雨课堂学堂在线学堂云《Finite Element Method (FEM) Analysis and Applications（清华）》单元测试考核答案

第1题在分析MH17客机遭外力作用而解体时，主要应考虑何种力学行为FortheanalysisoftheMH17crash,whichmechanicalbehaviourshouldbeconsidered?A质点masspointB刚体

rigidbodyC变形体

deformablebody第2题变形体的特殊情况可以包含刚体特性

Underspecialcircumstances,canrigidbodiesbeconsideredasdeformablebodies?A是

correctB不是incorrect第3题地球相对于太阳的运动可以简化为Theearth'smotionrelativetothesuncanbesimplifiedasA质点masspointB刚体rigidbodyC变形体deformablebody第1题在试样的单向拉伸试验中，单向应力定义为Duringanuniaxialtensiontest,theuniaxialstressisdefinedasA作用力×横截面面积force×crosssectionalareaB横截面面积/作用力crosssectionalarea/forceC作用力/横截面面积force/crosssectionalarea第2题在试样的单向拉伸试验中，单向应变定义为Duringanuniaxialtensiontest,theuniaxialstrainisdefinedasA总伸长量/横截面面积totalelongation/crosssectionalareaB总伸长量/试样原长totalelongation/originallengthofthespecimenC试样原长/总伸长量originallengthofthespecimen/totalelongation第3题在试样的单向拉伸试验中，定义应力及应变的目的是消除几何因素的影响，即应力可以消除试样的____因素的影响，即应变可以消除试样的____因素的影响。Whenanuniaxialtensiontestiscarriedout,thedefinitionofstressandstrainisnecessarytoeliminategeometryeffectsonthespecimen.Whichinparticularmeans,thatstresscaneliminatetheeffectofthe①,andstraincaneliminatetheeffectofthe②。正确答案：:横截面面积crosssectionalarea正确答案：:长度length1.3Test第1题在微分方程求解的试函数方法中，最后得到的关于待定系数的方程是Whenutilisingthetrialfunctionmethodforsolvingdifferentialequations,theundeterminedcoefficientoftheresultingequationisA积分方程integralequationB微分方程differentialequationC线性方程组linearequations第2题在微分方程求解的差分格式中，边界条件只影响对应边界的一个节点Whenutilisingthedifferenceschemetosolvedifferentialequations,boundaryconditionsonlyaffectthenodeonthecorrespondingboundaryA是correctB否incorrect第3题在微分方程求解的试函数方法中，对残差进行加权时，其加权函数一般都取为Whenusingthetrialfunctionmethodwithweightedresidualstosolvedifferentialequations,generallytheweightingfunctionisA三角函数TrigonometricB基底函数BasisfunctionC常数ConstantD多项式Polynomial1.4Test第1题在一个函数的全域展开逼近中，所选取的基底函数应该定义在Intheglobalexpansionapproximationofafunction,theselectedbasisfunctionshouldbedefinedinA无要求nopreferenceB全域fulldomainC子域subdomain第2题在一个函数的子域展开逼近中，所选取基底函数在相邻子域之间，往往是Insubdomainexpansionapproximationofafunction,theselectedbasisfunctionsbetweenadjacentsubdomains,generallyareA不连续的discontinuousB高阶导数不连续continuousbutdiscontinuousonhigherorderderivatives第3题在一个函数的子域展开逼近中，为提高逼近精度，最好的方法是Insubdomainexpansionapproximationofafunction,inordertoimprovetheaccuracyofapproximation,thebestwayistoA细分更多子域subdividemoresubdomainB适当增加从低阶到高阶的子域基底函数appropriatelyincreasethesubdomainbasisfunctionsfromlowerleveltohigherC适当细分子域+适当增加从低阶到高阶的子域基底函数appropriatelysubdividemoresubdomains+appropriatelyincreasethesubdomainbasisfunctionsfromlowerleveltohigher1.5Test第1题对于一个复杂几何域的2D问题，获得全域的基底函数的方式一般为Fora2Dproblemwithcomplexgeometricdomains,thegeneralmethodtoobtainthefulldomainbasisfunctionsisA全域的解析函数analyticfunctionsoffulldomainB子域拼接函数subdomainfunctionsplicingC不能给出cannotobtain第2题对于具有复杂几何域的力学问题，划分子域后的边界一般都是Formechanicalproblemswithcomplexgeometrydomains,generalboundryaftersubdomainsdemarcationisA函数连续的function-continuousB锯齿状的Serrated第3题若一个问题，既可以采用全域函数逼近，又可以采用子域函数拼接，两者的计算量Forthesameproblem,usingfulldomainfunctionapproximation,orusingthesub-domainfunctionsplicing,comparethecalculationamountoftwomethodA相当thesameB前者大theformerislargerC后者大thelatterislarger1.6Test第1题以下关于有限元方法中单元的描述正确的是WhichofthefollowingdescriptionsofthefiniteelementmethodisthecorrectA单元具有标准化及规范性ElementisstandardizedandnormativeB单元的几何形状的尺寸是特定的ThegeometryandsizeoftheelementisaspecificC单元是参数化的Elementisparameterized正确答案：AC第2题将复杂几何域划分为子域，其任意的子域就是单元Dividecomplexgeometrydomainintosubdomains,thenanyofitssub-domainsiselemenA是correctB否incorrect1.7Test第1题有限元的数学力学原理产生较早，而有限元的真正使用却较晚，其原因是Mathematicsmechanicsprincipleoffiniteelementgeneratemuchearlierthantherealuse,thereasonisA以前不进行结构分析canhardlydostructuralanalysisinearliertimeB计算机出现较晚ComputerappearedlaterC有限元原理太深奥Finiteelementtheoryistooesoteric第2题以下软件哪些具有有限元分析功能WhichofthefollowingsoftwarecandofiniteelementanalysisAPhotoshopBSketchupCANSYSDPowerpointEABAQUS正确答案：CEHomework第1题如图所示长度为l的简支梁，中间一部分受分布载荷p，其边界条件为：Aloadwiththedistributionpisappliedtothemiddlepartofasinglesupportedbeamwiththelengthlandhasthefollowingboundaryconditions则满足全部边界条件的试函数是：Whichofthefollowingtestfunctionsdoessatisfytheboundaryconditions：ABCD正确答案：AC第2题求，a1=____，a2=____，a3=____，a4=____Adifferentialequationisgivenas：dudx+A=0，x∈[0,1],whereAisaconstantandtheboundaryconditionisu|x=0=2A。Utilisethedifferencemethodtosolvethisproblem,wherethedomainx∈[0,1]isdividedintothreesegmentsandusethesegmentandnodenumbersasshowninthepicturebelow.Thedisplacementvaluesfornodesu1∼u4aregivenasu1=a1A,u2=a2A,u3=a3A,u4=a4A.Ifl=1,whatare:[填空5正确答案：:2正确答案：:5/3正确答案：:4/3正确答案：:1第3题α1=____,β1=____,α2=____,β2=____,α3=____,β3=____Singlevariablefunctionf(x)=27x3+9x2+3x+1,x∈[0,1]。Piecewiselinearfunctionareusedtoapproximatethefunction.definationdomainisdividedintothreesections,pleasefillfactorsofeachlinearfunction.：x∈[0,1/3),g1(x)=α1x+β1x∈[1/3,2/3),g2(x)=α2x+β2x∈[2/3,1],g3(x)=α3x+β3α1=β1=α2=β2=α3=β3=正确答案：:9正确答案：:1正确答案：:33正确答案：:-7正确答案：:75正确答案：:-352.1Test第1题（多选）以下表述不正确的是(MultipleChoice)Whichtwoofthefollowingdescriptionsareincorrect.A作用在弹簧两端的力是一对作用力与反作用力Forcesappliedatbothendsofaspringisapairofactionandreactionforce.B在进行组装时，需要对弹簧平衡方程的矩阵形式进行扩充，扩充后方程仍是线性方程组Whenassemblingtheexpandedspringequilibriumequationsinmatrixform,aftertheaugmentation,theequationsarestilllinear.C在进行组装时，仅需对K矩阵进行对应位置上元素进行叠加WhenassemblingthestiffnessmatrixK,oneneedsonlytosuperimposethedifferentelementsonthecorrespondingposition.正确答案：AC第2题弹簧的刚度系数为__________。Thestiffnesscoefficientofaspringis__________。A力/伸长量force/elongationB伸长量/力elongation/force2.2Test第1题弹簧与杆单元的系数转换关系为TherelationshipforthestiffnesscoefficientbetweenaspringandabarelementisAk=ElABk=EAlCk=lEA第2题（多选）关于弹簧单元和杆单元的以下表述正确的是(MultipleChoice)Whichtwoofthefollowingdescriptionsforaspringelementandabarelementarecorrect.A杆单元在受力后的伸长量，与杆件的原长无关Theelongationofbarelementwhenforceisappliedisunrelatedtotheoriginallength.B通过系数转换后，杆单元的表达与弹簧单元表达是一样的Aftertransformation,thestiffnesscoefficientofbarelementisthesamewithspringelement.C将杆单元的力学方程写成矩阵形式，它是单元规范性及标准化的一种表现形式It'snormativeandstandardtowritethemechanicalequationofbarelementintomatrixform.正确答案：BC2.3Test第1题对于杆单元，若进行平面直角坐标系之间的变换，需要_____个独立的角度来描述。Asforabarelement,whencarryingoutatransformationfroma2DCartesiancoordinatesystemtoanother2DCartesiancoordinatesystem,howmanyindependentangle(s)areneccassarytodescribeththecompletetranformation?____A1B2C3D4第2题对于杆单元，若进行空间直角坐标系之间的变换，需要_____个独立的角度来描述。Asforabarelement,whencarryingoutatransformationfroma3DCartesiancoordinatesystemtoanother3DCartesiancoordinatesystem,howmanyindependentangle(s)areneccassarytodescribeththecompletetranformation?____A1B2C3D4第3题杆单元的局部坐标就是ThelocalcoordinatesforabarelementareA沿杆的轴线方向alongtheaxialdirectionofthebarB沿x方向alongthexdirection第4题杆单元的局部坐标变换后，在整体坐标系下节点位移的各个位移分量可由局部坐标系上的节点位移投影得到。Afterthecoordinatetransformation,thedisplacementofeverynodedescribedinglobalcoordinatescanbeobtainedthroughtheprojectionofthedisplacementsdescribedinthelocalcordinatesA是correctB否incorrect2.4Test第1题节点的编号必须按照1,2,3…的次序，不可以跳编。Thenumberingofnodesmustbe1,2,3…,soitisnotpossibletoskipnumbersA正确correctB错误incorrect第2题节点的编号号码与单元的编号号码各自是独立的。Thenumberofanodeandthenumberofaelementareassignedseperately.A正确correctB错误incorrect3.1Test第1题以下说法中错误的是Whichofthefollowingdescriptionsis<b>incorrect</b>.A弹性力学中变形体材料的基本假设的要点是简化对材料行为的描述Thesimplificationforthedescriptionofthematerialbehavioristhekeypointinthebasicassumptionsfor

elasticmechanicsB弹性力学中变形体材料的基本假设一般有5个TherearefivebasicassumptionsfordeformablematerialinelasticmechanicsC材料力学与弹性力学的相同点都是要研究变形体的力学行为ThefocusofmaterialmechanicsandalsoofelasticmechanicsistostudythemechanicalbehaviorofdeformablebodysD微小体元是采用特征建模方式进行描述的Microvolumeelementsaredescribedwiththehelpofthecharacteristicmodelingmethod第2题哪个是采用特征建模方式进行描述的Whichofthefollowingelementsisdescribedwiththehelpofthecharacteristicmodelingmethod?A微小面元microsurfaceelementB微小体元microvolumeelementC梁beam3.2Test第1题指标记法中自由指标的下标的取值变化是Thefreeindexvaluewhileusingtheindexnotationchanges(accordingto)A针对坐标轴coordinateaxisB1、2、…、nC任意的arbitraril第2题在指标表达式的一项中，哑指标意味着在同一项内指标的出现次数是Accordingtotheindexnotation:adummyindexindicates,thatthesameindexappears_____time(s)AoneBtwoCthree第3题二阶张量σ=[123245356]按照Voigt规则写成一维列阵是Whenthissecond-ordertensorσ=⎡⎣⎢123245356⎤⎦⎥

istransformedintoanone-dimensionalarrayusingVoigtrule,theresultisAσ=[123456]TBσ=[132456]TCσ=[145236]TDσ=[146532]T3.3Test第1题（多选）以下说法中正确的是Whichofthefollowingdescriptionsis(are)<b>correct</b>A复杂形状变形体问题有边界条件，而简单形状变形体没有Problemsfordeformablebodyswithcomplexshapeshavealwaysboundaryconditions,butsimpleshapeddeformablebodysdon'thave.B处理复杂形状变形体时，采用“内部+表面”的建模思路The"internal+surface"modelingideaisusedwhendealingwithcomplexshapeddeformablebodys.C任意一个面的受力状态，都可以分解为正应力及剪应力ThestressonanysurfacecanbedecomposedintonormalstressandshearstressD由于体积力是作用于变形体内部，因此体积力是内力Sincethebodyforcesactinsidethedeformablebody,thebodyforceisconsideredasaninternalforce.正确答案：BC3.4Test第1题在应力随坐标增量的Taylor级数展开中，对于平衡方程来说，要取到AsforTaylorseriesexpansionoftheincrementalstressaccordingtothecoordinate,theequilibriumequationsshouldatleastincludeaA0阶增量项0-orderincrementaltermB1阶增量项1-orderincrementaltermC2阶增量项2-orderincrementalterm第2题平衡方程研究的是_____之间关系的方程式。Equilibriumequationsdescribetherelationshipbetween_____.A应变和位移strainanddisplacementB应力和位移stressanddisplacementC应力和体力stressandbodyforcesD应力和应变stressandstrain第3题对于平面微元，平衡方程有Fora2Ddifferentialelement,thereare_____equilibriumequations.A2个BthreeCfour3.5Test第1题几何方程研究的是_____之间关系的方程式。Theso-calledgeometricequationsdescribetherelationshipbetween_____.A应变和位移strainanddisplacementB应力和体力stressandbodyforcesC应力和位移stressanddisplacementD应力和应变stressandstrain第2题（多选）以下说法中正确的是(multiplechoice)Whichofthefollowigdescriptionsare<b>correct</b>?A由位移分量可以无条件地、唯一确定出应变分量Straincomponentscanbeunconditionallyanduniquelydeterminedbythedisplacementcomponents.B由应变分量可以无条件地、唯一确定出位移分量Displacementcomponentscanbeunconditionallyanduniquelydeterminedbythestraincomponents.C应变εxx的物理含义是微元的单位长度的线段在x方向上的位移增量Strainεxxindicatesthedisplacementincrement.Thedisplacementincrementisthedifferentialunitlengthinxdirection.D分量形式的剪切应变γij是指标形式的剪切应变εij的12Thecomponentformoftheshearstrainmatrixγijisequivalenttotheindexformεijdevidedbytwo.正确答案：AC第3题应变γxy的物理含义是原微元的直角在变形后Thegeometricmeaningofstrainγxyis____oftheoriginaldifferentialelement.A与x轴的夹角变化theanglechangebetweentheelementandthex-axisB与y轴的夹角变化theanglechangebetweentheelementandthey-axisC与x及y轴的总夹角变化

thesumofanglechangebetweentheelementandbothaxis3.6Test第1题物理方程研究的是_____之间关系的方程式。Hooke'slawdescribestherelationshipbetween_____.A应变和位移strainanddisplacementB应力和体力stressandbodyforcesC应力和位移stressanddisplacementD应力和应变stressandstrain第2题（多选）以下说法正确的是(multiplechoice)Whichofthefollowingdescriptionsare<b>correct</b>A在各向同性材料的物理方程中独立的材料系数有2个Foranisotropicmaterialaretwoindependentmaterialcoefficientsnecassarytofullydescribethestress-strainrelations(Hooke'slaw).B物理方程的性质是微分方程Thestress-strainrelationsaredifferentialequations.C应用Voigt规则，可以将张量形式的物理方程写成矩阵形式Thetensorformofthestress-strainrelationscanbetransformedintomatrixformbyusingtheVoigtrule正确答案：AC3.7Test第1题以下说法中正确的是Whichofthefollowingdescriptionsis<b>correct</b>A自由边界条件是力边界AconstraintlessboundaryconditionisalsoaforceboundaryconditionB位移边界与力边界可以重叠DirichletandforceboundaryconditionsmayoverlapC力边界上的平衡方程为微分方程Theequilibriumequationsforforceboundaryconditionsaredifferentialequations.4.1Test第1题以下关于平面问题的说法中正确的是Whichofthefollowingdescriptionsis<b>correct</b>A平面应力问题中沿厚度方向的正应力和正应变都为零Fora2Dproblem,thenormalstressandnormalstraininthicknessdirectionarebothzero.B当平面变形体仅有刚体位移时应变分量可以不为零Fora2Dproblem,whenonlytherigidbodydisplacementisappliedthedisplacementcomponentcannotbezero.C平面应变问题中沿厚度方向的正应力一般不为零Fora2Dstrainproblem,thenormalstressinthicknessdirectionisgenerallynotzero.D当平面变形体中仅有刚体位移时，有u为零，v为零Fora2Dproblem,uandvarezeroifonlytherigidbodydisplacementisapplied.第2题关于平面应力及平面应变问题，以下说法错误的是Whichofthefollowingdescriptionsfora2Dstressproblemand2Dstrainproblemis<b>incorrect</b>?A两类问题在平面内的基本变量的形式相同Thebasicvariableshavethesameform.B两类问题的物理方程不同Thestress-strainrelationsaredifferent.C两类问题的z方向（厚度方向）特征不同Thethickness（inz-direction)isdifferent.D两类问题的几何方程不同Thestrain-displacementrelationsaredifferent.4.2Test第1题以下关于简单拉杆问题的说法错误的是Whichofthefollowingdescriptionsforasimplebaris<b>incorrect</b>A用弹性力学方法求解，完整描述它的变量有3大类，方程有3大类，边界条件有2大类Thefulldescriptionofabarprobleminelasticmechanicsincludethreecategoriesofvariables,threecategoriesofequationsandtwocategoriesofboundaryconditions.B用弹性力学方法求解，简单拉杆问题是1D问题，描述它的方程都是线性代数方程Theequationstodescribeasimplebarprobleminelasticmechanicsarelinearalgebraicequations.C采用材料力学的方法处理简单拉杆问题是，需假设应力是均匀的Whenutilizematerialmechanicstosolvethesimplebarproblem,itisassumedthatstressisuniformdistributed.4.3Test第1题以下说法中错误的是Whichofthefollowingdescriptionsis<b>incorrect</b>A平面纯弯梁的中性层是伸长量为零的层Theelongationoftheneutrallayeriszeroduringthe2Dbending.B平面纯弯梁，其截面上的弯矩是由微段的力矩平衡方程得到的Fora2Dbendingproblem,thebendingmomentonthecrosssectionisobtainedbythetorquebalanceequationforaninfinitesimalsegment.C平面纯弯梁，对截面上应变沿高度方向分布的假设是线性变化Fora2Dbendingproblem,it'sassumedthatthestrainforacrosssectionalongtheheightdirectionis

lineardistributedinlengthdirection.4.4Test第1题空间问题中独立的应变协调方程应该有____个。Thenumberofindividualstraincompatibilityequationsfora3Dproblemare空间问题剪应力互等方程有____个。Thenumberofshearstressequations(itisassumedtobereciprocal),fora3Dproblemis空间问题中，由3个位移分量，可以唯一确定出____个独立的应变分量。Fora3Dproblem,_____individualstraincomponentscanbedeterminedbythethreedisplacementcomponents.第2题描述空间弹性问题的描述的力学变量中独立的位移分量的个数____Forthemechanicaldescriptionofa3Delasticproblem,thenumberofindividualdisplacementcomponentsare独立应力分量的个数thenumberofindividualstresscomponentsare____独立应变分量的个数thenumberofindividualstraincomponentsare____4.5Test第1题一阶张量即矢量，它的不变量就是TheinvariantforafirstordertensorvectoristheAx方向的分量xcomponentBy方向的分量ycomponentCz方向的分量zcomponentD矢量的模theEuclideanvectornorm5.1Test第1题以下哪项是解析方法的难点？Whichofthefollowingisthemostdifficultaspectoftheanalyticmethod？A复杂几何域及边界条件处理困难ComplexgeometriesanddifficultiesindealingwithboundaryconditionsB方程的阶次较高ThehighorderofequationsC方程中的变量较多ToomanyvariablesD结果精度较低Thelowaccuracyoftheresult第2题以下哪项是Galerkin法和残值最小二乘法的共同点？WhichofthefollowingaspectsdotheGalerkinmethodandtheleastsquaresmethodhaveincommon.A权函数相同ThesameweightfuntionsB残量加权积分为零TheintegraloftheresidualweightisequaltozeroC求解精度与试函数选择无关SolvingprecisionandtrialfunctionsareirrelevantD待定系数求解为线性方程组Linearequationsaresolvedtodeterminethecoefficients.5.2Test第1题试函数方法中的基底函数是_________。ThebasisfunctionofthetrialfunctionmethodisA已知的knownB未知的unknown第2题基底函数前面的系数是_________。ThebasisfunctionofthetrialfunctionmethodisA已知的knownB未知的unknown第3题一个二阶微分方程为：d2wdx2−q=0边界条件为：w|x=0=0,w|x=L=0以下哪项不能作为此问题加权残值法中的试函数？Asecondorderdifferentialequationsisgivenasfollows:d2/wdx2−q=0Theboundaryconditionsare:w|x=0=0,w|x=L=0Whichofthefollowingfunctionsisnotsuitableforthechoiceofthetrialfunction?Aw~=cx(L−x)Bw~=csin⁡πxLCw~=c(1−cos⁡πxL)Dw~=c1sin⁡πxL+c2sin⁡3πxL5.3Test第1题加权残值法的积分是计算Theintegraloftheweightedresidualmethodcalculates:A全域上的基底函数之和ThesumofbasisfunctionsonthewholedomainB全域上的试函数之和ThesumoftrialfunctionsonthewholedomainC全域上的误差之和Thesumoferrorsonthewholedomain第2题一般弹性问题，若以位移为基本变量，加权残值法中位移试函数的要求，正确的是Forageneralelasticproblem,ifthedisplacementisthevariable.Whichofthefollowingrequirementforthetrialfunctioniscorrect①要求四阶可导mustbefourthorderderivable②要求二阶可导mustbesecondorderderivable③要满足所有边界条件satisfytheboundaryconditions④只需满足位移边界条件satisfythedisplacementboundaryconditionsA①③B①④C②③D②④5.4Test第1题虚功原理是针对一个TheprincipleofvirtualworkisappliedtosolvetheproblemofA力的平衡系统forcebalancedsystemB非平衡系统unbalancedsystemC都可以bothoftheabove第2题平面弯曲梁求解的虚功原理中，虚位移表现在Whensolvingaplanarbendingbeamproblembyusingtheprincipleofvirtualwork,thevirtualitemistheA自变量上variableB基底函数上basisfunctionC基底函数前的待定系数上coefficientofthebasisfunction第3题加权残值法所用试函数的导数阶次要求是虚功原理中的______。Therequirementofthederivativeforthetrialfunctionusedinmethodofweightedresidualsis_____astherequirementfortheprincipleofvirtualworkA1倍(相同)thesameB2倍twiceC1/2half5.5Test第1题变分过程中的泛函极值实质上是以________为基本变量的复合函数求导过程。Findingthefunctionmaximumviausingvariationalmethodsconsider________asbasicvariables.A自变函数IndependentvariablefunctionB坐标变量Coordinatevariables第2题平面弯曲梁求解的最小势能原理中，降低试函数的导数要求是通过分部积分来实现导数的转移的。Asforaplanarbendingbeamproblem,thepricipleofminimumpotentialenergylowerstherequirmentforthederivative

ofthetrialfunctions.ThisisduetotheuseoftheintegrationbypartswhichlowersthederivativesA是correctB否incorrect第3题在针对平面梁弯曲问题最小势能原理的变分极值过程中，需要进行______次分部积分。Asforaplanarbendingbeamproblem,applyingthevariationalmethodofminimumpotentialenergy,______timesintegationbypartsisneeded.A1B2C3D4第4题如图所示的4弹簧系统受两个集中载荷的作用，q1,q2,q3分别为节点1，2，3的位移，则系统总势能为Afourspringelementsystemwithtwoconcentratedforcesappliedisgivenasshown.q1,q2,q3

arethedisplacementsfornode1,2and3.ThepotentialenergyforthewholesystemisAΠ=12k1q12+12k2q22+12k3q12+12k4q32BΠ=12k1q12+12k2q22+12k3q12+12k4q32−F1q1−F3q3CΠ=12k1(q1−q2)2+12k2q22+12k3(q1−q2)2+12k4(q3−q1)2DΠ=12k1(q1−q2)2+12k2q22+12k3(q1−q2)2+12k4(q3−q1)2−F1q1−F3q35.6Test第1题在针对一般弹性问题最小势能原理的变分极值过程中，所采用的Gauss-Green公式实质上与平面梁弯曲问题中的分部积分相对应Foranelasticproblem,duringthevariationoftheprincipleofminimumpotentialenergy,weusetheGauss-Greentheorem,whichcorrespondstotheintegrationbypartsoftheplanarbendingproblem.A是correctB否incorrect第2题一般弹性问题的最小势能原理中，降低试函数的导数要求是通过Gauss-Green公式来实现导数的转移的Foranelasticproblem,theprincipleofminimumpotentialenergylowerstherequirementforderivativesofthetrialfunctions.ThisisdoneviatheuseoftheGauss-Greentheoremtotransformthederivatives.A是correctB否incorrect第3题关于弹性问题最小势能原理的特点，不正确的是WhichofthefollowingdescriptionsabouttheprincipleofminimumpotentialenergyisincorrectA试函数为许可位移场TrialfunctionhastosatisfytheadmissibledisplacementfieldB试函数只需满足位移边界条件TrialfunctiononlyneedstosatisfythedisplacementboundaryconditionC对梁的弯曲问题，试函数最高阶导数为二阶Forabendingbeamproblem,thehighestorderofthetrialfunctionissecondorder.D对一般弹性问题，试函数最高阶导数为二阶Forageneralelasticproblem,thehighestorderofthetrialfunctionissecondorder.6.1Test第1题基于试函数的加权残值法及能量原理所得到的方程是：TheequationswhicharebasedontrialfunctionsandareobtainedbyusingtheweightedresidualmethodorbyusingminimumpotentialenergymethodareA常微分方程ordinarydifferentialequationsB偏微分方程partialdifferentialequationsC线性代数方程linearalgebraicequationsD非线性代数方程non-linearalgebraicequations第2题针对基于全域的经典方法与基于分段（片、块）的有限元方法，以下哪些说法是正确的：(MultipleChoice)Concerningtheclassicmethodandthefiniteelementmethod,whichofthefollowingdescriptionsarecorrect?A经典方法的基底函数构造简单Thebasedfunctionsfortheclassicmethodarebuildsimple.B有限元方法的基底函数可以规范化Thebasedfunctionsforthefinitemethodcanbenormalized.C相比经典方法，有限元方法的逼近效果在总体上适应性较好Comparedwiththeclassicmethod,thefiniteelementmethodgenerallydoesabetterapproximation.正确答案：BC6.2Test第1题针对有限元方法中的自然离散与逼近离散，以下哪些说法是正确的：(MultipleChoice)Whichofthefollowingstatementsconcerningthenaturaldiscretizationandapproximatediscretizationarecorrect:A杆、梁、板结构是离散体结构bars,beamsandplatesarealldiscretizedstructuresB自然离散方法一般具有较高的计算精度，甚至可以得到精确解thenaturaldiscretizationhasaveryhighaccuracy,itisevenpossibletoobtaintheexactsolutionC逼近离散方法的计算精度受到节点数量、单元类型等多方面因素的影响theaccuracyoftheapproximatediscretizationisinfluencedbythenumberofnodes,theelementD逼近离散方法的适用性不如自然离散方法theapplicabilityoftheapproximatediscretizationisnotasgoodasthenaturaldiscretization正确答案：ABC6.3Test第1题在单元研究步骤中，单元的位移场、应变场以及应力场函数均需要通过______来表达。Thedisplacementfield,thestrainfieldandthestressfieldareallexpressedbythe________A节点力nodeforceB节点位移nodedisplacementC节点应力nodestressD节点应变nodestrain第2题在组装得到总体刚度方程后，若某节点某方向上的节点位移分量已知，则该节点该方向上的节点力分量必然未知。Whenbuildingtheglobalstiffnessequationitistruethat,ifthedisplacementforanodeisknown,thenodeforceappliedonthisparticularnodemustbenotknown.A是correctB否incorrect6.4Test第1题有限元方法需要先构造单元内的试函数，再拼接为全域的试函数。Thefiniteelementmethodfirstneedstobuildthetrialfunctionwithinanelement,andthenthetrialfunctionforthewholedomainisputtogether.A是correctB否incorrect第2题以下哪种说法是错误的：Whichofthefollowingstatementisincorrect:A使用加权残值法求解问题时，试函数需高阶连续且满足所有边界条件whenusingtheweightedresidualmethod,thetrialfunctionneedstobecontinuouslyandofhigh

order,thetestfunctionalsohastosatisfyallboundaryconditionsB加权残值法针对的是问题的原控制方程theweightedresidualmethoddealswiththegoverningequationoftheproblemC使用基于能量原理的试函数方法求解问题时，试函数需满足力边界条件whenusingtrialfunctionsbasedonenergyprinciplestosolveproblems,thetrialfunctionhas

tosatisfytheforce'sboundaryconditionsD有限元方法是基于能量原理的试函数方法thefiniteelementmethodisbasedonthetrialfunctionsforenergyprinciples7.1Test第1题平面杆结构中的杆单元在局部坐标系下有____个自由度，在整体坐标系中有____个自由度。Aplanarbarelementhas___degreesoffreedominthelocalcoordinatesystemand___degreesoffreedomintheglobalcoordinatesystem.A1,2B2,2C2,4D2,67.2Test第1题以下哪些类型的载荷是杆单元不能承受而梁单元能够承受的？Whichofthefollowingtypesofloads,abarelementcannotendurebutabeamelementcan?A拉压tensionandcompressionB扭转torsionC垂直均布载荷verticaluniformloadD中部集中载荷concentratedloadinthecentralsection正确答案：CD第2题单元位移模式选取时，待定系数的个数与自由度的个数的关系是Whenthedisplacementmodelfortheelementisselected,whatistherelationshipbetweenthenumberofundeterminedcoefficientsandthenumberofdegreesoffreedom?A待定系数的个数与自由度的个数相同thenumberisthesameB待定系数的个数须小于自由度的个数thenumberofundeterminedcoefficientsissmallerC待定系数的个数须大于自由度的个数thenumberofundeterminedcoefficientsislargerD待定系数的个数与自由度的个数无关thereisnorelationshipbetweenbothnumbers7.4Test第1题平面梁单元中的转角分量在局部及整体坐标系中都是相同的,不需进行坐标变换Theangularcomponentsforaplanarbeamelementarethesameinlocalandglobalcoordinates,sothereisnoneedtotransformthem.A是correctB否incorrect第2题而空间梁单元中的关于转角自由度同样也不需要坐标变换Thatisalsotrueforspatialbeamelements(3D),theangularcomponentsdonotneedtobetransformed.A是correctB否incorrect第3题空间梁单元坐标转换矩阵T的维数是ThedimensionofthetransformationmatrixTforaspatialbeamelementisA2×6B6×2C6×6D12×127.5Test第1题计算梁单元分布力的等效节点载荷的原理是基于TheprincipleforthecalculationoftheequivalentnodeloadofabeamelementwithadistributedloadisbasedontheequivalentoftheA静力等效staticforceB外力功等效externalforceC应变能等效strainenergyD总势能等效totalpotentialenergy第2题由梁单元分布力得到的等效节点载荷的集中力是满足静力平衡等效的TheconcentratedforceobtainedfromtheequivalentnodalloadforabeamelementwithdistributedforcesatisfiesthestaticequilibriumA是correctB否incorrect第3题得到的集中力矩也是满足静力平衡等效的TheobtainedconcentratedmomentalsosatisfiesthestaticequilibriumA是correctB否incorrect8.1Test第1题关于平面3节点三角形单元，其位移场函数为______，应变场函数为______。Regardingaplane3-nodetriangularelement,itsdisplacementfieldis____functionandthestressfieldis____function.A完全线性函数，完全线性函数acompletelinear,

acompletelinearB不完全线性函数，完全线性函数notacompletelinear,

acompletelinearC完全线性函数，常数acompletelinear,aconstantD不完全线性函数，常数notacompletelinear,

aconstant第2题平面3节点三角形单元拥有______个自由度，其单元刚度矩阵的维数是______。Regardingaplane3-nodetriangularelement,ithas______degreesoffreedomanditselementstiffnessmatrixdimensionis______A3,3×3B3,6×6C6,3×3D6,6×68.2Test第1题关于平面4节点矩形单元，其位移场函数为______，应变场函数为______。Regardingaplane4-noderectangularelement,itsdisplacementfieldis____functionandthestressfieldis____function.A完全线性函数，完全线性函数acompletelinear,acompletelinearB完全线性函数+交叉项函数，完全线性函数acompletelinear+cross-term,acompletelinearC完全线性函数，不完全线性函数acompletelinear,

notacompletelinearD完全线性函数+交叉项函数，不完全线性函数acompletelinear+cross-term,notacompletelinear第2题平面4节点矩形单元拥有______个自由度，其单元刚度矩阵的维数是______。Regardingaplane4-noderectangularelement,ithas______degreesoffreedomanditselementstiffnessmatrixdimensionis______.A4,3×3B4,4×4C8,6×6D8,8×88.3Test第1题轴对称单元的弹性系数矩阵的维数为______。Thedimensionoftheelasticcoefficientmatrixforaaxisymmetricelementis____.A3×3B4×4C6×6第2题关于轴对称单元的单元刚度矩阵Ke=∫ΩeBTDBdΩ，其可以进一步表达为______。RegardingtheelementstiffnessmatrixforanaxisymmetricelementKe=∫ΩeBTDBdΩ,theintegralcanbefurtherexpressedas_____.A∫Ae∫02πBTDBrdθdrdzB∫AeBTDB2πzdrdzC∫AeBTDB2πrzdrD∫AeBTDB2πrdrdz正确答案：AD8.4Test第1题平面3节点三角形单元的一个侧边上受到分布力系，则该分布力系将仅被等效在与该侧边相关的节点力上。Aplanar3-nodetriangularelementisononesidesubjecttoadistributedforce,thisdistributedforcewillonlybeeffectiveontherelatednodesofthissideA是correctB否incorrect第2题平面3节点三角形单元受到如图所示的三角分布载荷侧压（分布载荷方向与节点1、2连线垂直）。若已知平面问题的厚度为t，单元节点的坐标列阵为[x1,y1,x2,y2,x3,y3]T，则节点等效外载列阵[Fx1,Fy1,Fx2,Fy2,Fx3,Fy3]T中Fx2一项的值为______。Aplanar3-nodetriangularelementreceivesadistributedloadononeside,asshowninthepicturebelow(thedirectionoftheloadisperpendiculartotheconnectinglinebetweenpoint1and2).Thethicknessisgivenast

,thevectorwiththecoordinatesfortheelementnodesis[x1,y1,x2,y2,x3,y3]T

,thentheequivalentexternalloadnodevectoris[Fx1,Fy1,Fx2,Fy2,Fx3,Fy3]T

withthevalueof____forFx2