```
TALK=F;RUN( 1, 1)

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Q1 created by VDI menu, Version 2007, Date 16/01/07
CPVNAM=VDI;SPPNAM=Core
************************************************************
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.
(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 =       504
************************************************************
Group 1. Run Title
TEXT(Pressurised long cylinder; 1Dy          )
************************************************************
Group 2. Transience
************************************************************
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
************************************************************
Group 6. Body-Fitted coordinates
************************************************************
Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS  =    T
* Non-default variable names
* Solved variables list
SOLVE(DISY)
* Stored variables list
STORE(P1,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,PO,RI,RO,POISSON,YOUNG)
PI=1.e7  ! inner pressure
PO=1.e6 ! outer pressure

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 = 1
======================================
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    = PO * 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-PO) * RISQ * ROSQ / ( 2.0*GG * (ROSQ-RISQ) )   ! Love's B

AA = (PI*RISQ-PO*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-PO*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 - PO*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 - PO*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 V1/T IS DISY/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
************************************************************
Group 8. Terms & Devices
************************************************************
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
************************************************************
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

PATCH (INNER   ,INIVAL,1,0,0,0,0,0,1,1)

PATCH (OUTER   ,INIVAL,2,0,0,0,0,0,1,1)

************************************************************
Echo InForm settings for Group 11
inform11begin
(INITIAL of P1 at INNER is :PI:)
(INITIAL of P1 at outer is :PO:)
inform11end
************************************************************
Group 12. Convection and diffusion adjustments
No PATCHes used for this Group
************************************************************
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,:PO:))
inform13end
************************************************************
Group 14. Downstream Pressure For PARAB
************************************************************
Group 15. Terminate Sweeps
LSWEEP  =       200
************************************************************
Group 16. Terminate Iterations
************************************************************
Group 17. Relaxation
RELAX(P1  ,LINRLX, 1.000000E+00)
************************************************************
Group 18. Limits
************************************************************
Group 19. EARTH Calls To GROUND Station
USEGRD  =    T  ;USEGRX =    T
STRA    =    T
ASAP    =    T
PARSOL  =    F
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
************************************************************
Group 20. Preliminary Printout
ECHO    =    T
************************************************************
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
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