材料力学 复习用review

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1、M.VableMechanicsofMaterials:ReviewREVIEWStress•Stressonasurfaceisaninternaldistributedforcesystem.•Therelationshipofexternalforces(andmoments)tointernalforcesandtherelationshipofinternalforcesandmomentstothestressdistributionaretwoditinctideas.Stressatapoint:----Isaninternalquantity.----Needstwo

2、directionsandamagnitudetospecifyit.(2ndordertensor).----Stressisasymmetrictensor.----Hasunitsofforceperunitarea.----Signisdeterminedbythedirectionoftheinternalforceandthedirectionoftheoutwardnormaloftheimaginarycutsurface.⎛⎞ΔFjOutwardnormaliInternalForceσ=lim⎜⎟----------ijΔA→0⎝⎠ΔAiiΔAidirectiono

3、fdirectionoftheΔFoutwardnormaltotheinternalforcecomponent.jimaginarycutsurface.Stressesonvariousplanespassingthroughapointintwodimensioncanbefoundbythe:----Wedgemethod(equilibriummethod).---Convertstressestoforcesanduseequilibriumequationstodeterminetheunknowns.----Mohr'scircle.----Apointontheci

4、rclerepresentsauniqueplaneandtheco-ordinatesofthepointrepresentthenormalandshearstressontheplane.Prefixesonstress:Normalstress,Shearstress,Principalstress,Maximumshearstress,Maximumin-planeshearstress,axialstress,flexturalstresses,torsionalshearingstress,maximumnormalstress,yieldstress,ultimates

5、tressetc.Printedfrom:http://www.me.mtu.edu/~mavable/MoM2nd.htm1M.VableMechanicsofMaterials:ReviewStrain•Measureofrelativemovementoftwopointsonthebody.(deformation).•Elongationsarepositivenormalstrains.•Decreasefromrightangleresultsinpositiveshearstrains.•SmallStrain(<0.01)approximationsimplifies

6、calculations.•InsmallstrainInnormalsmallstrain,thedeformationintheorignaldirectiononlyisrequired.Strainatapoint:----Needsmagnitudeandtwodirectiontospecifyit.----Tensornormalstrain=Engineeringnormalstrain;Tensorshearstrain=Engineeringshearstrain/2;Isrelatedtothefirstpartialderivativeofdeformation

7、.(3)Strainisasymmetrictensor.In3-D:6componentsareneededtospecifystrainatapoint.In2-D:3componentsareneededtospecifystrainatapoint.(4)StrainsindifferentcoordinatesystemscanbefoundusingMohr'scircleforstrains.Straingagesmeasureo