This simple thermal-stress analysis problem demonstrates a solution of a load transfer coupled-field analysis with one-way coupling:
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°F | E = 30 x 106 psi | E = 10.6 x 106 psi |
| b = .40 in. | To = 70°F | α = .65 x 10-5 in/in°F | α = 1.35 x 10-5 in/in°F |
| c = .60 in. | ν = 0.3 | ν = 0.33 | |
| K = 2.2 btu/hr-in-°F | K = 10.8 btu/hr-in-°F | ||
Define and solve the thermal problem.
Return to PREP7 and modify the database. You will need to switch element types, specify additional material properties, and specify structural boundary conditions.
Read the temperatures from the thermal results file.
Solve the structural problem.
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