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SUBROUTINE STRAP1
C
C THIS ROUTINE IS PHASE I OF STRESS DATA RECOVERY FOR THE
C TRAPEZOIDAL CROSS SECTION RING
C
C ECPT FOR THE TRAPEZOIDAL RING
C TYPE
C ECPT( 1) ELEMENT IDENTIFICATION I
C ECPT( 2) SCALAR INDEX NO. FOR GRID POINT A I
C ECPT( 3) SCALAR INDEX NO. FOR GRID POINT B I
C ECPT( 4) SCALAR INDEX NO. FOR GRID POINT C I
C ECPT( 5) SCALAR INDEX NO. FOR GRID POINT D I
C ECPT( 6) MATERIAL ORIENTATION ANGLE(DEGREES) R
C ECPT( 7) MATERIAL IDENTIFICATION I
C ECPT( 8) COOR. SYS. ID. FOR GRID POINT A I
C ECPT( 9) X-COOR. OF GRID POINT A (IN BASIC COOR.) R
C ECPT(10) Y-COOR. OF GRID POINT A (IN BASIC COOR.) R
C ECPT(11) Z-COOR. OF GRID POINT A (IN BASIC COOR.) R
C ECPT(12) COOR. SYS. ID. FOR GRID POINT B I
C ECPT(13) X-COOR. OF GRID POINT B (IN BASIC COOR.) R
C ECPT(14) Y-COOR. OF GRID POINT B (IN BASIC COOR.) R
C ECPT(15) Z-COOR. OF GRID POINT B (IN BASIC COOR.) R
C ECPT(16) COOR. SYS. ID. FOR GRID POINT C I
C ECPT(17) X-COOR. OF GRID POINT C (IN BASIC COOR.) R
C ECPT(18) Y-COOR. OF GRID POINT C (IN BASIC COOR.) R
C ECPT(19) Z-COOR. OF GRID POINT C (IN BASIC COOR.) R
C ECPT(20) COOR. SYS. ID. FOR GRID POINT D I
C ECPT(21) X-COOR. OF GRID POINT D (IN BASIC COOR.) R
C ECPT(22) Y-COOR. OF GRID POINT D (IN BASIC COOR.) R
C ECPT(23) Z-COOR. OF GRID POINT D (IN BASIC COOR.) R
C ECPT(24) EL. TEMPERATURE FOR MATERIAL PROPERTIES R
C
DIMENSION IECPT(24),ICS(4),GAMBQ(64),DZERO(32),SP(24),
1 ALFB(4),TEO(16),EE(16),DELINT(12),GAMQS(96),JRZ(2)
CHARACTER UFM*23
COMMON /XMSSG / UFM
COMMON /CONDAS/ CONSTS(5)
COMMON /SDR2X5/ ECPT(24),DUM5(76),IDEL,IGP(4),TZ,SEL(240),TS(4),
1 AK(144)
COMMON /MATIN / MATIDC,MATFLG,ELTEMP,STRESS,SINTH,COSTH
COMMON /MATOUT/ E(3),ANU(3),RHO,G(3),ALF(3),TZERO
COMMON /SDR2X6/ D(144),GAMBL(144),R(5),Z(5)
COMMON /SYSTEM/ IBUF,IOUT
EQUIVALENCE (CONSTS(2),TWOPI),(CONSTS(4),DEGRA),
1 (IECPT(1),ECPT(1)),(R(1),R1),(R(2),R2),(R(3),R3),
2 (R(4),R4),(Z(1),Z1),(Z(2),Z2),(Z(3),Z3),(Z(4),Z4),
3 (GAMBL(1),SP(1)),(GAMBL(1),TEO(1)),
4 (GAMBL(17),DELINT(1))
C
C STORE ECPT PARAMETERS IN LOCAL VARIABLES
C
IDEL = IECPT(1)
IGP(1) = IECPT(2)
IGP(2) = IECPT(3)
IGP(3) = IECPT(4)
IGP(4) = IECPT(5)
MATID = IECPT(7)
ICS(1) = IECPT(8)
ICS(2) = IECPT(12)
ICS(3) = IECPT(16)
ICS(4) = IECPT(20)
R(1) = ECPT(9)
D(1) = ECPT(10)
Z(1) = ECPT(11)
R(2) = ECPT(13)
D(2) = ECPT(14)
Z(2) = ECPT(15)
R(3) = ECPT(17)
D(3) = ECPT(18)
Z(3) = ECPT(19)
R(4) = ECPT(21)
D(4) = ECPT(22)
Z(4) = ECPT(23)
TEMPE = ECPT(24)
DGAMA = ECPT(6)
C
C TEST THE VALIDITY OF THE GRID POINT COORDINATES
C
DO 200 I = 1,4
IF (R(I) .LT. 0.0) CALL MESAGE (-30,37,IDEL)
IF (D(I) .NE. 0.0) CALL MESAGE (-30,37,IDEL)
200 CONTINUE
C
C COMPUTE THE ELEMENT COORDINATES
C
ZMIN = AMIN1(Z1,Z2,Z3,Z4)
Z1 = Z1 - ZMIN
Z2 = Z2 - ZMIN
Z3 = Z3 - ZMIN
Z4 = Z4 - ZMIN
RMIN = AMIN1(R1,R2,R3,R4)
RMAX = AMAX1(R1,R2,R3,R4)
IF (RMIN .EQ. 0.) GO TO 206
IF (RMAX/RMIN .LE. 10.) GO TO 206
C
C RATIO OF RADII IS TOO LARGE FOR GAUSS QUADRATURE FOR IP=-1
C
WRITE (IOUT,205) UFM,IDEL
205 FORMAT (A23,', TRAPRG ELEMENT',I9,' HAS A MAXIMUM TO MINIMUM ',
1 'RADIUS RATIO EXCEEDING 10.', /5X,
2 'ACCURACY OF NUMERICAL INTEGRATION WOULD BE IN DOUBT.')
CALL MESAGE (-30,37,IDEL)
206 CONTINUE
ICORE = 0
J = 1
DO 210 I = 1,4
IF (R(I) .NE. 0.) GO TO 210
ICORE = ICORE + 1
JRZ(J) = I
J = 2
210 CONTINUE
IF (ICORE.NE.0 .AND. ICORE.NE.2) CALL MESAGE (-30,37,IDEL)
C
C FORM THE TRANSFORMATION MATRIX (8X8) FROM FIELD COORDINATES TO
C GRID POINT DEGREES OF FREEDOM
C
DO 300 I = 1,64
GAMBQ(I) = 0.0
300 CONTINUE
GAMBQ( 1) = 1.0
GAMBQ( 2) = R1
GAMBQ( 3) = Z1
GAMBQ( 4) = R1*Z1
GAMBQ(13) = 1.0
GAMBQ(14) = R1
GAMBQ(15) = Z1
GAMBQ(16) = GAMBQ(4)
GAMBQ(17) = 1.0
GAMBQ(18) = R2
GAMBQ(19) = Z2
GAMBQ(20) = R2*Z2
GAMBQ(29) = 1.0
GAMBQ(30) = R2
GAMBQ(31) = Z2
GAMBQ(32) = GAMBQ(20)
GAMBQ(33) = 1.0
GAMBQ(34) = R3
GAMBQ(35) = Z3
GAMBQ(36) = R3*Z3
GAMBQ(45) = 1.0
GAMBQ(46) = R3
GAMBQ(47) = Z3
GAMBQ(48) = GAMBQ(36)
GAMBQ(49) = 1.0
GAMBQ(50) = R4
GAMBQ(51) = Z4
GAMBQ(52) = R4*Z4
GAMBQ(61) = 1.0
GAMBQ(62) = R4
GAMBQ(63) = Z4
GAMBQ(64) = GAMBQ(52)
C
C NO NEED TO COMPUTE DETERMINANT SINCE IT IS NOT USED SUBSEQUENTLY.
C
ISING = -1
CALL INVERS (8,GAMBQ(1),8,D(10),0,D(11),ISING,SP)
C
IF (ISING .EQ. 2) CALL MESAGE (-30,26,IDEL)
C
C MODIFY THE TRANSFORMATION MATRIX IF ELEMENT IS A CORE ELEMENT
C
IF (ICORE .EQ. 0) GO TO 305
JJ1 = 2*JRZ(1) - 1
JJ2 = 2*JRZ(2) - 1
C
DO 303 I = 1,8
J = 8*(I-1)
GAMBQ(I ) = 0.0
GAMBQ(I+ 16) = 0.0
GAMBQ(J+JJ1) = 0.
GAMBQ(J+JJ2) = 0.
303 CONTINUE
305 CONTINUE
C
C CALCULATE THE INTEGRAL VALUES IN ARRAY DELINT WHERE THE ORDER IS
C INDICATED BY THE FOLLOWING TABLE
C
C DELINT( 1) - (-1,0)
C DELINT( 2) - (-1,1)
C DELINT( 3) - (-1,2)
C DELINT( 4) - ( 0,0)
C DELINT( 5) - ( 0,1)
C DELINT( 6) - ( 0,2)
C DELINT( 7) - ( 1,0)
C DELINT( 8) - ( 1,1)
C DELINT( 9) - ( 1,2)
C DELINT(10) - ( 2,0)
C DELINT(11) - ( 2,1)
C DELINT(12) - ( 3,0)
C
I1 = 0
DO 400 I = 1,4
IP = I - 2
DO 350 J = 1,3
IQ = J - 1
I1 = I1 + 1
IF (I1 .NE. 12) GO TO 340
IP = 3
IQ = 0
340 CONTINUE
IF (ICORE .EQ. 0) GO TO 345
IF (I1 .GT. 3) GO TO 345
DELINT(I1) = 0.0
GO TO 350
345 CONTINUE
DELINT(I1) = RZINTS(IP,IQ,R,Z,4)
350 CONTINUE
400 CONTINUE
C
C LOCATE THE MATERIAL PROPERTIES IN THE MAT1 OR MAT3 TABLE
C
MATIDC = MATID
MATFLG = 7
ELTEMP = TEMPE
CALL MAT (IDEL)
C
C SET MATERIAL PROPERTIES IN LOCAL VARIABLES
C
ER = E(1)
ET = E(2)
EZ = E(3)
VRT = ANU(1)
VTZ = ANU(2)
VZR = ANU(3)
GRZ = G(3)
TZ = TZERO
VTR = VRT*ET/ER
VZT = VTZ*EZ/ET
VRZ = VZR*ER/EZ
DEL = 1.0 - VRT*VTR - VTZ*VZT - VZR*VRZ - VRT*VTZ*VZR
1 - VRZ*VTR*VZT
C
C GENERATE ELASTIC CONSTANTS MATRIX (4X4)
C
EE( 1) = ER*(1.0 - VTZ*VZT)/DEL
EE( 2) = ER*(VTR + VZR*VTZ)/DEL
EE( 3) = ER*(VZR + VTR*VZT)/DEL
EE( 4) = 0.0
EE( 5) = EE(2)
EE( 6) = ET*(1.0 - VRZ*VZR)/DEL
EE( 7) = ET*(VZT + VRT*VZR)/DEL
EE( 8) = 0.0
EE( 9) = EE(3)
EE(10) = EE(7)
EE(11) = EZ*(1.0 - VRT*VTR)/DEL
EE(12) = 0.0
EE(13) = 0.0
EE(14) = 0.0
EE(15) = 0.0
EE(16) = GRZ
C
C FORM TRANSFORMATION MATRIX (4X4) FROM MATERIAL AXIS TO ELEMENT
C GEOMETRIC AXIS
C
DGAMR = DGAMA*DEGRA
COSG = COS(DGAMR)
SING = SIN(DGAMR)
TEO( 1) = COSG**2
TEO( 2) = 0.0
TEO( 3) = SING**2
TEO( 4) = SING*COSG
TEO( 5) = 0.0
TEO( 6) = 1.0
TEO( 7) = 0.0
TEO( 8) = 0.0
TEO( 9) = TEO(3)
TEO(10) = 0.0
TEO(11) = TEO(1)
TEO(12) =-TEO(4)
TEO(13) =-2.0*TEO(4)
TEO(14) = 0.0
TEO(15) =-TEO(13)
TEO(16) = TEO(1) - TEO(3)
C
C TRANSFORM THE ELASTIC CONSTANTS MATRIX FROM MATERIAL
C TO ELEMENT GEOMETRIC AXIS
C
CALL GMMATS (TEO,4,4,1, EE ,4,4,0, D )
CALL GMMATS (D ,4,4,0, TEO,4,4,0, EE)
C
C FORM THE ELEMENT STIFFNESS MATRIX IN FIELD COORDINATES
C
EE48 = EE(4) + EE(8)
D ( 1) = EE(1) + 2.0 * EE(2) + EE(6)
AK( 1) = EE(6) * DELINT(1)
AK( 2) = (EE(2) + EE(6)) * DELINT(4)
AK( 3) = EE(6) * DELINT(2) + EE(8) * DELINT(4)
AK( 4) = (EE(2) + EE(6)) * DELINT(5) + EE(8) * DELINT(7)
AK( 5) = 0.0
AK( 6) = EE(8) * DELINT(4)
AK( 7) = EE(7) * DELINT(4)
AK( 8) = EE(7) * DELINT(7) + EE(8) * DELINT(5)
AK( 9) = AK(2)
AK(10) = D(1) * DELINT(7)
AK(11) = (EE(2) + EE(6)) * DELINT(5) + EE48 * DELINT(7)
AK(12) = D(1) * DELINT(8) + EE48 * DELINT(10)
AK(13) = 0.0
AK(14) = EE48 * DELINT(7)
AK(15) = (EE(3) + EE(7)) * DELINT(7)
AK(16) = (EE(3) + EE(7)) * DELINT(10) + EE48 * DELINT(8)
AK(17) = AK( 3)
AK(18) = AK(11)
AK(19) = EE(6) * DELINT(3) + EE(16)* DELINT(7)
1 + (EE(8) + EE(14)) * DELINT(5)
AK(20) = (EE(2) + EE(6)) * DELINT(6) + EE(16) * DELINT(10)
1 + (EE(8) + EE(13) + EE(14)) * DELINT(8)
AK(21) = 0.0
AK(22) = EE(16) * DELINT(7) + EE(8) * DELINT(5)
AK(23) = EE(7) * DELINT(5) + EE(15) * DELINT(7)
AK(24) = (EE(7) + EE(16)) * DELINT(8)
1 + EE(8) *DELINT(6) + EE(15) * DELINT(10)
AK(25) = AK(4)
AK(26) = AK(12)
AK(27) = AK(20)
AK(28) = D(1) * DELINT(9) + EE(16) * DELINT(12)
1 + (EE48 + EE(13) + EE(14)) * DELINT(11)
AK(29) = 0.0
AK(30) = EE(16) * DELINT(10) + EE48 * DELINT(8)
AK(31) = (EE(3) + EE(7)) * DELINT(8) + EE(15) * DELINT(10)
AK(32) = (EE(3) + EE(7) + EE(16)) * DELINT(11)
1 + EE(15) * DELINT(12) + EE48 * DELINT(9)
AK(33) = 0.0
AK(34) = 0.0
AK(35) = 0.0
AK(36) = 0.0
AK(37) = 0.0
AK(38) = 0.0
AK(39) = 0.0
AK(40) = 0.0
AK(41) = AK( 6)
AK(42) = AK(14)
AK(43) = AK(22)
AK(44) = AK(30)
AK(45) = 0.0
AK(46) = EE(16)*DELINT(7)
AK(47) = EE(15)*DELINT(7)
AK(48) = EE(16)*DELINT(8) + EE(15) * DELINT(10)
AK(49) = AK( 7)
AK(50) = AK(15)
AK(51) = AK(23)
AK(52) = AK(31)
AK(53) = 0.0
AK(54) = AK(47)
AK(55) = EE(11)*DELINT( 7)
AK(56) = EE(11)*DELINT(10) + EE(12) * DELINT(8)
AK(57) = AK( 8)
AK(58) = AK(16)
AK(59) = AK(24)
AK(60) = AK(32)
AK(61) = 0.0
AK(62) = AK(48)
AK(63) = AK(56)
AK(64) = EE(11) * DELINT(12) + EE(16) * DELINT(9)
1 + (EE(12) + EE(13)) * DELINT(11)
C
DO 600 I = 1,64
AK(I) = TWOPI*AK(I)
600 CONTINUE
C
C TRANSFORM THE ELEMENT STIFFNESS MATRIX FROM FIELD COORDINATES
C TO GRID POINT DEGREES OF FREEDOM
C
CALL GMMATS (GAMBQ,8,8,1, AK ,8,8,0, D )
CALL GMMATS (D ,8,8,0, GAMBQ,8,8,0, AK)
C
C GENERATE THE TRANSFORMATION MATRIX FROM TWO TO THREE DEGREES OF
C FREEDOM PER POINT
C
DO 700 I = 1,96
GAMQS( I) = 0.0
700 CONTINUE
GAMQS( 1) = 1.0
GAMQS(15) = 1.0
GAMQS(28) = 1.0
GAMQS(42) = 1.0
GAMQS(55) = 1.0
GAMQS(69) = 1.0
GAMQS(82) = 1.0
GAMQS(96) = 1.0
C
C TRANSFORM THE STIFFNESS MATRIX FROM TWO TO THREE DEGREES OF
C FREEDOM PER POINT
C
CALL GMMATS (GAMQS(1),8,12,1, AK(1) ,8, 8,0, D(1) )
CALL GMMATS (D(1) ,12,8,0, GAMQS(1),8,12,0, AK(1))
C
C LOCATE THE TRANSFORMATION MATRICES FOR THE FOUR GRID POINTS
C
DO 750 I = 1,144
GAMBL(I) = 0.0
750 CONTINUE
DO 800 I = 1,4
CALL TRANSS (ICS(I),D(1))
K = 39*(I-1) + 1
DO 800 J = 1,3
KK = K + 12*(J-1)
JJ = 3 *(J-1) + 1
GAMBL(KK ) = D(JJ )
GAMBL(KK+1) = D(JJ+1)
GAMBL(KK+2) = D(JJ+2)
800 CONTINUE
C
C TRANSFORM THE STIFFNESS MATRIX FROM BASIC TO LOCAL COORDINATES
C
CALL GMMATS (GAMBL(1),12,12,1, AK(1) ,12,12,0, D(1) )
CALL GMMATS (D(1) ,12,12,0, GAMBL(1),12,12,0, AK(1))
C
C COMPUTE THE FIFTH GRID POINT TO BE THE AVERAGE OF THE FOUR
C CORNER POINTS
C
R(5) = (R1 + R2 + R3 + R4)/4.0
Z(5) = (Z1 + Z2 + Z3 + Z4)/4.0
C
C INITIALIZE THE CONSTANT PORTION OF THE D SUB 0 MATRIX
C
DO 850 I = 1,32
DZERO(I) = 0.0
850 CONTINUE
DZERO( 2) = 1.0
DZERO(10) = 1.0
DZERO(23) = 1.0
DZERO(27) = 1.0
DZERO(30) = 1.0
C
C START THE LOOP TO COMPUTE THE STRESS MATRIX FOR EACH GRID POINT
C
DO 950 J = 1,5
C
C COMPUTE THE VARIABLE PORTION OF THE D SUB 0 MATRIX
C
DZERO( 4) = Z(J)
IF (ICORE .NE. 0) GO TO 875
DZERO( 9) = 1.00/R(J)
DZERO(11) = Z(J)/R(J)
875 CONTINUE
DZERO(12) = Z(J)
DZERO(24) = R(J)
DZERO(28) = R(J)
DZERO(32) = Z(J)
C
C COMPUTE THE STRESS MATRIX IN FIELD COORDINATES
C
CALL GMMATS (EE(1),4,4,0, DZERO(1),4,8,0, D(1))
C
C TRANSFORM THE STRESS MATRIX TO GRID POINT DEGREES OF FREEDOM
C
CALL GMMATS (D(1),4,8,0, GAMBQ(1),8,8,0, D(37))
C
C TRANSFORM THE STRESS MATRIX FROM TWO TO THREE DEGREES OF FREEDOM
C PER POINT
C
CALL GMMATS (D(37),4,8,0, GAMQS(1),8,12,0, D(73))
C
C TRANSFORM THE STRESS MATRIX FROM BASIC TO LOCAL COORDINATES
C
K = 48*(J-1) + 1
CALL GMMATS (D(73),4,12,0, GAMBL(1),12,12,0, SEL(K))
C
950 CONTINUE
C
C COMPUTE THE THERMAL STRAIN VECTOR
C
DO 900 I = 1,3
ALFB(I) = ALF(I)
900 CONTINUE
ALFB(4) = 0.0
C
C COMPUTE THE THERMAL STRESS VECTOR
C
CALL GMMATS (EE(1),4,4,0, ALFB(1),4,1,0, TS(1))
RETURN
END
|
