3.4. Example Thermal-Stress Analysis

This simple thermal-stress analysis problem demonstrates a solution of a load transfer coupled-field analysis with one-way coupling:

3.4.1. Problem Description

Two long, thick-walled cylinders, concentric about the cylinder axis, are maintained at a temperature (Ti) on the inner surface and on the outer surface (To). The object of the problem is to determine the temperature distribution, axial stress, and hoop stress in the cylinders.

 

Geometric Properties Loading Material Properties
Inner Cylinder (steel) Outer Cylinder (aluminum)
a = .1875 in.Ti = 200°FE = 30 x 106 psiE = 10.6 x 106 psi
b = .40 in.To = 70°Fα = .65 x 10-5 in/in°Fα = 1.35 x 10-5 in/in°F
c = .60 in. ν = 0.3ν = 0.33
K = 2.2 btu/hr-in-°FK = 10.8 btu/hr-in-°F

3.4.2. Procedure

  1. Define and solve the thermal problem.

  2. Return to PREP7 and modify the database. You will need to switch element types, specify additional material properties, and specify structural boundary conditions.

  3. Read the temperatures from the thermal results file.

  4. Solve the structural problem.

3.4.3. Command Listing

All text prefaced with an exclamation point (!) is a comment.

/batch,list
/show
/title, thermal stress in concentric cylinders - indirect method
/prep7
et,1,plane77,,,1     ! PLANE77 axisymmetric option
mp,kxx,1,2.2         ! Steel conductivity
mp,kxx,2,10.8        ! Aluminum conductivity
rectng,.1875,.4,0,.05! Model
rectng,.4,.6,0,.05
aglue,all
numcmp,area
asel,s,area,,1       ! Assign attributes to solid model
aatt,1,1,1
asel,s,area,,2
aatt,2,1,1
asel,all
esize,.05
amesh,all            ! Mesh model
nsel,s,loc,x,.1875
d,all,temp,200       ! Apply thermal loads
nsel,s,loc,x,.6
d,all,temp,70
nsel,all
finish 
/solu
solve
finish
/post1
path,radial,2        ! Define path name and number of path points
ppath,1,,.1875       ! Define path by location
ppath,2,,.6
pdef,temp,temp       ! Interpret temperature to path
pasave,radial,filea  ! Save path to an external file
plpath,temp          ! Plot temperature solution
finish
/prep7
et,1,82,,,1          ! Switch to structural element, SOLID82
mp,ex,1,30e6         ! Define structural steel properties
mp,alpx,1,.65e-5
mp,nuxy,1,.3
mp,ex,2,10.6e6       ! Define aluminum structural properties
mp,alpx,2,1.35e-5
mp,nuxy,2,.33
nsel,s,loc,y,.05     ! Apply structural boundary conditions
cp,1,uy,all
nsel,s,loc,x,.1875
cp,2,ux,all
nsel,s,loc,y,0
d,all,uy,0
nsel,all
finish
/solu
tref,70
ldread,temp,,,,,,rth  ! Read in temperatures from thermal run
solve
finish
/post1
paresu,radial,filea !Restore path
pmap,,mat           ! Set path mapping to handle material discontinuity
pdef,sx,s,x         ! Interpret radial stress
pdef,sz,s,z         ! Interpret hoop stress
plpath,sx,sz        ! Plot stresses
plpagm,sx,,node     ! Plot radial stress on path geometry
finish