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csf2d.f
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csf2d.f
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SUBROUTINE CSF2D(MDIM,NGNOD,XI,ETA, SF, DSF, IERR)
!
! the standard element
!
! 1 ^ 4 - - - 7 - - - 3
! | | | |
! | | | |
! 0 xi 8 - - - 9 - - - 6
! | | | |
! | | | |
! -1 1 - - - 5 - - - 2
!
! ----- eta ---->
! -1 0 1
!
! INPUT MEANING
! ----- -------
! ETA eta location
! MDIM max number of dimensions
! NGNOD number of global nodes on element
! XI xi location
!
! OUTPUT MEANING
! ------ -------
! DSF derivative of shape fns at xi / eta
! IERR error flag
! SF shape functions at xi / eta
!
!.... variable declarations
IMPLICIT NONE
REAL*8, INTENT(IN) :: XI, ETA
INTEGER*4, INTENT(IN) :: MDIM, NGNOD
REAL*8, INTENT(OUT) :: SF(NGNOD), DSF(MDIM,*)
INTEGER*4, INTENT(OUT) :: IERR
INTEGER*4 I
REAL*8 SUM1, SUM2, SUM3, EPS
PARAMETER(EPS = 2.2204D-16)
!
!----------------------------------------------------------------------!
!
!.... 4 noded element
IERR = 0
IF (NGNOD.EQ.4) THEN
!
!....... hat shape functions
SF(1) = .25D0*(1.D0 - XI)*(1.D0 - ETA)
SF(2) = .25D0*(1.D0 + XI)*(1.D0 - ETA)
SF(3) = .25D0*(1.D0 + XI)*(1.D0 + ETA)
SF(4) = .25D0*(1.D0 - XI)*(1.D0 + ETA)
IF (DABS(SF(1)).LT.EPS) SF(1) = 0.D0
IF (DABS(SF(2)).LT.EPS) SF(2) = 0.D0
IF (DABS(SF(3)).LT.EPS) SF(3) = 0.D0
IF (DABS(SF(4)).LT.EPS) SF(4) = 0.D0
!
!....... their derivatives w.r.t. xi
DSF(1,1) = .25D0*(-1.D0)*(1.D0 - ETA)
DSF(1,2) = .25D0*( 1.D0)*(1.D0 - ETA)
DSF(1,3) = .25D0*( 1.D0)*(1.D0 + ETA)
DSF(1,4) = .25D0*(-1.D0)*(1.D0 + ETA)
!
!....... their derivatives w.r.t. eta
DSF(2,1) = .25D0*(1.D0 - XI)*(-1.D0)
DSF(2,2) = .25D0*(1.D0 + XI)*(-1.D0)
DSF(2,3) = .25D0*(1.D0 + XI)*( 1.D0)
DSF(2,4) = .25D0*(1.D0 - XI)*( 1.D0)
!
!.... 9 noded element
ELSEIF(NGNOD.EQ.9) THEN
!
!....... bubble functions
SF(1) = .25D0*XI*(XI - 1.D0)*ETA*(ETA - 1.D0)
SF(2) = .25D0*XI*(XI + 1.D0)*ETA*(ETA - 1.D0)
SF(3) = .25D0*XI*(XI + 1.D0)*ETA*(ETA + 1.D0)
SF(4) = .25D0*XI*(XI - 1.D0)*ETA*(ETA + 1.D0)
SF(5) = .5D0*(1.D0 - XI**2)*ETA*(ETA - 1.D0)
SF(7) = .5D0*(1.D0 - XI**2)*ETA*(ETA + 1.D0)
SF(6) = .5D0*XI*(XI + 1.D0)*(1.D0 - ETA**2)
SF(8) = .5D0*XI*(XI - 1.D0)*(1.D0 - ETA**2)
SF(9) = (1.D0 - XI**2)*(1.D0 - ETA**2)
!
!....... their derivatives w.r.t xi
DSF(1,1) = .5D0*(XI - .5D0)*ETA*(ETA - 1.D0)
DSF(1,2) = .5D0*(XI + .5D0)*ETA*(ETA - 1.D0)
DSF(1,3) = .5D0*(XI + .5D0)*ETA*(ETA + 1.D0)
DSF(1,4) = .5D0*(XI - .5D0)*ETA*(ETA + 1.D0)
DSF(1,5) = -XI*ETA*(ETA - 1.D0)
DSF(1,7) = -XI*ETA*(ETA + 1.D0)
DSF(1,6) = (XI + .5D0) * (1.D0 - ETA**2)
DSF(1,8) = (XI - .5D0) * (1.D0 - ETA**2)
DSF(1,9) = -2.D0*XI*(1.D0 - ETA**2)
!
!....... their derivatives w.r.t. eta
DSF(2,1) = .5D0*XI*(XI - 1.D0)*(ETA - .5D0)
DSF(2,2) = .5D0*XI*(XI + 1.D0)*(ETA - .5D0)
DSF(2,3) = .5D0*XI*(XI + 1.D0)*(ETA + .5D0)
DSF(2,4) = .5D0*XI*(XI - 1.D0)*(ETA + .5D0)
DSF(2,5) = (1.D0 - XI**2)*(ETA - .5D0)
DSF(2,7) = (1.D0 - XI**2)*(ETA + .5D0)
DSF(2,6) = XI*(XI + 1.D0)*(-ETA)
DSF(2,8) = XI*(XI - 1.D0)*(-ETA)
DSF(2,9) = -2.D0*ETA*(1.D0 - XI**2)
ELSE !no serendipity nodes yet and pry ever
WRITE(*,*) 'csf2d: only 4 or 9 nodes supported'
IERR = 1
RETURN
ENDIF
!
!.... i like this simple check in komatisch and tromp
SUM1 = 0.D0
SUM2 = 0.D0
SUM3 = 0.D0
DO 1 I=1,NGNOD
IF (DABS(SF(I)).LT.EPS) SF(I) = 0.D0
IF (DABS(DSF(1,I)).LT.EPS) DSF(1,I) = 0.D0
IF (DABS(DSF(2,I)).LT.EPS) DSF(2,I) = 0.D0
SUM1 = SUM1 + SF(I)
SUM2 = SUM2 + DSF(1,I)
SUM3 = SUM3 + DSF(2,I)
1 CONTINUE
IF (DABS(SUM2).GT.EPS) THEN
WRITE(*,*) 'csf2d: Error in xi shape functions'
IERR = 1
RETURN
ENDIF
IF (DABS(SUM3).GT.EPS) THEN
WRITE(*,*) 'csf2d: Error in eta shape functions'
IERR = 1
RETURN
ENDIF
RETURN
END
! !
!======================================================================!
! !
SUBROUTINE CSF2DND(NGNOD,XI,ETA, SF, IERR)
!
! Calculates 2D shape functions for interpolation
!
! 1 ^ 4 - - - 7 - - - 3
! | | | |
! | | | |
! 0 xi 8 - - - 9 - - - 6
! | | | |
! | | | |
! -1 1 - - - 5 - - - 2
!
! ----- eta ---->
! -1 0 1
!
! INPUT MEANING
! ----- -------
! ETA eta location
! NGNOD number of global nodes on element
! XI xi location
!
! OUTPUT MEANING
! ------ -------
! IERR error flag
! SF shape functions at xi / eta
!
!.... variable declarations
IMPLICIT NONE
REAL*8, INTENT(IN) :: XI, ETA
INTEGER*4, INTENT(IN) :: NGNOD
REAL*8, INTENT(OUT) :: SF(NGNOD)
INTEGER*4, INTENT(OUT) :: IERR
!.... local variables
INTEGER*4 I
REAL*8 EPS
PARAMETER(EPS = 2.2204D-16)
!
!----------------------------------------------------------------------!
!
!.... 4 noded element
IERR = 0
IF (NGNOD.EQ.4) THEN !4 node element; hat shape fns
SF(1) = .25D0*(1.D0 - XI)*(1.D0 - ETA)
SF(2) = .25D0*(1.D0 + XI)*(1.D0 - ETA)
SF(3) = .25D0*(1.D0 + XI)*(1.D0 + ETA)
SF(4) = .25D0*(1.D0 - XI)*(1.D0 + ETA)
ELSEIF(NGNOD.EQ.9) THEN !9 node element; bubble shape fns
SF(1) = .25D0*XI*(XI - 1.D0)*ETA*(ETA - 1.D0)
SF(2) = .25D0*XI*(XI + 1.D0)*ETA*(ETA - 1.D0)
SF(3) = .25D0*XI*(XI + 1.D0)*ETA*(ETA + 1.D0)
SF(4) = .25D0*XI*(XI - 1.D0)*ETA*(ETA + 1.D0)
SF(5) = .5D0*(1.D0 - XI**2)*ETA*(ETA - 1.D0)
SF(7) = .5D0*(1.D0 - XI**2)*ETA*(ETA + 1.D0)
SF(6) = .5D0*XI*(XI + 1.D0)*(1.D0 - ETA**2)
SF(8) = .5D0*XI*(XI - 1.D0)*(1.D0 - ETA**2)
SF(9) = (1.D0 - XI**2)*(1.D0 - ETA**2)
ELSE !no serenditity nodes as of now
WRITE(*,*) 'csf2dnd: only 4 or 9 nodes supported'
IERR = 1
RETURN
ENDIF
DO 1 I=1,NGNOD
IF (DABS(SF(I)).LT.EPS) SF(I) = 0.D0
1 CONTINUE
RETURN
END
! !
!======================================================================!
! !
SUBROUTINE CSFT2D(MDIM,NGNOD, R,S, SF,DSF)
!
! Triangle shape functions from Hughes pg 167-168
!
! 2 (1,3,1) x
! |\ |\
! | \ | \
! 5 4 (1,2,1) x x (2,2,1)
! | \ | \
! | \ | \
! 3 -6- 1 (1,1,3) x -x- x (3,1,1)
! (2,1,2)
!
! INPUT MEANING
! ----- -------
! MDIM leading dimension for DSF
! NGNOD number of anchor nodes (3, or 6, 3 default)
! R r local coordinate
! S s local coordinate
!
! OUTPUT MEANING
! ------ -------
! DSF derivatives of shape functions in r,s at (r,s)
! SF shape functions evaluated at (r,s)
!
!.... variable declarations
INTEGER*4, INTENT(IN) :: MDIM,NGNOD
REAL*8, INTENT(IN) :: R, S
REAL*8, INTENT(OUT) :: DSF(MDIM,NGNOD), SF(NGNOD)
REAL*8 T, DTDS, DTDR, SUM1, SUM2, SUM3, EPS
PARAMETER(EPS = 2.2204D-16)
!
!----------------------------------------------------------------------1
!
!.... quadratic
IF (NGNOD.EQ.6) THEN
T = 1.D0 - R - S
SF(1) = R*(2.D0*R - 1.D0)
SF(2) = S*(2.D0*S - 1.D0)
SF(3) = T*(2.D0*T - 1.D0)
SF(4) = 4.D0*R*S
SF(5) = 4.D0*S*T
SF(6) = 4.D0*R*T
DTDR =-1.D0
DTDS =-1.D0
DSF(1,1) = 4.D0*R - 1.D0
DSF(1,2) = 0.D0
DSF(1,3) = (4.D0*T - 1.D0)*DTDR
DSF(1,4) = 4.D0*S
DSF(1,5) = 4.D0*S*DTDR
DSF(1,6) = 4.D0*(T + R*DTDR)
DSF(2,1) = 0.D0
DSF(2,2) = 4.D0*S - 1.D0
DSF(2,3) = (4.D0*T - 1.D0)*DTDS
DSF(2,4) = 4.D0*R
DSF(2,5) = 4.D0*(T + S*DTDS)
DSF(2,6) = 4.D0*R*DTDS
ELSE !linear default
SF(1) = R
SF(2) = S
SF(3) = 1.D0 - R - S
DSF(1,1) = 1.D0
DSF(1,2) = 0.D0
DSF(1,3) =-1.D0
DSF(2,1) = 0.D0
DSF(2,2) = 1.D0
DSF(2,3) =-1.D0
ENDIF
!
!.... clean up
SUM1 = 0.D0
SUM2 = 0.D0
SUM3 = 0.D0
DO 1 I=1,NGNOD
IF (DABS(SF(I)).LT.EPS) SF(I) = 0.D0
IF (DABS(DSF(1,I)).LT.EPS) DSF(1,I) = 0.D0
IF (DABS(DSF(2,I)).LT.EPS) DSF(2,I) = 0.D0
SUM1 = SUM1 + SF(I)
SUM2 = SUM2 + DSF(1,I)
SUM3 = SUM3 + DSF(2,I)
1 CONTINUE
RETURN
END
! !
!======================================================================!
! !
SUBROUTINE CSFT2DND(NGNOD, R,S, SF)
!
! Triangle shape functions from Hughes pg 167-168
!
! 2 (1,3,1) x
! |\ |\
! | \ | \
! 5 4 (1,2,1) x x (2,2,1)
! | \ | \
! | \ | \
! 3 -6- 1 (1,1,3) x -x- x (3,1,1)
! (2,1,2)
!
! INPUT MEANING
! ----- -------
! NGNOD number of anchor nodes (3, or 6, 3 default)
! R r local coordinate
! S s local coordinate
!
! OUTPUT MEANING
! ------ -------
! SF shape functions evaluated at (r,s)
!
!.... variable declarations
REAL*8, INTENT(IN) :: R, S
INTEGER*4, INTENT(IN) :: NGNOD
REAL*8, INTENT(OUT) :: SF(NGNOD)
REAL*8 T, EPS
PARAMETER(EPS = 2.2204D-16)
!
!----------------------------------------------------------------------1
!
!.... quadratic
IF (NGNOD.EQ.6) THEN
T = 1.D0 - R - S
SF(1) = R*(2.D0*R - 1.D0)
SF(2) = S*(2.D0*S - 1.D0)
SF(3) = T*(2.D0*T - 1.D0)
SF(4) = 4.D0*R*S
SF(5) = 4.D0*S*T
SF(6) = 4.D0*R*T
ELSE !linear default
SF(1) = R
SF(2) = S
SF(3) = 1.D0 - R - S
ENDIF
!
!.... clean up
DO 1 I=1,NGNOD
IF (DABS(SF(I)).LT.EPS) SF(I) = 0.D0
1 CONTINUE
RETURN
END