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

************************************************************
Q1 created by VDI menu, Version 2007, Date 26/09/07
CPVNAM=VDI;SPPNAM=Core
************************************************************
Echo DISPLAY / USE settings
DISPLAY
A rectangular plate with a centrally-placed CIRCULAR hole is
extended by uniform equal forces on its Top and Bottom
surfaces, which are allowed to distort.
By reason of symmetry, only one quarter of the plate is analysed.
For calculation is used POLAR coordinates and Boundary Flow
Cells.
Comparison - a analytical solution (Timoshenko )

Boundary Condition:
===================

V ( UR) :
---------
Y = RO :   StrY = FX/2*(1-RI^2/RO^2) + FX/2*(1 + 3*RI^4/RO^4 -
4*RI^2/RO^2)*COS(2*X)

U ( UTeta) :
------------
X = 0, PI/2 :  U = 0,
Y = RO      :  StXY = - FX/2 * (1 - 3*RI^4/RO^4 + 2*RI^2/RO^2)
*SIN(2*X)

Exact Solution:
===============
Displacements
-------------
V = FX/(2*E)* R* {(1-P) + RI^2/R^2*(1+P) + [(1 - RI^4/R^4)*(1+P)
+ 4*RI^2/R^2]*COS(2*X) }
U = -FX/(2*E)* R* [(1 + RI^4/R^4)*(1+P) + 2*RI^2/R^2*(1-P)]*
SIN(2*X)

Strains
-------
EpsY  = FX/(2*E)* {(1-P) - RI^2/R^2*(1+P) + [(1+P)*(1 +
3*RI^4/R^4) - 4*RI^2/R^2]*COS(2*X)}
EpsX  = FX/(2*E)* {(1-P) + RI^2/R^2*(1+P) - [(1+P)*(1 +
3*RI^4/R^4) - P * 4*RI^2/R^2]*COS(2*X)}
EpsZ  = - P * FX/(2*E) * [ 2 - 4*RI^2/R^2*COS(2*X) ]
D     = FX/E*(1-2*P) * [1 - 2*RI^2/R^2*COS(2*X) ]

Stress
------
StrY = FX/2*(1-RI^2/R^2) + FX/2*(1 + 3*RI^4/R^4 - 4*RI^2/R^2)*
COS(2*X)
StrX = FX/2*(1+RI^2/R^2) - FX/2*(1 + 3*RI^4/R^4)*COS(2*X)
StXY = - FX/2 * (1 - 3*RI^4/R^4 + 2*RI^2/R^2)*SIN(2*X)
StrZ = 0
ENDDIS
PHOTON USE
p;;;;

set prop off
msg
msg Grid
msg
gr Z 1
pause

cl
msg
msg V1 contours
msg
cont V1 z 1 fil;.0001
vec z 1 col 0
pause

cl
msg
msg V1TH contours
msg
cont V1TH z 1 fil;.0001
pause

cl
msg
msg V1/T contours
msg
cont V1/T z 1 fil;.0001
pause

cl
msg
msg U1 contours
msg
cont U1 z 1 fil;.0001
vec z 1 col 0
pause

cl
msg
msg U1TH contours
msg
cont U1TH z 1 fil;.0001
pause

cl
msg
msg U1/T contours
msg
cont U1/T z 1 fil;.0001
pause

cl
msg
msg STRX contours
msg
cont STRX z 1 fil;.0001
pause

cl
msg
msg SXTH contours
msg
cont SXTH z 1 fil;.0001
pause

cl
msg
msg SX/T contours
msg
cont SX/T z 1 fil;.0001
pause

cl
msg
msg STRY contours
msg
cont STRY z 1 fil;.0001
pause

cl
msg
msg SYTH contours
msg
cont SYTH z 1 fil;.0001
pause

cl
msg
msg SY/T contours
msg
cont SY/T z 1 fil;.0001
pause

cl
msg
msg STXY contours
msg
cont STXY z 1 fil;.0001
pause

cl
msg
msg XYTH contours
msg
cont XYTH z 1 fil;.0001
pause

ENDUSE
************************************************************
IRUNN   =         1 ;LIBREF =       203
************************************************************
Group 1. Run Title
TEXT(Polar Plate with CIRCULAR hole          )
************************************************************
Group 2. Transience
************************************************************
Groups 3, 4, 5  Grid Information
* Overall number of cells, RSET(M,NX,NY,NZ,tolerance)
RSET(M,22,32,1)
* Cylindrical-polar grid
CARTES=F;RINNER=4.850000E-01
************************************************************
Group 6. Body-Fitted coordinates
************************************************************
Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS  =    T
* Non-default variable names
NAME(122) =EZ/T ; NAME(123) =EY/T
NAME(124) =EX/T ; NAME(125) =P1/T
NAME(126) =V1/T ; NAME(127) =U1/T
NAME(128) =V1TH ; NAME(129) =U1TH
NAME(130) =P1TH ; NAME(131) =XY/T
NAME(132) =SY/T ; NAME(133) =SX/T
NAME(134) =XYTH ; NAME(135) =SYTH
NAME(136) =SXTH ; NAME(137) =STXY
NAME(138) =STRY ; NAME(139) =STRX
NAME(140) =EZTH ; NAME(141) =EYTH
NAME(142) =EXTH ; NAME(143) =EPSZ
NAME(144) =EPSY ; NAME(145) =EPSX
NAME(146) =DRH1 ; NAME(147) =DVO1
NAME(148) =ENUL ; NAME(149) =DEN1
NAME(150) =PRPS
* Solved variables list
SOLVE(P1  ,U1  ,V1  )
* Stored variables list
STORE(PRPS,DEN1,ENUL,DVO1,DRH1,EPSX,EPSY,EPSZ)
STORE(EXTH,EYTH,EZTH,STRX,STRY,STXY,SXTH,SYTH)
STORE(XYTH,SX/T,SY/T,XY/T,P1TH,U1TH,V1TH,U1/T)
STORE(V1/T,P1/T,EX/T,EY/T,EZ/T)

************************************************************
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)
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(EZ/T) =  1.001000E-10 ;FIINIT(EY/T) =  1.001000E-10
FIINIT(EX/T) =  1.001000E-10 ;FIINIT(P1/T) =  1.001000E-10
FIINIT(V1/T) =  1.001000E-10 ;FIINIT(U1/T) =  1.001000E-10
FIINIT(V1TH) =  1.001000E-10 ;FIINIT(U1TH) =  1.001000E-10
FIINIT(P1TH) =  1.001000E-10 ;FIINIT(XY/T) =  1.001000E-10
FIINIT(SY/T) =  1.001000E-10 ;FIINIT(SX/T) =  1.001000E-10
FIINIT(XYTH) =  1.001000E-10 ;FIINIT(SYTH) =  1.001000E-10
FIINIT(SXTH) =  1.001000E-10 ;FIINIT(STXY) =  1.001000E-10
FIINIT(STRY) =  1.001000E-10 ;FIINIT(STRX) =  1.001000E-10
FIINIT(EZTH) =  1.001000E-10 ;FIINIT(EYTH) =  1.001000E-10
FIINIT(EXTH) =  1.001000E-10 ;FIINIT(EPSZ) =  1.001000E-10
FIINIT(EPSY) =  1.001000E-10 ;FIINIT(EPSX) =  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
No PATCHes used for this Group

************************************************************
Echo InForm settings for Group 11
inform11BEGIN

REAL(RI,RO,POISSON,YOUNG,FX,LR,LTETA,LLX)

RI=0.5   ! inner radius
RO=2     ! outer radius
LR = RO-RI
FX= 1.0e4
LTETA=3.1416/2
LLX = LTETA*0.01

YOUNG   = 1/(0.5E-11) ! Young's modulus
POISSON=0.3           ! Poisson's ratio

********* Exact Solution: Stress ********
char(ag2,ag4,av2,av4)
real(FX2)
FX2=FX/2
ag2=(:RI:/RG)^2
ag4=(:RI:/RG)^4
av2=(:RI:/RV)^2
av4=(:RI:/RV)^4

char(bg,bu)
bg=(XG-:LLX:)
bu=(XU-:LLX:)
char(FSY1,FSY2,FBY1,FBY2, FSX1,FSX2,FSXY1,FSXY2)
FSY1=:FX2:*((1-:ag2:)+(1+3*:ag4:
FSY2=-4*:ag2:)*COS(2*:bg:))

FBY1=:FX2:*((1-:av2:)+(1+3*:av4:
FBY2=-4*:av2:)*COS(2*:bg:))

FSX1=:FX2:*((1+:ag2:)-(1+3*:ag4:)
FSX2=*COS(2*:bg:))
FSXY1=-:FX2:*(1-3*:av4:+2*:av2:)
FSXY2=*SIN(2*:bu:)
(STORED VAR SXTH IS :FSX1::FSX2: with imat>100)
(STORED VAR SX/T IS STRX/SXTH with imat>100)
(STORED VAR SYTH IS :FSY1::FSY2: with imat>100)
(STORED VAR SY/T IS STRY/SYTH with imat>100)
(STORED VAR XYTH IS :FSXY1::FSXY2: with imat>100)
(STORED VAR XY/T IS STXY/XYTH with imat>100)

****** Polar Source for U ****
STORE(PUTH)
char(FPOU1,FPOU2)
real(FX211)
FX211 = FX2*1.e-11
FPOU1=-:FX211:*(1-3*:ag4:+2*:ag2:)
FPOU2=*SIN(2*:bu:)/RG
(STORED VAR PUTH IS :FPOU1::FPOU2: with imat>100)

********* Exact Solution: Displacement ********
char(FU1,FU2,FV1,FV2,FV3)
real(ONEPLP,ONEMNP,FX2E)
ONEPLP = 1.0 + POISSON
ONEMNP = 1.0 - POISSON
FX2E = FX/2/YOUNG

FU1=-:FX2E:*RG*(:ONEPLP:*(1+:ag4:)+2*:ag2:
FU2=*:ONEMNP:)*SIN(2*:bu:)

FV1=:FX2E:*RV*(:ONEMNP:+:av2:*:ONEPLP:+
FV2=((1-:av4:)*:ONEPLP:+4*:av2:)
FV3=*COS(2*:bg:))

(STORED VAR U1TH IS :FU1::FU2: with imat>100)
(STORED VAR U1/T IS U1/U1TH with imat>100)

(STORED VAR V1TH IS :FV1::FV2::FV3: with imat>100)
(STORED VAR V1/T IS V1/V1TH with imat>100)

********* Exact Solution: Strains ********
char(FEY1,FEY2,FEX1,FEX2,FEX3,FEZ,FEP)
real(FXZ,FXP)
FXZ = -POISSON*FX/2/YOUNG
FXP = FX/YOUNG*(1-2*POISSON)

FEX1=:FX2E:*(:ONEMNP:+:ag2:*:ONEPLP:-(:ONEPLP:*
FEX2=(1+3*:ag4:)-4*:ag2:*POISSON)
FEX3=*COS(2*:bg:))

FEY1=:FX2E:*(:ONEMNP:-:ag2:*:ONEPLP:+(:ONEPLP:*
FEY2=(1+3*:ag4:)-4*:ag2:)*COS(2*:bg:))

FEZ=:FXZ:*(2 - 4*:ag2:*COS(2*:bg:))
FEP=:FXP:*(1 - 2*:ag2:*COS(2*:bg:))

(STORED VAR EXTH IS :FEX1::FEX2::FEX3: with imat>100)
(STORED VAR EX/T IS EPSX/EXTH with imat>100)

(STORED VAR EYTH IS :FEY1::FEY2: with imat>100)
(STORED VAR EY/T IS EPSY/EYTH with imat>100)

(STORED VAR EZTH IS :FEZ: with imat>100)
(STORED VAR EZ/T IS EPSZ/EZTH with imat>100)

(STORED VAR P1TH IS :FEP: with imat>100)
(STORED VAR P1/T IS P1/P1TH with imat>100)
inform11END

************************************************************
Group 12. Convection and diffusion adjustments
No PATCHes used for this Group
************************************************************
Group 13. Boundary & Special Sources

PATCH (DMN     ,CELL  ,0,0,0,0,0,0,1,1)
COVAL (DMN     ,P1  , FIXVAL      , 0.000000E+00)

PATCH (OUTV    ,NORTH ,2,0,0,0,0,0,1,1)

PATCH (LOWX    ,WEST  ,3,0,0,0,0,0,1,1)
COVAL (LOWX    ,U1  , 1.000000E+06, 0.000000E+00)

PATCH (HIGHX   ,EAST  ,4,0,0,0,0,0,1,1)
COVAL (HIGHX   ,U1  , 1.000000E+06, 0.000000E+00)

PATCH (OUTU    ,NORTH ,5,0,0,0,0,0,1,1)

EGWF    =    T
************************************************************
Echo InForm settings for Group 13
inform13BEGIN
(source of V1 at OUTV is COVAL(FIXFLU,:FBY1::FBY2:))
(source of U1 at OUTU is COVAL(FIXFLU,:FSXY1::FSXY2:))
inform13END

************************************************************
Group 14. Downstream Pressure For PARAB
************************************************************
Group 15. Terminate Sweeps
LSWEEP  =       400
RESREF(U1  ) =  0.000000E+00 ;RESREF(V1  ) =  0.000000E+00
RESFAC  = 1.000000E-07
************************************************************
Group 16. Terminate Iterations
LITER (U1  ) =       40 ;LITER (V1  ) =       40
ENDIT (U1  ) =  0.000000E+00 ;ENDIT (V1  ) =  0.000000E+00
************************************************************
Group 17. Relaxation
RELAX(P1  ,LINRLX, 1.000000E+00)
************************************************************
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   =       400
ISG52   =         1
ISG59   =         1
CSG10   ='Q1'
************************************************************
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
IXMON   =        11 ;IYMON  =        31 ;IZMON  =         1
NPRMON  =    100000
NPRMNT  =         1
TSTSWP  =        -1
************************************************************
Group 23.Field Print-Out & Plot Control
NPRINT  =    100000
ISWPRF  =         1 ;ISWPRL =    100000
No PATCHes used for this Group
************************************************************
Group 24. Dumps For Restarts

GVIEW(P,2.996888E-01,1.411412E-01,9.435390E-01)
GVIEW(UP,-1.591936E-02,9.895984E-01,-1.429747E-01)

> DOM,    SIZE,        1.602216E+00, 1.530000E+00, 1.000000E+00
> DOM,    MONIT,       7.618380E-01, 1.480235E+00, 5.000000E-01
> DOM,    SCALE,       1.000000E+00, 1.000000E+00, 1.000000E+00
> GRID,   RSET_X_1,      1, 1.000000E+00
> GRID,   RSET_X_2,     20, 1.000000E+00
> GRID,   RSET_X_3,      1, 1.000000E+00
> GRID,   RSET_Y_1,      1, 1.000000E+00
> GRID,   RSET_Y_2,     30, 1.400000E+00
> GRID,   RSET_Y_3,      1, 1.000000E+00
> GRID,   RSET_Z_1,      1, 1.000000E+00

> OBJ,    NAME,        BODY
> OBJ,    POSITION,    1.570800E-02, 1.500000E-02, 0.000000E+00
> OBJ,    SIZE,        1.570800E+00, 1.500000E+00, 1.000000E+00
> OBJ,    GEOMETRY,    polcu8
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        BLOCKAGE
> OBJ,    MATERIAL,    160,NOTSET

> OBJ,    NAME,        OUTV
> OBJ,    POSITION,    1.570800E-02, 1.515000E+00, 0.000000E+00
> OBJ,    SIZE,        1.570800E+00, 0.000000E+00, 1.000000E+00
> OBJ,    GEOMETRY,    poldef
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        USER_DEFINED

> OBJ,    NAME,        LOWX
> OBJ,    POSITION,    0.000000E+00, 1.500000E-02, 0.000000E+00
> OBJ,    SIZE,        0.000000E+00, 1.500000E+00, 1.000000E+00
> OBJ,    GEOMETRY,    poldef
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        USER_DEFINED

> OBJ,    NAME,        HIGHX
> OBJ,    POSITION,    1.586508E+00, 1.500000E-02, 0.000000E+00
> OBJ,    SIZE,        0.000000E+00, 1.500000E+00, 1.000000E+00
> OBJ,    GEOMETRY,    poldef
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        USER_DEFINED

> OBJ,    NAME,        OUTU
> OBJ,    POSITION,    0.000000E+00, 1.515000E+00, 0.000000E+00
> OBJ,    SIZE,        1.586508E+00, 0.000000E+00, 1.000000E+00
> OBJ,    GEOMETRY,    poldef
> OBJ,    ROTATION24,        1
> OBJ,    TYPE,        USER_DEFINED
************************************************************
STOP
```