/COM,ANSYS MEDIA REL. 2024R2 (05/10/2024) REF. VERIF. MANUAL: REL. 2024R2 /VERIFY,vm296 /TITLE,vm296,RADIAL EXPANSION OF A THERMOPLASTIC CYLINDER /COM, /COM, REFERENCE: "THERMOMECHANICAL MODELING OF METALS AT FINITE STRAINS: /COM, FIRST AND MIXED ORDER FINITE ELEMENTS", LAURENT ADAM, JEAN-PHILIPPE PONTHOT, /COM, INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 42 (2005) 5615-5655 /COM, /COM, /COM, ***** USING PLANE222 ***** /COM, RI=0.1 ! INTERNAL RADIUS RE=0.2 ! EXTERNAL RADIUS DX=0.13 ! RADIAL DISPLACEMENT TREF=293 ! REFERENCE TEMPERATURE, K /PREP7 ET,1,PLANE222,11 ! STRUCTRAL-THERMAL COUPLING KEYOPT,1,3,1 ! AXISYMMETRIC KEYOPT,1,9,1 ! SUPPRESSED THERMOELASTIC DAMPING MP,EX,1,7.E10 ! YOUNG'S MODULUS MP,NUXY,1,0.3 ! POISSON'S RATIO MP,ALPX,1,23.8E-6 ! THERMAL EXPANSION COEFFICIENT MP,KXX,1,150 ! CONDUCTIVITY MP,DENS,1,2700 ! DENSITY MP,C,1,900 ! SPECIFIC HEAT MP,QRATE,1,0.9 ! TAYLOR-QUINNEY FACTOR EX=7.E10 ET=210E6 EP=EX*ET/(EX-ET) TB,PLAS,1,6,2,BISO ! BILINEAR ISOTROPIC HARDENING MATERIAL TBTEMP,293 TBDATA,1,70E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=293K TBTEMP,313 TBDATA,1,69.58E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=313K TBTEMP,333 TBDATA,1,69.16E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=333K TBTEMP,353 TBDATA,1,68.74E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=353K TBTEMP,373 TBDATA,1,68.32E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=373K TBTEMP,393 TBDATA,1,67.9E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=393K RECT,RI,RE,0,RE-RI TYPE,1 MAT,1 LESIZE,1,,,10 LESIZE,2,,,1 LESIZE,3,,,10 LESIZE,4,,,1 AMESH,1 ! GENERATE AXISYMMETRIC PLANE222 ELEMENTS ALLSEL,ALL NSEL,S,LOC,Y,0 NSEL,A,LOC,Y,RE-RI D,ALL,UY,0 ! CONSTRAIN UY DOF AT TOP AND BOTTOM FACES TO ! SIMULATE INFINETLY LONG CYLINDER NSEL,S,LOC,X,RI D,ALL,UX,DX ! APPLY RADIAL DISPLACEMENT ALONG INNER SURFACE OF CYLINDER ALLSEL,ALL TREF,TREF ! REFERENCE TEMPERATURE IC,ALL,TEMP,TREF ! INITIAL CONDITION FINISH /COM, /COM, ***** SOLUTION IN TIME = 0.001 SEC (ADIABATIC PROCESS) ***** /COM, /SOLUTION /OUT,SCRATCH ANTYPE,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON TINTP,,,,1.0 ! TRANSIENT INTEGRATION PARAMETER KBC,0 ! RAMPED LOADING AUTOTS,OFF NSUB,20,100,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCE TIME,0.001 ! END TIME SOLVE FINISH /POST26 /OUT,SCRATCH NSEL,S,LOC,X,0.1 NSEL,R,LOC,Y,0.1 ND=NDNEXT(0) NSOL,2,ND,TEMP ! TEMPERATURE AT NODE =ND FILLDATA,3,,,,-1 FILLDATA,4,,,,293.0 PROD,5,3,4 ADD,6,2,5 NSOL,7,ND,U,X,UX ! UX AT NODE=ND /OUT PRVAR,7,6 /OUT,SCRATCH /GRID,1 /AXLAB,X,Displacement of inner surface[m] /AXLAB,Y,Temperature variation [K] /XRANGE,0,0.14 /GROPT,DIVX,14 /YRANGE,0,60 /GROPT,DIVY,6 XVAR,7 /SHOW,PNG PLVAR,6 ALLSEL,ALL FINISH /POST1 SET,1,LAST /SHOW,PNG PLNSOL,TEMP *GET,MAX_TEMP,PLNSOL,0,MAX ! MAXIMUM TEMPERATURE AT TIME=0.001SECONDS *GET,MIN_TEMP,PLNSOL,0,MIN ! MINIMUM TEMPERATURE AT TIME=0.001 SECONDS PLNSOL,EPPL,EQV *GET,MAX_EPPLEQV,PLNSOL,0,MAX ! MAXIMUM PLASTIC STRAIN AT TIME=0.001 SECONDS *GET,MIN_EPPLEQV,PLNSOL,0,MIN ! MINIMUM PLASTIC STRAIN AT TIME=0.001 SECONDS /SHOW,CLOSE MAX_DT = MAX_TEMP - TREF MIN_DT = MIN_TEMP - TREF /OUT *STAT,MAX_DT *STAT,MIN_DT *STAT,MAX_EPPLEQV *STAT,MIN_EPPLEQV *DIM,LABEL1,CHAR,4,1 *DIM,VALUE1,,4,3 *DIM,VALUE1_REF,,4,3 *DIM,VALUE1_RATIO,,4,3 LABEL1(1,1) = 'DT_MIN ','DT_MAX ','EPPL_MIN ','EPPL_MAX ' *VFILL,VALUE1(1,1),DATA,MIN_DT,MAX_DT,MIN_EPPLEQV,MAX_EPPLEQV *VFILL,VALUE1_REF(1,2),DATA,16.5,57.0,0.426,0.932 ! FROM TABLE2 *VFILL,VALUE1_RATIO(1,3),DATA,ABS(MIN_DT/16.5),ABS(MAX_DT/57.0),ABS(MIN_EPPLEQV/0.426),ABS(MAX_EPPLEQV/0.932) SAVE,TABLE_1 PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP1,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP1 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP1 FINISH /COM, /COM, ***** SOLUTION IN TIME = 1.3 SEC ***** /COM, /SOLUTION /OUT,SCRATCH ANTYPE,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON KBC,0 ! RAMPED LOADING TINTP,,,,1.0 ! TRANSIENT INTEGRATION PARAMETER NSUB,20,100,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCE TIME,1.3 ! END TIME SOLVE FINISH /POST1 SET,LAST PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP2,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP2 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP2 ALLSEL,ALL FINISH /COM, /COM, ***** SOLUTION IN TIME = 13 SEC ***** /COM, /SOLUTION /OUT,SCRATCH ANTYPE,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON TINTP,,,,1.0 ! TRANSIENT TIME INTEGRATION PARAMETERS KBC,0 ! RAMPED LOADING NSUB,20,100,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCES TIME,13.0 ! END TIME SOLVE FINISH /POST1 SET,LAST PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP3,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP3 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP3 ALLSEL,ALL FINISH /COM, /COM, ***** SOLUTION IN TIME = 130 SEC ***** /COM, /SOLUTION /OUT,SCRATCH ANTY,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON TINTP,,,,1.0 ! TRANSIENT TIME INTEGRATION PARAMETERS KBC,0 ! RAMPED LOADING NSUB,50,200,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCE TIME,130 ! END TIME SOLVE FINISH /POST1 SET,LAST PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP4,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP4 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP4 ALLS FINISH /CLEAR,NOSTART /COM, /COM, ***** USING PLANE223 ***** /COM, /NOPR RI=0.1 ! INTERNAL RADIUS RE=0.2 ! EXTERNAL RADIUS DX=0.13 ! RADIAL DISPLACEMENT TREF=293 ! REFERENCE TEMPERATURE, K /PREP7 ET,1,PLANE223,11 ! STRUCTRAL-THERMAL COUPLING KEYO,1,3,1 ! AXISYMMETRIC KEYO,1,9,1 ! SUPPRESSED THERMOELASTIC DAMPING MP,EX,1,7.E10 ! YOUNG'S MODULUS MP,NUXY,1,0.3 ! POISSON'S RATIO MP,ALPX,1,23.8E-6 ! THERMAL EXPANSION COEFFICIENT MP,KXX,1,150 ! THERMAL CONDUCTIVITY MP,DENS,1,2700 ! DENSITY MP,C,1,900 ! SPECIFIC HEAT MP,QRATE,1,0.9 ! TAYLOR-QUINNEY FACTOR EX=7.E10 ET=210E6 EP=EX*ET/(EX-ET) TB,PLAS,1,6,2,BISO ! BILINEAR ISOTROPIC HARDENING MATERIAL TBTEMP,293 TBDATA,1,70E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=293K TBTEMP,313 TBDATA,1,69.58E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=313K TBTEMP,333 TBDATA,1,69.16E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=333K TBTEMP,353 TBDATA,1,68.74E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=353K TBTEMP,373 TBDATA,1,68.32E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=373K TBTEMP,393 TBDATA,1,67.9E6,EP ! YIELD STRESS AND PLASTIC TANGENT MODULUS AT T=393K RECT,RI,RE,0,RE-RI TYPE,1 MAT,1 LESIZE,1,,,10 LESIZE,2,,,1 LESIZE,3,,,10 LESIZE,4,,,1 AMESH,1 ! GENERATE AXISYMMETRIC PLANE223 ELEMENTS ALLSEL,ALL NSEL,S,LOC,Y,0 NSEL,A,LOC,Y,RE-RI D,ALL,UY,0 ! CONSTRAIN UY DOF AT TOP AND BOTTOM FACES TO ! SIMULATE INFINETLY LONG CYLINDER NSEL,S,LOC,X,RI D,ALL,UX,DX ! APPLY RADIAL DISPLACEMENT ALONG INNER SURFACE OF CYLINDER ALLSEL,ALL TREF,TREF ! REFERENCE TEMPERATURE IC,ALL,TEMP,TREF ! INITIAL CONDITION FINISH /COM, /COM, ***** SOLUTION IN TIME = 0.001 SEC (ADIABATIC PROCESS) ***** /COM, /SOLUTION /OUT,SCRATCH ANTY,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON TINTP,,,,1.0 ! TRANSIENT INTEGRATION PARAMETER KBC,0 ! RAMPED LOADING NSUB,20,100,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCE TIME,0.001 ! END TIME SOLVE FINISH /POST26 /OUT,SCRATCH NSEL,S,LOC,X,0.1 NSEL,R,LOC,Y,0.1 ND=NDNEXT(0) NSOL,2,ND,TEMP ! TEMPERATURE AT NODE =ND FILLDATA,3,,,,-1 FILLDATA,4,,,,293.0 PROD,5,3,4 ADD,6,2,5 NSOL,7,ND,U,X,UX ! UX AT NODE=ND /OUT PRVAR,7,6 /OUT,SCRATCH /GRID,1 /AXLAB,X,Displacement of inner surface[m] /AXLAB,Y,Temperature variation [K] /XRANGE,0,0.14 /GROPT,DIVX,14 /YRANGE,0,70 /GROPT,DIVY,7 XVAR,7 /SHOW,PNG PLVAR,6 ALLSEL,ALL FINISH /POST1 SET,1,LAST /SHOW,PNG PLNSOL,TEMP *GET,MAX_TEMP,PLNSOL,0,MAX ! MAXIMUM TEMPERATURE AT TIME=0.001SECONDS *GET,MIN_TEMP,PLNSOL,0,MIN ! MINIMUM TEMPERATURE AT TIME=0.001 SECONDS PLNSOL,EPPL,EQV *GET,MAX_EPPLEQV,PLNSOL,0,MAX ! MAXIMUM PLASTIC STRAIN AT TIME=0.001 SECONDS *GET,MIN_EPPLEQV,PLNSOL,0,MIN ! MINIMUM PLASTIC STRAIN AT TIME=0.001 SECONDS /SHOW,CLOSE MAX_DT = MAX_TEMP - TREF MIN_DT = MIN_TEMP - TREF /OUT *STAT,MAX_DT *STAT,MIN_DT *STAT,MAX_EPPLEQV *STAT,MIN_EPPLEQV *DIM,LABEL2,CHAR,4,1 *DIM,VALUE2,,4,3 *DIM,VALUE2_REF,,4,3 *DIM,VALUE2_RATIO,,4,3 LABEL2(1,1) = 'DT_MIN ','DT_MAX ','EPPL_MIN ','EPPL_MAX ' *VFILL,VALUE2(1,1),DATA,MIN_DT,MAX_DT,MIN_EPPLEQV,MAX_EPPLEQV *VFILL,VALUE2_REF(1,2),DATA,17.4,58.9,0.426,0.935 *VFILL,VALUE2_RATIO(1,3),DATA,ABS(MIN_DT/17.4),ABS(MAX_DT/58.9),ABS(MIN_EPPLEQV/0.426),ABS(MAX_EPPLEQV/0.935) SAVE,TABLE_2 PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP1,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP1 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP1 FINISH /COM, /COM, ***** SOLUTION IN TIME = 1.3 SEC ***** /COM, /SOLUTION /OUT,SCRATCH ANTYPE,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON KBC,0 ! RAMPED LOADING TINTP,,,,1.0 ! TRANSIENT INTEGRATION PARAMETER NSUB,20,100,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCE TIME,1.3 ! END TIME SOLVE FINISH /POST1 SET,LAST PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP2,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP2 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP2 ALLSEL,ALL FINISH /COM, /COM, ***** SOLUTION IN TIME = 13 SEC ***** /COM, /SOLUTION /OUT,SCRATCH ANTYPE,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON TINTP,,,,1.0 ! TRANSIENT TIME INTEGRATION PARAMETERS KBC,0 ! RAMPED LOADING NSUB,20,100,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCES TIME,13.0 ! END TIME SOLVE FINISH /POST1 SET,LAST PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP3,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP3 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP3 ALLSEL,ALL FINISH /COM, /COM, ***** SOLUTION IN TIME = 130 SEC ***** /COM, /SOLUTION /OUT,SCRATCH ANTY,TRANSIENT ! TRANSIENT ANALYSIS NLGEOM,ON ! LARGE DEFLECTION ON TINTP,,,,1.0 ! TRANSIENT TIME INTEGRATION PARAMETERS KBC,0 ! RAMPED LOADING NSUB,20,100,5 ! NUMBER OF SUBSTEPS OUTRES,ALL,ALL CNVTOL,HEAT,1.E-2,1.E-2 ! CONVERGENCE TOLERANCE TIME,130 ! END TIME SOLVE FINISH /POST1 SET,LAST PATH,TEMP1,2,,100 ! DEFINE PATH NAME,NUMBER OF POINTS AND DIVISION PPATH,1,NODE,0.1,0.1,0 ! NODES TO DEFINE PATH GEOMETRY PPATH,2,NODE,0.2,0.1,0 PDEF,TEMP4,TEMP,,NOAV ! INTERPOLATE TEMPERATURE RESULTS PDEF,UX,U,X,NOAV ! INTERPOLATE UX RESULTS /OUT PRPATH,UX,TEMP4 ! PRINT PATH ITEMS /SHOW,PNG PLPATH,TEMP4 ALLSEL,ALL /COM, RESUME,TABLE_1 /OUT,vm296,vrt /COM,---------------------- RESULT COMPARISON: PLANE222 ----------------------- /COM, /COM, | TARGET | MECHANICAL APDL | RATIO /COM, /COM, /GOPR *VWRITE,LABEL1(1,1),VALUE1_REF(1,2),VALUE1(1,1),VALUE1_RATIO(1,3) (1X,A8,' ',F10.3,' ',F14.3,' ',1F15.3) /COM, /NOPR RESUME,TABLE_2 /COM,-------------------------------------------------------------------------- /COM, /COM,---------------------- RESULT COMPARISON: PLANE223 ----------------------- /COM, /COM, | TARGET | MECHANICAL APDL | RATIO /COM, /COM, /GOPR *VWRITE,LABEL2(1,1),VALUE2_REF(1,2),VALUE2(1,1),VALUE2_RATIO(1,3) (1X,A8,' ',F10.3,' ',F14.3,' ',1F15.3) /COM, /COM,-------------------------------------------------------------------------- /COM, /OUT, *LIST,vm296,vrt FINISH