殲el價(jià)as創(chuàng)ti杠ci泊ty襪b左y廈th孟edi到sc分re茄ti尿za枯ti影onof喚t牌he豈b青od遍y調(diào)co瘋nc場(chǎng)er穗ne束d旦an車d注th驚en齊t安he賴a宰pp南li虛ca紫ti遵on塌o絞f祥th蹤蝶e原di剖sp拳la揮ce逢me柜nt撤m鋤et項(xiàng)ho雅d,怎t擠he逃f征or筐ce壯m皆et得ho豬d,鄭o屑r叔th瓣e程mi少xe熄d蛙me袋th扛od衰i篇n哥st粉ru辭ct舊ur跨al思m室ec蚊ha添ni叮cs晌.Mo嚼re嗎ov詳er元,鴉in啄t方he跑d壩es散ig削n傷of類a文s揀tr翼uc曠tu撞re跪,荷we結(jié)c奧an疊u駐ti膚li頌ze設(shè)t蠟he拌d蹦if育fe革re船nt竄b驕ra烘nc歡he餅s駁of呀s碗ol揉id晶m本ec界ha訂ni描cs霜f爐or鵝d剝if蒸fe美re鐵nt尼m亦em步be螺rs癥o惰f將th臣e昨st殼ru往ct無ur玻e,掀a秒nd冤e確ve猜n疼fo留r嶄di椅ff扎er愉en題t蘋pa趣rt麥s姿of餅a抵s津in蠅gl矛e館me乳mb泳er貢,跨to削g猜et著t改he撿m蘿os標(biāo)t倒sa耀ti重sf廊ac天to慢ry塊r腥es糧ul招ts竹w育it瓦h(yuǎn)純th腹e駁le鉛as靠t滿am割ou冬nt者o櫻f司wo伯rk逝.We茶s饅ho孔u(yù)l刪d飾no度t嶼pa章y玩to香o勉mu屬ch費(fèi)a組tt押en膨ti恒on摩t胳o挪th艱e細(xì)fu盜zz覽y咱an顧d刑te堪mp掩or品ar聞y昆di訓(xùn)vi旋di焦ng排l暮in耽es臘b像et娛we斬en繼t耀he沉t萍hr宴ee貫c刪ou闊rs盒es番i懂n寫so制li開d陣me配ch暫an遇ic閘s.采O計(jì)n焰th慰e遷co望nt程ra乘ry高,刊we囑s光ho粗ul援d田no驚te蓋a閉ll廚t敲he掀p重os魂si謊bi戚li肢ti士es侄o景f鋼th撥e逼jo太in矩t良ap良pl屢ic不at夸io震n嫂of舒t準(zhǔn)he塔t款hr堵ee克c茅ou弟rs肝es柄.1.幼2SO脫ME柏I欄MP膜OR是TA笑NT耳C露ON溉CE字PT褲S驗(yàn)IN手T遇HE滴OR胖Y嗓OF示E刪LA榜ST銅IC殿I(lǐng)T瞧Yex御te削rn屠al秤f莫or表ce將s,柱s罪tr謊es鍋se廊s,稻d獵ef朵or污ma有ti澡on敬s仆an文d捧di咳sp漁la絞ce弱me事nt駝sBodyforces:externalforces,ortheload,distributedoverthevolumeofthebody.Surfaceforces:externalforces,ortheload,distributedoverthesurfaceofthebodyExternalforces(ortheloads):1.Surfaceforces:Suchasthepressureofonebodyonanotherorhydrostaticpressure2.Bo倡dy瓣f罵or哭ce絹s:Su紡ch姻a失s轎gr買av辛it毅at從io敏na龍l夏fo肢rc淘es奪,彎or帳i員ne酸rt需ia付f鍋or我ce憐s胖in秒t賴he浪c嶼as潮e見of榆bo鴿dy停i所n繪mo撲ti嫁on3.In央di盾ca賺ti蘋on森o未f裁ex書te址rn柜al攏f嘆or制ce躁s:a.Surfaceforcesxlim

S0yzoYXZ

S

FF:theintensityofsurfaceforceatPTheprojectionsofF

onthex,y,zaxesaredenotedbyX,YandZrespectivelyandcalledthesurfaceforcescomponentsatP.Su勁ch濱a捉c眨om外po劍ne兼nt草i肉s溜co喉ns捧id喘er努ed掉p弱os納it吐iv克e蝕or箏n廳eg慢at描iv份e詠ac鏟co拳rd晃in斜g鋤as責(zé)i獅t患ac是ts榴i理n屋th竊e茂po租si晴ti牛ve適o曾r呀ne紅ga膨ti周ve騙d睜ir春ec蘆ti否on若o棄f稼th腰e紋co竟or輩di工na緞te姑a樂xi拜s.It彈s旗di龍me滿ns拾io漁n裕is芹[嘩fo碑rc褲e]/[le莖ng米th羞]2.b.

Bodyforceslim

V0yzoYXZ

V

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onthex,y,zaxesaredenotedbyX,YandZrespectivelyandcalledthebodyforcescomponentsatP.2)In介te甲rn財(cái)al兄f租or終ce鼠s(in肝te陪rn電al濁f晴or冷ce剪s盆at爛a漫c絹er鉗ta仍in皆p飽oi缸nt還a隸t屈P)Th忽e略st番re候ss落i胸s祝re見so妹lv科ed哭i障nt記o挪a種no偶rm消al標(biāo)c邪om錯(cuò)po桿ne田nt

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ca感l(wèi)l渴edth評(píng)e天sh捏ea拳ri樓ng民s等tr父es征s.S:thestressonthesectionmnatpointPanditsdirectionisthelimitingdirectionof

Q.lim

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A

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