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

************************************************************
Q1 created by VDI menu, Version 2007, Date 16/01/07
CPVNAM=VDI;SPPNAM=Core
************************************************************
Echo DISPLAY / USE settings
DISPLAY

This problem is the same as that of s104; but nx is given a value
greater than 1 as a test of capability, while nz retains its unity
value.

The stresses, strains and  displacements should be independent of\$
x.
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 distributions in x and y (via POWERX and
POWERY)

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
************************************************************
IRUNN   =         1 ;LIBREF =       622
************************************************************
Group 1. Run Title
TEXT(Pressurised long cylinder [X,Y]         )
************************************************************
Group 2. Transience
************************************************************
Groups 3, 4, 5  Grid Information
* Overall number of cells, RSET(M,NX,NY,NZ,tolerance)
RSET(M,10,22,1,8.000020E-04)
* Cylindrical-polar grid
CARTES=F
************************************************************
Group 6. Body-Fitted coordinates
************************************************************
Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS  =    T
* Non-default variable names
NAME(132) =EZTH ; NAME(133) =EPSZ
NAME(134) =SZTH ; NAME(135) =STRZ
NAME(136) =EYTH ; NAME(137) =EPSY
NAME(138) =SYTH ; NAME(139) =STRY
NAME(140) =EXTH ; NAME(141) =EPSX
NAME(142) =SXTH ; NAME(143) =STRX
NAME(144) =DRH1 ; NAME(145) =DVO1
NAME(146) =ENUL ; NAME(147) =DEN1
NAME(148) =PRPS ; NAME(149) =DISY
NAME(150) =DISX
* Solved variables list
SOLVE(DISY,DISX)
* Stored variables list
STORE(PRPS,DEN1,ENUL,DVO1,DRH1,STRX,SXTH,EPSX)
STORE(EXTH,STRY,SYTH,EPSY,EYTH,STRZ,SZTH,EPSZ)
STORE(EZTH,V1  ,U1  ,P1  )
SOLUTN(DISY,Y,Y,Y,N,N,Y)
SOLUTN(DISX,Y,Y,Y,N,N,Y)

************************************************************
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:*RG + BB/RG)
(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
TERMS (DISY,N,N,Y,N,Y,N)
TERMS (DISX,N,N,Y,N,Y,N)
************************************************************
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
************************************************************
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(DISY) =  1.001000E-10
FIINIT(DISX) =  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)

************************************************************
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 (LOWX    ,WWALL ,4,0,0,0,0,0,1,1)
COVAL (LOWX    ,DISX, 1.000000E+00, 0.000000E+00)

PATCH (HIGHX   ,EWALL ,5,0,0,0,0,0,1,1)
COVAL (HIGHX   ,DISX, 1.000000E+00, 0.000000E+00)

EGWF    =    T
************************************************************
Echo InForm settings for Group 13
inform13begin
inform13end
************************************************************
Group 14. Downstream Pressure For PARAB
************************************************************
Group 15. Terminate Sweeps
LSWEEP  =       100
RESFAC  = 1.000000E-03
************************************************************
Group 16. Terminate Iterations
************************************************************
Group 17. Relaxation
************************************************************
Group 18. Limits
VARMAX(U1  ) = 1.000000E+06 ;VARMIN(U1  ) =-1.000000E+06
VARMAX(V1  ) = 1.000000E+06 ;VARMIN(V1  ) =-1.000000E+06
************************************************************
Group 19. EARTH Calls To GROUND Station
USEGRD  =    T  ;USEGRX =    T
STRA    =    T
ASAP    =    T
PARSOL  =    T
CONWIZ  =    T
ISG21   =       100
ISG52   =         3
CSG10   ='Q1'
SPEDAT(SET,BOUNDARY,ZCONST,R,0.00000E+00)
************************************************************
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(U1  ,Y,N,Y,Y,Y,Y)
OUTPUT(V1  ,Y,N,Y,Y,Y,Y)
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)
************************************************************
Group 22. Monitor Print-Out
IXMON   =         5 ;IYMON  =        21 ;IZMON  =         1
NPRMON  =    100000
NPRMNT  =         1
TSTSWP  =        -1
************************************************************
Group 23.Field Print-Out & Plot Control
NPRINT  =    100000
NXPRIN  =         1
NYPRIN  =         1
ISWPRF  =         1 ;ISWPRL =    100000
No PATCHes used for this Group
************************************************************
Group 24. Dumps For Restarts

GVIEW(P,3.554405E-01,-2.449153E-02,9.343786E-01)
GVIEW(UP,-1.507587E-01,9.850658E-01,8.316907E-02)

> DOM,    SIZE,        2.000000E-01, 8.080000E-01, 1.000000E+00
> DOM,    MONIT,       9.000000E-02, 7.850000E-01, 5.000000E-01
> DOM,    SCALE,       1.000000E+00, 1.000000E+00, 1.000000E+00
> DOM,    SNAPSIZE,    1.000000E-02
> GRID,   RSET_X_1,     10, 1.000000E+00
> GRID,   RSET_Y_1,      1, 1.000000E+00
> GRID,   RSET_Y_2,     20, 1.000000E+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, 7.999957E-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

> OBJ,    NAME,        LOWX
> OBJ,    POSITION,    0.000000E+00, 2.000000E-01, 0.000000E+00
> OBJ,    SIZE,        0.000000E+00, 6.000000E-01, 1.000000E+00
> OBJ,    GEOMETRY,    poldef
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        USER_DEFINED

> OBJ,    NAME,        HIGHX
> OBJ,    POSITION,    2.000000E-01, 2.000000E-01, 0.000000E+00
> OBJ,    SIZE,        0.000000E+00, 6.000000E-01, 1.000000E+00
> OBJ,    GEOMETRY,    poldef
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        USER_DEFINED
************************************************************
STOP
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