南航07 09年有限元

1、NANJINGUNIVERSITYOFAERONAUTICSASTRONAUTICSFINITEELEMENTMETHODINMECHANICALENGINEERINGFinalExamination:June212007Time:10:0012:001.Pleasewrite5specialtermsinfiniteelementmethod.(5points)五個(gè)專用術(shù)語，可以寫很多，單元，節(jié)點(diǎn)，網(wǎng)格，形函數(shù)，剛度矩陣，質(zhì)量矩陣等等

2、Elementnodegridshapefunctionstiffnessmatrixmassmatrixstraindisplacementmatrix2.Whatarebasicstepsinthefiniteelementmethod(10points)這個(gè)書上有。43頁(yè)6條。（lecture2（3）18頁(yè)）1)elementtypesdiscretize選擇單元對(duì)物體離散2)adisplacementfunction構(gòu)造位移函數(shù)

3、3)Definethestressdisplacementstressstrainrelationships確定應(yīng)力位移和應(yīng)力應(yīng)變關(guān)系4)Derivetheelementstiffnessmatrixequations推導(dǎo)單元?jiǎng)偠染仃嚭头匠?)Assembletheelementequationstoobtaintheglobaltotalequationsintroduceboundarycondition組裝單元方程形成總方程，并引

4、入邊界條件6)Solvefthegeneralizeddisplacements求解位移3.Whataretheprinciplesofderivationofelementstiffnessequation這個(gè)在24頁(yè)，虛功原理（lecture1第31頁(yè)）Ifthesolutionoftheproblemthedeflectionisperturbedbyaddingavirtualdefmationcompatiblewiththe

5、supptconditionsthenthewkdonebytheinternalstressesalongthevirtualstrainsequalstheexternalwkdonebytheappliedfcesalongthevirtualdefmations.(如果位移的解受到滿足邊界支撐條件虛位移的擾動(dòng)，則內(nèi)應(yīng)力在虛應(yīng)變上做的內(nèi)功（虛應(yīng)變能）等于外力在虛位移上做的功)Derivethestiffnessequationof

6、barelement(Fig.1).(20points)這個(gè)也在24頁(yè)（lecture2第2427頁(yè)）ijfiuifjujAELL—lengthA—crosssectionalareaE—elasticmodulusuiuj—nodaldisplacementsfifj—nodalfcesFig.14.WhatarepropertiesofshapefunctionsFtheelementshowninFig.2determineN1N

7、2intermsof??.(20points)Note:LagrangianInterpolation:Fig.2()()0()0ijmiijmiijmfNfatnodeifatothernodes?????????????????????????（插值法見lecture5（1）2023頁(yè)）這個(gè)給孔哥講過，找直線。（找直線法，具體見lecture5（1）24、25頁(yè)）設(shè)1(1)(1)(1)NA?????????然后將1點(diǎn)坐標(biāo)（11）代入