刘刚连续介质力学作业3.docx
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刘刚连续介质力学作业3
May16th,2013
ComputerExerciseofContinuumMechanics
Major:
MechanicalEngineering
Course:
ContinuumMechanics
Studentname:
LiuGang
StudentID:
12S057007
Director:
Prof.TongtongGuo
Basicmethod:
Applications/Scales
Basicconditions
Assumptions
Analysis
Summery
Example1:
Acantileverbeamwithitsdimensionsshowninthefigure,bearingacentroidforceandamomentontherightsideofthebeam.Theforcecanbedenotedby
andthemomentby
.
Solution:
1.Application:
balcony,bookshelves,divingplatform,towercrane,dinnertable...
2.BasicConditions:
Acantileverbeamwithleft-fixedandrightsidefree.ThefreeendloadedaforceFandmomentM.
4.Analysis:
a:
Considerthewholebeamasafreebody.Studythefixedend:
and
Wecanget
b:
Modelparameters:
concrete,EX=2GPa.u=0.3,L=5m,h=0.6m,b=0.4m,F=10000N,Mz=50000N·m
c:
Algorithms:
/PREP7
ET,1,PLANE82
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,2e9
MPDATA,PRXY,1,,0.3
RECTNG,0,5,0,0.6,
AESIZE,ALL,0.1,
MSHKEY,0
CM,_Y,AREA
ASEL,,,,1
CM,_Y1,AREA
CHKMSH,'AREA'
CMSEL,S,_Y
AMESH,_Y1
CMDELE,_Y
CMDELE,_Y1
CMDELE,_Y2
MSHKEY,0
/SOL
/STATUS,SOLU
FLST,2,1,1,ORDE,1
FITEM,2,108
F,P51X,FY,10000
FLST,2,1,4,ORDE,1
FITEM,2,4
DL,P51X,,ALL,
SAVE
FLST,2,1,1,ORDE,1
FITEM,2,2
FK,P51X,MZ,-50000
AndIcapturedsomediagramswhenmodeling
5:
Summery:
Inthisexample,Ilearnedhowtoapplyamomenttoastructure.WecanseethatwhenF=10000N,M=50000N.m,themaximumdeflection（Uy=0.01172m）occursonthefreeendofthecantileverbeam.Whilethelargeststress（
515858pa）andthelargeststrain（
0.458mm）appearonthefixedendofthebeam.Soinactualengineering,thecontactorthefixedendisthemostdangerouspositions.
Example2:
Alongslenderblockwithitsdimensionsshowninthefiguresubjectedtoauniformed-pressure
onthelateralside.Thebottomisfixedandthetopisfree.
Solution
1.Application:
runningtrain,transformingbends...
2.Basicconditions:
bottomareafixed,topareafree
andlateralloadedbyuniformed-pressure.
3.Assumptions:
simplifiedtoaplanestress
problemandignoreweightandobeysmalldisplacement,continuum,isotropicassumptions.
4.Analysis:
a:
Modelparameters:
concrete,EX=200MPa.u=0.3,b=10m,h=100m,q=1000N/m2
b:
Algorithms:
/PREP7
ET,1,PLANE82
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,2e8
MPDATA,PRXY,1,,0.3
RECTNG,0,10,0,100,
AESIZE,ALL,1,
MSHKEY,0
CM,_Y,AREA
ASEL,,,,1
CM,_Y1,AREA
CHKMSH,'AREA'
CMSEL,S,_Y
AMESH,_Y1
CMDELE,_Y
CMDELE,_Y1
CMDELE,_Y2
MSHKEY,0
FINISH
/SOL
FLST,2,1,4,ORDE,1
FITEM,2,1
DL,P51X,,ALL,
SAVE
FLST,2,201,1,ORDE,4
FITEM,2,1
FITEM,2,222
FITEM,2,242
FITEM,2,-440
F,P51X,FY,-1000
FLST,2,201,1,ORDE,3
FITEM,2,2
FITEM,2,22
FITEM,2,-221
F,P51X,FY,1000
FINISH
/POST1
FINISH
AndIcapturedsomediagramswhenmodeling:
5.Summery:
（1）Thoughhandcalculation,wege
and
.
（2）Wecanseethatwhenq=1000N/m2,themaximumdeflection（Ux=0.402444m）occursontopfreeareaoftheblock.Whilethelargeststress（
143308pa）andthelargeststrain（
0.00392754m）allappearonthefixedbottomoftheblock.Soinactualengineering,thebottomareaoftheblockisthemostdangerousarea.Becausetheblockisratherhuge,sothemaximumdisplacementisquitesmallcomparingtothewholeblockThebiggeststrainandstresscomparingtotheextremestrainandstressofisquitesmall,whichcanreach100GPa.Thankstoanti-symmetry,therearenoshearforce.WhenIworkonthisproblem,Istilldon’tknowhowtoapplyauniformpressureonanarea.Infuturestudy,Iwilllookthoughmorebooksandpaperstosloveaseriesproblems.
Example3:
AnannulardiscwithitsdimensiononthefollowingfigureappliedwithamomentMalongitsouterboundary.
Solution:
1.Application:
Flywheels,discs,wheels,
bearings,pulleys...
2.BasicConditions:
Fixedaroundtheinter
SurfacearealoadedamomentMalongtheouter-surfacearea.
3.Assumption:
Homogeneousandisotropic.Consideringweight,obeysmalldisplacement,continuum,isotropicassumptions.
4.Analysis:
a:
Bythegivenformulation:
where
WesetaseriesofparameterslikeE1,,
;E2,
....Considerwhen
or
thevalueofthe
and
.
b:
Modelparameters:
soft-steel,EX=2GPa,u=0.3,r1=100m,r2=60m.M=5000N.m.
c:
Algorithms:
/PREP7
ET,1,SOLID95
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,EX,1,,2e9
MPDATA,PRXY,1,,0.3
MPTEMP,,,,,,,,
MPTEMP,1,0
MPDATA,DENS,1,,2500
CYLIND,100,60,0,10,0,360,
SMRT,6
SMRT,5
SMRT,4
SMRT,3
MSHAPE,1,3D
MSHKEY,0
CM,_Y,VOLU
VSEL,,,,1
CM,_Y1,VOLU
CHKMSH,'VOLU'
CMSEL,S,_Y
VMESH,_Y1
CMDELE,_Y
CMDELE,_Y1
CMDELE,_Y2
APLOT
ET,2,SURF154
KEYOPT,2,2,0
KEYOPT,2,4,0
KEYOPT,2,6,0
KEYOPT,2,7,0
KEYOPT,2,11,0
KEYOPT,2,12,0
ASEL,S,,,3,4
NSLA,,1
NPLOT
TYPE,2
MAT,1
REAL,
ESYS,0
SECNUM,
FLST,5,208,1,ORDE,10
FITEM,5,1
FITEM,5,-4
FITEM,5,9
FITEM,5,-12
FITEM,5,17
FITEM,5,-76
FITEM,5,121
FITEM,5,-180
FITEM,5,1803
FITEM,5,-1882
CM,_Y,NODE
NSEL,,,,P51X
CM,_Y1,NODE
CMSEL,,_Y
CMSEL,,_Y1
ESURF,0
CMSEL,,_Y
CMDELE,_Y
CMDELE,_Y1
LOCAL,11,1,0,0,0
FLST,2,2734,2,ORDE,2
FITEM,2,1
FITEM,2,-2734
EMODIF,P51X,ESYS,11,
FINISH
/SOL
FLST,5,2734,2,ORDE,2
FITEM,5,1
FITEM,5,-2734
CM,_Y,ELEM
ESEL,,,,P51X
CM,_Y1,ELEM
CMSEL,S,_Y
CMDELE,_Y
SFE,_Y1,2,PRES,,5000,,,
/PSF,PRES,TANX,2
EPLOT
ALLSEL
EPOLT
FLST,2,2,5,ORDE,2
FITEM,2,5
FITEM,2,-6
DA,P51X,ALL,
EQSLV,PCG
SOLVE
FINISH
AndIcapturedsomediagramswhenmodeling:
5.Summery:
WecanseethatthemaximumdeformationUx=0.067926mwhichisverysmallcomparedtothedimensionofthedisc,themaximumstressoccursonasmallzoneoftheinterareaofthedisc,whichiswellcoincidedwiththeactualsituationofhardcomputing,Fromthisexample,I’velearnedhowtoapplyanmomentonacurvedsurfaceandhowtodefineseveralelementtypesandmeshonavolume.
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