TALK=F;RUN( 1, 1)
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Q1 created by VDI menu, Version 2007, Date 16/01/07
CPVNAM=VDI;SPPNAM=Core
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Echo DISPLAY / USE settings
DISPLAY
A long, hollow, thick-walled cylinder, immersed in an outer fluid,
contains a second fluid having a different pressure.
Since conditions vary with radius alone, nx and nz are set = 1 .
Two constraints on its length are considered, namely:
1. the cylinder length may extend freely; and
2. the cylinder length may not extend at all.
To enable the computed stresses and strains to be compared with
theoretical (text-book) values, the latter have been computed.
So as to make comparison easy, variables named P1/T etc have also
been computed. They represent the calculated values divided by
text-book ones. They should all be, and indeed are, close to 1.0;
but zero is printed when the text-book value is zero
Parameters which may be changed by editing this file include:
(a) Material properties: Young's modulus and Poisson's ratio
(b) Geometric quantities: inner and outer radius, and length.
(c) Mechanical loadings: inner and outer pressures
(d) The grid fineness (via NYCYL)
(e) The grid-fineness distribution (via POWER)
The text-book solution may be found in section 14.4 of Benham,
Crawford and Armstrong, Mechanics of Engineering Materials; and
also in Love's Mathematical Theory of Elasticity p144 .
ENDDIS
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IRUNN = 1 ;LIBREF = 104
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Group 1. Run Title
TEXT(Pressurised long cylinder; 1Dy )
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Group 2. Transience
STEADY = T
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Groups 3, 4, 5 Grid Information
* Overall number of cells, RSET(M,NX,NY,NZ,tolerance)
RSET(M,1,33,1,1.000000E-05)
* Cylindrical-polar grid
CARTES=F
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Group 6. Body-Fitted coordinates
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Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS = T
* Non-default variable names
NAME(133) =EZTH ; NAME(134) =EPSZ
NAME(135) =SZTH ; NAME(136) =STRZ
NAME(137) =EYTH ; NAME(138) =EPSY
NAME(139) =SYTH ; NAME(140) =STRY
NAME(141) =EXTH ; NAME(142) =EPSX
NAME(143) =SXTH ; NAME(144) =STRX
NAME(145) =DRH1 ; NAME(146) =DVO1
NAME(147) =ENUL ; NAME(148) =DEN1
NAME(149) =PRPS ; NAME(150) =P1TH
* Solved variables list
SOLVE(P1 ,V1 )
* Stored variables list
STORE(P1TH,PRPS,DEN1,ENUL,DVO1,DRH1,STRX,SXTH)
STORE(EPSX,EXTH,STRY,SYTH,EPSY,EYTH,STRZ,SZTH)
STORE(EPSZ,EZTH)
************************************************************
Echo InForm settings for Group 7
inform7begin
REAL(PI,POU,RI,RO,POISSON,YOUNG)
PI=1.e7 ! inner pressure
POU=1.e6 ! outer pressure
RI=0.2 ! inner radius
RO=0.8 ! outer radius
YOUNG = 1/(0.5E-11) ! Young's modulus
POISSON=0.3 ! Poisson's ratio
integer(caseno)
Length-constraint settings:
caseno=1 : expansion in z allowed
caseno=2 : expansion in z not allowed
======================================
caseno = 2
======================================
Theoretical values according to Benham et al
and Love (Mathematical Theory of Electricity)
to be conveyed to earth by way of InForm
statements.
! Declarations first:
REAL(RODRI, RISQ, ROSQ, RODRISQ, CONI, CONO, TERM)
REAL( AA, BB, EE)
REAL(LL,GG) ! Lame's constants
! deductions
! Lame's constants Lamda+LL, mu=GG
LL = YOUNG*POISSON/((1+POISSON)*(1-2.0*POISSON)) ! in terms of YOUNG
GG = YOUNG/(2.0*(1.0+POISSON)) ! and POISSON
RISQ = RI * RI
ROSQ = RO * RO
RODRISQ = ROSQ / RISQ
! settings from formulae in the above text books
! all cases
CONI = PI / (RODRISQ - 1)
CONO = POU * RODRISQ / (RODRISQ - 1)
(STORED VAR SYTH IS :CONI:*(1.0 - :ROSQ:/ Rg^2 ) - :CONO:*(1.0 - :R$
ISQ:/RG^2) with imat>100)
(STORED VAR SXTH IS :CONI:*(1.0 + :ROSQ:/ Rg^2 ) - :CONO:*(1.0 + :R$
ISQ:/RG^2) with imat>100)
BB = (PI-POU) * RISQ * ROSQ / ( 2.0*GG * (ROSQ-RISQ) ) ! Love's B
AA = (PI*RISQ-POU*ROSQ) / ( 2.0*(LL+GG) * (ROSQ-RISQ) ) ! Love's A
! first part
IF(CASENO.EQ.1) THEN ! ee and aa for no stress
EE = - LL * (PI*RISQ-POU*ROSQ) / ( GG * (3.0*LL+2.0*GG) )! Love's e
EE = EE / (ROSQ-RISQ) ! concluded
AA = AA - EE*LL/( 2.0* (LL + GG)) ! Love's A concluded
(STORED VAR SZTH IS 0.0 WITH IMAT>100)
TERM = - LL / (GG * (3.0*LL + 2.0*GG) )
TERM = TERM * ( PI*RISQ - POU*ROSQ)
TERM = TERM / ( ROSQ - RISQ )
(STORED VAR EZTH IS :TERM: WITH IMAT>100)
ENDIF
IF(CASENO.EQ.2) THEN ! fixed end
(STORED VAR EZTH IS 0 WITH IMAT>100)
TERM = LL/(LL+GG)
TERM = TERM * ( PI*RISQ - POU*ROSQ)
TERM = TERM / ( ROSQ - RISQ )
(STORED VAR SZTH IS :TERM: WITH IMAT>100)
ENDIF
! all cases
(STORED VAR V1TH IS :AA:*RV + BB/RV)
(STORED VAR EXTH IS (SXTH - :POISSON:*(SYTH+SZTH))/:YOUNG:)
(STORED VAR EYTH IS (SYTH - :POISSON:*(SXTH+SZTH))/:YOUNG:)
(STORED VAR P1TH IS (EXTH + EYTH + EZTH) WITH IMAT>100)
(STORED VAR P1/T IS P1/P1TH)
(STORED VAR V1/T IS V1/V1TH)
(STORED VAR EX/T IS EPSX/EXTH)
(STORED VAR EY/T IS EPSY/EYTH)
IF(CASENO.EQ.1) THEN
(STORED VAR EZ/T IS EPSZ/EZTH)
ENDIF
IF(CASENO.EQ.2) THEN ! cases 1 and 2 distinguished
(STORED VAR SZ/T IS STRZ/SZTH)
ENDIF
inform7end
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Group 8. Terms & Devices
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Group 9. Properties
* Domain material index is 0 signifying:
* Air at 20 deg C, 1 atm, treated as incompressible
SETPRPS(1, 0,Q1)
RHO1 = 0.000000E+00
ENUL = 0.000000E+00
ENUT = 0.000000E+00
DVO1DT = 3.410000E-03
* List of user-defined materials to be read by EARTH
MATFLG=T;IMAT=1
* Name
*Ind. Dens. Viscos. Spec.heat Conduct. Expans. Compr.
*
160 7800.0 0.3 473.0 43.0 1.0E-5 0.5E-11
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Group 10.Inter-Phase Transfer Processes
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Group 11.Initialise Var/Porosity Fields
FIINIT(EZTH) = 1.001000E-10 ;FIINIT(EPSZ) = 1.001000E-10
FIINIT(SZTH) = 1.001000E-10 ;FIINIT(STRZ) = 1.001000E-10
FIINIT(EYTH) = 1.001000E-10 ;FIINIT(EPSY) = 1.001000E-10
FIINIT(SYTH) = 1.001000E-10 ;FIINIT(STRY) = 1.001000E-10
FIINIT(EXTH) = 1.001000E-10 ;FIINIT(EPSX) = 1.001000E-10
FIINIT(SXTH) = 1.001000E-10 ;FIINIT(STRX) = 1.001000E-10
FIINIT(DRH1) = 1.001000E-10 ;FIINIT(DVO1) = 1.001000E-10
FIINIT(ENUL) = 1.001000E-10 ;FIINIT(DEN1) = 1.001000E-10
FIINIT(PRPS) = 0.000000E+00 ;FIINIT(P1TH) = 1.001000E-10
PATCH (INNER ,INIVAL,1,0,0,0,0,0,1,1)
PATCH (OUTER ,INIVAL,2,0,0,0,0,0,1,1)
INIADD = F
************************************************************
Echo InForm settings for Group 11
inform11begin
(INITIAL of P1 at INNER is :PI:)
(INITIAL of P1 at outer is :POU:)
inform11end
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Group 12. Convection and diffusion adjustments
No PATCHes used for this Group
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Group 13. Boundary & Special Sources
PATCH (IN ,VOLUME,1,0,0,0,0,0,1,1)
PATCH (OUT ,VOLUME,2,0,0,0,0,0,1,1)
EGWF = T
************************************************************
Echo InForm settings for Group 13
inform13begin
(SOURCE of P1 at IN is COVAL(FIXVAL,:PI:))
(SOURCE of P1 at OUT is COVAL(FIXVAL,:POU:))
inform13end
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Group 14. Downstream Pressure For PARAB
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Group 15. Terminate Sweeps
LSWEEP = 200
RESREF(V1 ) = 0.000000E+00
RESFAC = 1.000000E-07
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Group 16. Terminate Iterations
LITER (V1 ) = 20
ENDIT (V1 ) = 0.000000E+00
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Group 17. Relaxation
RELAX(P1 ,LINRLX, 1.000000E+00)
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Group 18. Limits
VARMAX(V1 ) = 1.000000E+06 ;VARMIN(V1 ) =-1.000000E+06
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Group 19. EARTH Calls To GROUND Station
USEGRD = T ;USEGRX = T
STRA = T
ASAP = T
PARSOL = T
CONWIZ = T
ISG21 = 200
ISG52 = 3
ISG59 = 1
CSG10 ='Q1'
SPEDAT(SET,BOUNDARY,XCONST,R,1.00000E+20)
SPEDAT(SET,BOUNDARY,ZCONST,R,0.00000E+00)
SPEDAT(SET,RLXFAC,RLXV1D,R,5.00000E-01)
************************************************************
Echo InForm settings for Group 19
inform19begin
IF(CASENO.EQ.2) THEN
SPEDAT(BOUNDARY,ZCONST,R,1.e20) ! z contraction prevented
ELSE
SPEDAT(BOUNDARY,ZCONST,R,0.0) ! z contraction allowed
ENDIF
inform19end
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Group 20. Preliminary Printout
ECHO = T
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Group 21. Print-out of Variables
OUTPUT(DRH1,N,N,N,N,N,N)
OUTPUT(DVO1,N,N,N,N,N,N)
OUTPUT(ENUL,N,N,N,N,N,N)
OUTPUT(DEN1,N,N,N,N,N,N)
OUTPUT(PRPS,N,N,N,N,N,N)
************************************************************
Group 22. Monitor Print-Out
NPRMON = 100000
NPRMNT = 1
TSTSWP = -1
************************************************************
Group 23.Field Print-Out & Plot Control
NPRINT = 100000
NYPRIN = 1
IYPRF = 1 ;IYPRL = 33
ISWPRF = 1 ;ISWPRL = 100000
No PATCHes used for this Group
************************************************************
Group 24. Dumps For Restarts
GVIEW(P,-6.321333E-02,3.384783E-01,-9.388485E-01)
GVIEW(UP,3.886831E-01,8.748021E-01,2.892177E-01)
> DOM, SIZE, 2.000000E-01, 8.080000E-01, 1.000000E+00
> DOM, MONIT, 1.000000E-01, 1.000000E-01, 5.000000E-01
> DOM, SCALE, 1.000000E+00, 1.000000E+00, 1.000000E+00
> DOM, SNAPSIZE, 1.000000E-02
> GRID, RSET_X_1, 1, 1.000000E+00
> GRID, RSET_Y_1, 1, 1.000000E+00
> GRID, RSET_Y_2, 31, 2.000000E+00
> GRID, RSET_Y_3, 1, 1.000000E+00
> GRID, RSET_Z_1, 1, 1.000000E+00
> OBJ, NAME, INNER
> OBJ, POSITION, 0.000000E+00, 0.000000E+00, 0.000000E+00
> OBJ, SIZE, 2.000000E-01, 2.000000E-01, 1.000000E+00
> OBJ, GEOMETRY, poldef
> OBJ, ROTATION24, 1
> OBJ, TYPE, USER_DEFINED
> OBJ, NAME, OUTER
> OBJ, POSITION, 0.000000E+00, 8.000000E-01, 0.000000E+00
> OBJ, SIZE, 2.000000E-01, 8.000000E-03, 1.000000E+00
> OBJ, GEOMETRY, poldef
> OBJ, ROTATION24, 1
> OBJ, TYPE, USER_DEFINED
> OBJ, NAME, CYLINDER
> OBJ, POSITION, 0.000000E+00, 2.000000E-01, 0.000000E+00
> OBJ, SIZE, 2.000000E-01, 6.000000E-01, 1.000000E+00
> OBJ, GEOMETRY, polcu8
> OBJ, ROTATION24, 1
> OBJ, TYPE, BLOCKAGE
> OBJ, MATERIAL, 160,NOTSET
************************************************************
STOP