材料力学总结.docx

材料力学总结.docx

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材料力学总结

材料力学总结

材料力学总结

材料力学名词解释及填空

名词解释

1、Stress（应力）

theforceperunitarea,orintensityoftheforcedistributedoveragivensection,iscalledstress.

σ=F/A

2、normalstress（正应力）

Theinternalforceisthereforenormaltotheplaneofthesectionandthecorrespondingstressisdescribedasthenormalstress.

3、Shearingstress（剪应力）

Theinternalforceistheshearontheplaneofthesectionandthecorrespondingstressisdescribedastheshearingstress.

4、LinearStrain（应变）

Thenormalstrainεinamembercanbedefinedasthedeformationofthemeteroftheperunitlength.

5、Themainobjectiveofthestudythemechanicsofmaterials（材料力学的任务）istoprovidethefutureengineerwiththemeansofanalyzinganddesigningvariousmachinesandloading-bearingstructures.

6、Saint-venant’sprinciple（圣维南原理）

Fortwosetsofstaticallyequivalentforces,exceptintheimmediatevicinityofthepointsofapplicationoftheloads,thestressdistributionmaybeassumedindependentoftheactualmodeofapplicationoftheloads（thisstatementisnotonlytoaxialload,buttopracticallyanytypeofload）

7、Work-energyprinciple（功能原理）

TheWork-energyPrinciple:

Intheprocessofthedeformationofaelastomer,thestrainenergywhichisstoredinelastomerisequaltotheworkoftheexternalforceinnumber.ThisistheWork-energyPrincipleanditcanberepresentedasVε=W.

8、effectivelength（有效长度）isdefinedasreallengthmultipliedbyfactoroflength

9、principleplane（主平面）

istheplaneinwhichtheshearingstressequalszero,andnormalstressesachievemaximumorminimum.

Principlestress（主应力）

Thenormalstresswhichisexertedontheprincipleplaneiscalledtheprinciplestress.

10、Radiusofradiusofgyration【revolution】（惯性半径）ofanareacanbecalculatedbythefollowingformulai=I/A

Wherei=themomentofinertiaofanarea

A=theareaofancrosssection

11、isotropicmaterials（各向同性材料）arethematerialswhoseelasticconstantsareindependentofdirection.

12、homogeneousmaterials（均匀性材料）arethematerialswhoseelasticpropertiesarethesameeverywhere.

13、Thestrainenergydensity（应变能密度）

Thestrainenergyintheunitvolumecanbedefinedasthestrainenergydensity.

14、Hooke’slaw（胡克定律）maybeexpressedmorefullybysayingthat

1】whenthestressincreases,themeasuredstrainincreasesinthesameratio

2】whenthestressdiminishes,themeasuredstraindiminishesinthesameratio

3】whenthestressisremoved,nostraincanbemeasured

Forasmalldeformation,thestressisdirectlyproportionaltothestrain.

15、Hooke’slawforshearingstress（剪切胡克定律）

Therelationτ=GγisknownasHooke’slawforshearingstress.StrainandconstantGiscalledthemodulusofrigidityorshearmodulusofmaterial.

16、GeneralizedHooke’slaw（广义胡可定律）

17、Poissonratio（泊松比）isdefinedastheratiooflateralcontraction（strain）tolongitudinalextension（strain）ofabarunderterminaltension.

18、factorofsafety（安全因数）ultimateloadoverallowableload

19、stress-concentrationfactork（应力集中因数K）=maximumstressoveraveragestress

20、staticallyindeterminateproblem（静不定问题）istheprobleminwhichthereactionsandinternalforcescannotbedeterminedbystaticonly,analysisofdeformationisneeded.

21、neutralsurface（中性层）isdefinedasthesurfacebetweenthetopandbottomofabeaminwhichlongitudinallinedonotchange.

22、Neutralaxis（中性轴）

①Theneutralsurfaceintersectsatransversesectionalongastraightlinecalledtheneutralaxisofthesection.

②Theintersectionoftheneutralsurfacewithatransversesectioniscalledtheneutralaxisofthesection.

23、principleofsuperposition（叠加原理）

 foralllinearsystems （a beam canbemodeledasalinearsystem）,

24、thequantitythetermλ=μl/i（柔度）isknownastheslendernessratioofthecolumn.

Whereμl=effectivelength

i=theradiusofgyration

25、Thetheoryofstrength（强度理论）

Theassumptionconcerningthedamageorthelosingeffectofthematerialiscalledthetheoryofstrength.

26、buckling（失稳）

Astagewhenthecolumnsuddenlybecomessharplycurvedinsteadofremainingstraightastheloadisappliediscalledbuckling.

27、Thecriticalforce（临界压力）

Thevalueofthecompressiveforcewhichisrightontheboundarybetweenthestablebalanceandtheunstablebalanceiscalledthecriticalforce.

28、Thecriticalstress（临界应力）

Thecorrespondingstressofthecriticalforceisdescribedasthecriticalforce.

29、Euler’sFormula（欧拉公式）

Euler’sFormulacanbeexpressedas

Fcr=π²EI／le²

inwhich:

Fcrdenotesthecriticalload

Edenotesthemodulus

Idenotestheminimummomentofinertiaofarea

ledenotestheequivalentlength

30、Assumptionforabar（拉压的平面假设）

Thehypothesisassumesthatthesectionkeepsbeingaplaneafterdeformation.

31、Assumptionfortorsion（扭转平面假设）

Whenacircularshaftissubjectedtoatorsion,everycrosssectionremainsplaneandundamaged.

32、Assumptionforbending（弯曲平面假设）

Underbending,thecrosssectionofthebeamremainsplaneandhasaconstantcurvature.Andthenewcrosssectionstillperpendiculartoaxis.

32、极惯性矩

ThepolarmomentofinertiaofanareaisdefinedasthepolarmomentofinertiaofanareawithrespecttoapointastheintegralIp=∫ρ²dA

33、惯性矩

ThemomentofinertiaofanareaisdefinedasthesecondmomentoftheareawithrespecttoanaxisastheintegralI=∫y²dA.

34、静矩

ThestaticmomentofanareaisdefinedasthefirstmomentofanareawithrespecttoanaxisastheintegralSz=∫ydA.

填空题

1三个材料假设

Homogeneousityassumption、Continuityassumption、Isotropyassumption

2三个关系

Geometricrelation、Physicalrelation、Equilibriumrelation

3限制梁挠度的三个条件

Boundarycondition、Constraintcondition、Continuitycondition

4三种约束方式

1）固定端fixedend

2）固定铰支座fixedsupportofpinjoint

3）可动铰支座rollersupportofpinjoint

5三种梁

1）简支梁simplysupportedbeam

2）外伸梁overhangbeam

3）悬臂梁cantileverbeam

6Forperfectcolumn,thefactoroflengthforconditionsbothpinned;bothfixed;onefixedtheotherfree;onefixedtheotherpinnedare1、0.5、2、0.7respectively.

7Thefourclassicstrengththeoriesincludemaximumtensilestresstheory、maximumelongatednormalstraintheory、maximumshearingstresstheoryandmaximumdistortionalstrainenergytheory.

8Thetensilediagramoflowcarbonsteelconsistoffourstages:

elasticstage、yieldingstage、hardeningstageandneckingstage.