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SUBROUTINE IHEXSD (TYPE,SHP,DSHP,JACOB,DETJ,EID,XI,ETA,ZETA,BXYZ)
C
C DOUBLE PRECISION VERSION
C
C ISOPARAMETRIC UTILITY ROUTINE. THIS ROUTINE WILL COMPUTE
C VALUES OF THE SHAPE FUNCTIONS, THEIR DERIVATIVES WITH RESPECT TO
C XI,ETA, AND ZETA, THE JACOBIAN MATRIX INVERSE, AND ITS DETERMINANT
C
C TYPE = 1 IHEX1
C TYPE = 2 IHEX2
C TYPE = 3 IHEX3
C
C SHP = VALUES OF SHAPE FUNCTIONS
C DSHP = DERIVATIVES OF SHAPE FUNCTIONS W.R.T. XI, ETA, ZETA
C JACOB = JACOBIAN MATRIX INVERSE
C DETJ = DETERMINANT OF JACOBIAN MATRIX
C XI, ETA, ZETA = ELEMENT COORDINATES AT WHICH THESE COMPUTATIONS
C TAKE PLACE
C BXYZ = BASIC SYSTEM COORDINATES FOR GRID POINTS
C
C LOCAL VARIABLES
C X,Y,Z = CONSTANTS FOR EACH SHAPE FUNCTION
C NGP = NUMBER OF SHAPE FUNCTIONS, ALSO NUMBER OF GRID POINTS
C
INTEGER TYPE ,EID ,OP
REAL BXYZ(3,8)
DOUBLE PRECISION SHP(8) ,DSHP(3,8) ,JACOB(3,3) ,
1 DETJ ,XI ,ETA ,ZETA ,
2 X ,Y ,Z ,QXI ,
3 QETA ,QZETA ,QXYZ ,WORK(3,3)
CHARACTER UFM*23
COMMON /XMSSG / UFM
COMMON /SYSTEM/ SYSBUF ,OP
C
NGP = 12*TYPE - 4
Y =-1.0
Z =-1.0
GO TO (100,200,310), TYPE
C
C LINEAR ELEMENT IHEX1
C
100 DO 110 J = 1,2
IF (J .EQ. 2) Z = 1.0
X =-1.0
Y =-1.0
DO 110 I = 1,4
IF (I .EQ. 3) Y = 1.0
IF (I .EQ. 2) X = 1.0
IF (I .EQ. 4) X =-1.0
K = I + (J-1)*4
QXI = 1.0 + XI*X
QETA = 1.0 + ETA*Y
QZETA = 1.0 + ZETA*Z
SHP(K) = QXI*QETA*QZETA/8.0
DSHP(1,K) = X*QETA*QZETA/8.0
DSHP(2,K) = Y*QXI*QZETA/8.0
DSHP(3,K) = Z*QXI*QETA/8.0
110 CONTINUE
GO TO 430
C
C QUADRATIC ELEMENT IHEX2
C
200 D = 1.0
X = 0.0
DO 300 I = 1,20
C 1 2 3 4 5 6 7 8 9 10
GO TO (220,210,210,230,230,220,220,240,250,210,
1 230,220,250,210,210,230,230,220,220,240), I
210 X = X + D
GO TO 260
220 X = X - D
GO TO 260
230 Y = Y + D
GO TO 260
240 Y = Y - D
GO TO 260
250 Z = Z + 1.0
Y =-1.0
D = 3.0-D
260 IF (X .EQ. 0.0) GO TO 270
IF (Y .EQ. 0.0) GO TO 280
IF (Z .EQ. 0.0) GO TO 290
C
C CORNER POINT
C
QXI = 1.0 + X*XI
QETA = 1.0 + Y*ETA
QZETA = 1.0 + Z*ZETA
QXYZ = X*XI + Y*ETA + Z*ZETA
SHP(I)= QXI*QETA*QZETA*(QXYZ-2.0)/8.0
DSHP(1,I) = X*QETA*QZETA*(X*XI+QXYZ-1.0)/8.0
DSHP(2,I) = Y*QXI*QZETA*(Y*ETA+QXYZ-1.0)/8.0
DSHP(3,I) = Z*QXI*QETA*(Z*ZETA+QXYZ-1.0)/8.0
GO TO 300
C
C MID-EDGE POINT, X=0.0
C
270 QXI = 1.0 - XI**2
QETA = 1.0 + Y*ETA
QZETA = 1.0 + Z*ZETA
SHP(I)= QXI*QETA*QZETA/4.0
DSHP(1,I) =-XI*QETA*QZETA/2.0
DSHP(2,I) = QXI*QZETA*Y/4.0
DSHP(3,I) = QXI*QETA*Z/4.0
GO TO 300
C
C MID-EDGE POINT, Y=0.0
C
280 QXI = 1.0 + X*XI
QETA = 1.0 - ETA**2
QZETA = 1.0 + Z*ZETA
SHP(I)= QETA*QXI*QZETA/4.0
DSHP(1,I) = QETA*QZETA*X/4.0
DSHP(2,I) =-ETA*QZETA*QXI/2.0
DSHP(3,I) = QETA*QXI*Z/4.0
GO TO 300
C
C MID-EDGE POINT, Z=0.0
C
290 QXI = 1.0 + X*XI
QETA = 1.0 + Y*ETA
QZETA = 1.0 - ZETA**2
SHP(I)= QZETA*QXI*QETA/4.0
DSHP(1,I) = QZETA*QETA*X/4.0
DSHP(2,I) = QZETA*QXI*Y/4.0
DSHP(3,I) =-ZETA*QXI*QETA/2.0
300 CONTINUE
GO TO 430
C
C CUBIC ELEMENT IHEX3
C
310 D = 2.0/3.0
X =-1.0/3.0
DO 420 I = 1,32
C 1 2 3 4 5 6 7 8 9 10
GO TO (320,330,330,330,340,340,340,320,320,320,
2 350,350,360,330,340,320,360,330,340,320,
3 360,330,330,330,340,340,340,320,320,320,
4 350,350),I
320 X = X - D
GO TO 370
330 X = X + D
GO TO 370
340 Y = Y + D
GO TO 370
350 Y = Y - D
GO TO 370
360 Y =-1.0
Z = Z + 2.0/3.0
IF (Z .GT. -1.0) D = 2.0
IF (Z .GT. 0.4) D = 2.0/3.0
370 IF (DABS(X) .LT. 0.4) GO TO 390
IF (DABS(Y) .LT. 0.4) GO TO 400
IF (DABS(Z) .LT. 0.4) GO TO 410
C
C CORNER POINT
C
QXI = 1.0 + X*XI
QETA = 1.0 + Y*ETA
QZETA = 1.0 + Z*ZETA
QXYZ = XI**2+ETA**2+ZETA**2 - 19.0/9.0
SHP(I)= 9.0*QXI*QETA*QZETA*QXYZ/64.0
DSHP(1,I) = 9.0*QETA*QZETA*(X*(2.0*XI**2+QXYZ)+2.0*XI)/64.0
DSHP(2,I) = 9.0*QXI*QZETA*(Y*(2.0*ETA**2+QXYZ)+2.0*ETA)/64.0
DSHP(3,I) = 9.0*QXI*QETA*(Z*(2.0*ZETA**2+QXYZ)+2.0*ZETA)/64.0
GO TO 420
C
C MID-EDGE POINT, X = + OR - 1/3
C
390 QXI = 9.0*(1.0-XI**2)*(1.0+9.0*X*XI)/64.0
QETA = 1.0 + Y*ETA
QZETA = 1.0 + Z*ZETA
QXYZ = 9.0*(-2.0*XI+9.0*X-27.0*XI*X*XI)/64.0
SHP(I)= QXI*QETA*QZETA
DSHP(1,I) = QETA*QZETA*QXYZ
DSHP(2,I) = QXI*QZETA*Y
DSHP(3,I) = QXI*QETA*Z
GO TO 420
C
C MID-EDGE POINT Y = + OR - 1/3
C
400 QXI = 1.0 + X*XI
QETA = 9.0*(1.0-ETA**2)*(1.0+9.0*ETA*Y)/64.0
QZETA = 1.0 + Z*ZETA
QXYZ = 9.0*(-2.0*ETA+9.0*Y-27.0*ETA*Y*ETA)/64.0
SHP(I)= QETA*QXI*QZETA
DSHP(1,I) = QETA*QZETA*X
DSHP(2,I) = QXI*QZETA*QXYZ
DSHP(3,I) = QETA*QXI*Z
GO TO 420
C
C MID-EDGE POINTS Z = + OR - 1/3
C
410 QXI = 1.0 + X*XI
QETA = 1.0 + Y*ETA
QZETA = 9.0*(1.0-ZETA**2)*(1.0+9.0*Z*ZETA)/64.0
QXYZ = 9.0*(-2.0*ZETA+9.0*Z-27.0*Z*ZETA**2)/64.0
SHP(I)= QZETA*QXI*QETA
DSHP(1,I) = QZETA*QETA*X
DSHP(2,I) = QZETA*QXI*Y
DSHP(3,I) = QXI*QETA*QXYZ
420 CONTINUE
C
C COMPUTE JACOBIAN MATRIX
C
430 DO 440 I = 1,3
DO 440 J = 1,3
JACOB(I,J) = 0.0
DO 440 K = 1,NGP
JACOB(I,J) = JACOB(I,J) + DSHP(I,K)*DBLE(BXYZ(J,K))
440 CONTINUE
C
C COMPUTE INVERSE AND DETERMINANT OF JACOBIAN MATRIX
C
WORK(1,1) = JACOB(2,2)*JACOB(3,3) - JACOB(2,3)*JACOB(3,2)
WORK(2,1) = JACOB(2,3)*JACOB(3,1) - JACOB(2,1)*JACOB(3,3)
WORK(3,1) = JACOB(2,1)*JACOB(3,2) - JACOB(2,2)*JACOB(3,1)
WORK(1,2) = JACOB(1,3)*JACOB(3,2) - JACOB(1,2)*JACOB(3,3)
WORK(2,2) = JACOB(1,1)*JACOB(3,3) - JACOB(1,3)*JACOB(3,1)
WORK(3,2) = JACOB(1,2)*JACOB(3,1) - JACOB(1,1)*JACOB(3,2)
WORK(1,3) = JACOB(1,2)*JACOB(2,3) - JACOB(1,3)*JACOB(2,2)
WORK(2,3) = JACOB(1,3)*JACOB(2,1) - JACOB(1,1)*JACOB(2,3)
WORK(3,3) = JACOB(1,1)*JACOB(2,2) - JACOB(1,2)*JACOB(2,1)
DETJ = 0.0
DO 450 I = 1,3
DETJ = DETJ + JACOB(I,2)*WORK(2,I)
450 CONTINUE
IF (DETJ .EQ. 0.0) GO TO 470
DO 460 I = 1,3
DO 460 J = 1,3
JACOB(I,J) = WORK(I,J)/DETJ
460 CONTINUE
RETURN
C
C JACOBIAN MATRIX WAS SINGULAR.
C
470 WRITE (OP,480) UFM,EID
480 FORMAT (A23,' 3306, SINGULAR JACOBIAN MATRIX FOR ISOPARAMETRIC ',
1 'ELEMENT NO.',I9)
RETURN
END
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