TALK=f;RUN(1,1)
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
************************************************************
Group 1. Run Title and Number
************************************************************
readq1=t
READQ1_BEGIN
TEXT(Pressurised long cylinder; 1Dy
Declarations and settings
REAL(PI,PO,RI,RO,POISSON,YOUNG)
PI=1.e7 ! inner pressure
PO=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,NYCYL) ! nycyl is y-direction cell number in solid
Length-constraint settings
mesga(CASENO=1 means expansion in z allowed
mesgb(CASENO=2 means expansion in z not allowed
caseno=1
mesgm(caseno is :caseno: OK? (Y/n)
readvdu(ans,char,Y)
if(:ans:.eq.n) then
caseno=2
endif
caseno
NYCYL=11
NYCYL=31
NYCYL=100
REAL(POWER) ! used for creating non uniform grid
POWER=2
READQ1_END
************************************************************
Group 2. Time dependence
STEADY = T
************************************************************
Group 3. X-Direction Grid Spacing
CARTES = F
XULAST = 1.000000E-03
XFRAC ( 1) = 1.000000E+00
************************************************************
Group 4. Y-Direction Grid Spacing
NREGY=3 ! 3 regions
IREGY=1;GRDPWR(Y,1,RI,1.0) ! single inner fluid cell
IREGY=2;GRDPWR(Y,NYCYL,RO-RI,POWER) ! ncyl solid cells
IREGY=3;GRDPWR(Y,1,0.01*RO,1.0) ! single outer fluid cell
************************************************************
Group 5. Z-Direction Grid Spacing
NZ=1
ZWLAST = 1.000000E+00
************************************************************
Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS = T
SOLVE(DISY)
STORE(P1)
STORE(P1TH,PRPS,DEN1,ENUL,DVO1,DRH1) ! TH means theoretical
STORE(STRX,SXTH,EPSX,EXTH,STRY,SYTH) ! provide storage for
STORE(EPSY,EYTH,STRZ,SZTH,EPSZ,EZTH) ! text-book values
************************************************************
GROUP 8. ITERATION NUMBERS ETC
************************************************************
GROUP 9. PROPERTIES
CSG10='Q1' ! materials with various POISSON ratios
MATFLG=T;NMAT=1
160 7800.0 0.3 473.0 43.0 1.0e-5 0.5E-11
161 7800.0 0.2 473.0 43.0 1.0e-5 0.5E-11
162 7800.0 0.1 473.0 43.0 1.0e-5 0.5E-11
163 7800.0 0.0 473.0 43.0 1.0e-5 0.5E-11
164 7800.0 0.4 473.0 43.0 1.0e-5 0.5E-11
165 7800.0 0.05 473.0 43.0 1.0e-5 0.5E-11
166 7800.0 0.01 473.0 43.0 1.0e-5 0.5E-11
************************************************************
GROUP 11. INITIAL VALUES
FIINIT(PRPS)=0
PATCH(INNER,INIVAL,1,NX,1,1,1,1,1,1) ! inner fluid
COVAL(INNER,P1,FIXVAL,PI)
PATCH(OUTER,INIVAL,1,NX,NY,NY,1,1,1,1) ! outer fluid
COVAL(OUTER,P1,FIXVAL,PO)
PATCH(CYLINDER,INIVAL,1,NX,2,NY-1,1,1,1,1) ! solid
INIT(CYLINDER,PRPS,FIXVAL,160) ! material. Insert other
************************************************************
GROUP 13. BOUNDARY & SPECIAL SOURCES
PATCH(IN,CELL,1,NX,1,1,1,1,1,1) ! pressurizing inner
COVAL(IN,P1,FIXVAL,PI) ! fluid
PATCH(OUT,CELL,1,NX,NY,NY,1,1,1,1) ! pressurizing outer
COVAL(OUT,P1,FIXVAL,PO) ! fluid
SPEDAT(BOUNDARY,XCONST,R,1.E20) ! because total angle is fixed
IF(CASENO.EQ.1) THEN
SPEDAT(BOUNDARY,ZCONST,R,0.0) ! because axial motion allowed
ENDIF
IF(CASENO.EQ.2) THEN
SPEDAT(BOUNDARY,ZCONST,R,1.E20) ! because axial motion not allowed
ENDIF
************************************************************
GROUP 15. TERMINATE SWEEPS
LSWEEP = 200
ISG21 = LSWEEP
************************************************************
GROUP 17. RELAXATION
#CONPROM
************************************************************
GROUP 19. DATA TRANSMITTED TO GROUND
STRA = T
************************************************************
GROUP 23.FIELD PRINT-OUT & PLOT CONTROL
output(den1,n,n,n,n,n,n)
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(prps,n,n,n,n,n,n)
NYPRIN=1
TSTSWP=-1
IYPRF=1
IYPRL=NY
ISG52 = 3 ! probe & res
Theoretical values according to Benham et al
and Love (Mathematical Theory of Elasticity)
to be conveyed to earth by way of InForm
statements.
inform7begin
! 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 - :RISQ:/RG^2) with imat>100)
(STORED VAR SXTH IS :CONI:*(1.0 + :ROSQ:/ Rg^2 ) - $
:CONO:*(1.0 + :RISQ:/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 = EE / (ROSQ-RISQ) ! concluded
ee
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
! print to screen and satlog.txt
caseno
AA
BB
EE
! 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
STOP