add documents
This commit is contained in:
김경종
+586
@@ -0,0 +1,586 @@
|
||||
<!-- source-page: 351 -->
|
||||
|
||||
# 9.5.8 Subroutine MINDPB
|
||||
|
||||
This subroutine simply reads some additional information required for controlling the convergence check and inserting additional constraints for the Heterosis element.
|
||||
|
||||
```asm
|
||||
SUBROUTINE MINDPB (IFDIS, IFFIX, IFRES, LNODS, MELEM, MTOTV, MIND 1
|
||||
. NCDIS, NCRES, NELEM, NTYPE) MIND 2
|
||||
C*****************************************************************************************MIND 3
|
||||
C MIND 4
|
||||
C*** READS ADDITIONAL DATA FOR MINDLIN PLATE ANALYSIS MIND 5
|
||||
C MIND 6
|
||||
C*****************************************************************************************MIND 7
|
||||
DIMENSION DERIV(2,9), IFFIX(MTOTV), MIND 8
|
||||
. LNODS(MELEM,9), NCDIS(4), NCRES(4), SHAPE(9) MIND 9
|
||||
C MIND 10
|
||||
C*** READ DATA CONTROLLING CONVERGENCE CHECK MIND 11
|
||||
C MIND 12
|
||||
10 READ(5,900) IFDIS, (NCDIS(I), I=1,4) MIND 13
|
||||
. ,IFRES, (NCRES(I), I=1,4) MIND 14
|
||||
900 FORMAT(5I1) MIND 15
|
||||
WRITE(6,901) IFDIS, (NCDIS(I), I=1,4) MIND 16
|
||||
. ,IFRES, (NCRES(I), I=1,4) MIND 17
|
||||
901 FORMAT(/,23H CONVERGENCE PARAMETERS,/, MIND 18
|
||||
. 8H IFDIS =, I2,5X, 8H NCDIS =, 4I1,/, MIND 19
|
||||
. 8H IFRES =, I2,5X, 8H NCRES =, 4I1, //) MIND 20
|
||||
C*** INSERT ADDITIONAL CONSTRAINT FOR HETEROSIS ELEMENT MIND 21
|
||||
IF(NTYPE.NE.5) GO TO 30 MIND 22
|
||||
DO 20 IELEM=1, NELEM MIND 23
|
||||
LNODE=LNODS(IELEM,9) MIND 24
|
||||
NLOCA=LNODE*3-2 MIND 25
|
||||
20 IFFIX(NLOCA)=-1 MIND 26
|
||||
30 CONTINUE MIND 27
|
||||
RETURN MIND 28
|
||||
END MIND 29
|
||||
```
|
||||
|
||||
# 9.5.9 Subroutine NODEXY
|
||||
|
||||
This subroutine evaluates midside nodes for straight sided 8 and 9-node quadrilateral elements. In the original subroutine described in Section 6.4.1 this routine also evaluated the coordinates of the central node. Here, as we are choosing a hierarchical formulation, the values at the central node and the departures from the interpolated Serendipity values are always taken as zero.
|
||||
|
||||
Thus the revised subroutine NODEXY is almost identical to its namesake given earlier in Section 6.4.1 and is listed below.
|
||||
|
||||
```c
|
||||
SUBROUTINE NODEXY (COORD, LNODS, MELEM, MPOIN, NDIME, NELEM, NNODE) NODE 1
|
||||
C***** NODE 2
|
||||
C***** NODE 3
|
||||
C***** NODE 4
|
||||
C*** INTERPOLATES MIDSIDE NODE COORDINATES FOR 8-NODED ELEMENTS NODE 5
|
||||
C*** INTERPOLATES CENTRAL AND MIDSIDE NODE COORDINATES FOR NODE 6
|
||||
C*** 9-NODE ELEMENTS PROVIDED THAT THE SIDES ARE STRAIGHT NODE 7
|
||||
C***** NODE 8
|
||||
C***** NODE 9
|
||||
```
|
||||
|
||||
<!-- source-page: 352 -->
|
||||
|
||||
```fortran
|
||||
DIMENSION COORD(MPOIN,2),LNODS(MELEM,9) NODE 10
|
||||
IF(NNODE.EQ.4) GO TO 60 NODE 11
|
||||
C NODE 12
|
||||
C*** LOOP OVER EACH ELEMENT NODE 13
|
||||
C NODE 14
|
||||
DO 30 IELEM=1,NELEM NODE 15
|
||||
C NODE 16
|
||||
C*** LOOP OVER EACH ELEMENT EDGE NODE 17
|
||||
C NODE 18
|
||||
NNOD1=NNODE NODE 19
|
||||
IF(NNODE.EQ.8).NNOD1=9 NODE 20
|
||||
DO 20 INODE=1,NNOD1,2 NODE 21
|
||||
IF(INODE.EQ.9.AND.NNODE.EQ.8) GO TO 30 NODE 22
|
||||
IF(INODE.EQ.9) GO TO 50 NODE 23
|
||||
C NODE 24
|
||||
C*** COMPUTE THE NODE NUMBER OF THE FIRST NODE NODE 25
|
||||
C NODE 26
|
||||
NODST=LNODS(IELEM,INODE) NODE 27
|
||||
IGASH=INODE+2 NODE 28
|
||||
IF(IGASH.GE.NNODE) IGASH=1 NODE 29
|
||||
C NODE 30
|
||||
C*** COMPUTE THE NODE NUMBER OF THE LAST NODE NODE 31
|
||||
C NODE 32
|
||||
NODFN=LNODS(IELEM,IGASH) NODE 33
|
||||
MIDPT=INODE+1 NODE 34
|
||||
C NODE 35
|
||||
C*** COMPUTE THE NODE NUMBER OF THE INTERMEDIATE NODE NODE 36
|
||||
C NODE 37
|
||||
NODMD=LNODS(IELEM,MIDPT) NODE 38
|
||||
TOTAL=ABS(COORD(NODMD,1))+ABS(COORD(NODMD,2)) NODE 39
|
||||
C NODE 40
|
||||
C*** IF THE COORDINATES OF THE INTERMEDIATE NODE ARE BOTH ZERO NODE 41
|
||||
C INTERPOLATE BY A STRAIGHT LINE NODE 42
|
||||
C NODE 43
|
||||
IF(TOTAL.GT.0.0) GO TO 20 NODE 44
|
||||
KOUNT=1 NODE 45
|
||||
10 COORD(NODMD,KOUNT)=(COORD(NODST,KOUNT)+COORD(NODFN,KOUNT))/2.0 NODE 46
|
||||
KOUNT=KOUNT+1 NODE 47
|
||||
IF(KOUNT.EQ.2) GO TO 10 NODE 48
|
||||
20 CONTINUE NODE 49
|
||||
50 LNODE=LNODS(IELEM,INODE) NODE 50
|
||||
30 CONTINUE NODE 51
|
||||
60 CONTINUE NODE 52
|
||||
RETURN NODE 53
|
||||
END NODE 54
|
||||
```
|
||||
|
||||
# 9.5.10 Subroutine OUTMP
|
||||
|
||||
This subroutine outputs nodal displacements and reactions and also the Gauss point stress resultants.
|
||||
|
||||
```csv
|
||||
SUBROUTINE OUTMP (EPSTN,IITER,MTOTG,MTOTV,MVFIX,NELEM, OUTP 1
|
||||
. NGAUS,NOFIX,NOUTP,NPOIN,NVFIX,STRSG, OUTP 2
|
||||
. TDISP,TREAC) OUTP 3
|
||||
C**********OUTP 4
|
||||
C OUTP 5
|
||||
C*** OUTPUT DISPLACEMENTS,REACTIONS AND GAUSS POINT STRESS OUTP 6
|
||||
C*** RESULTANTS FOR EP MINDLIN PLATE ANALYSIS OUTP 7
|
||||
C OUTP 8
|
||||
C**********OUTP 9
|
||||
```
|
||||
|
||||
<!-- source-page: 353 -->
|
||||
|
||||
```csv
|
||||
DIMENSION EPSTN(MTOTG), GPCOD(2,9), NOFIX(MVFIX), NOUTP(2), OUTP 10
|
||||
. STRSG(5, MTOTG), TDISP(MTOTV), TREAC(MVFIX, 3) OUTP 11
|
||||
KOUTP=NOUTP(1) OUTP 12
|
||||
IF(IITER.GT.1) KOUTP=NOUTP(2) OUTP 13
|
||||
C
|
||||
C*** OUTPUT DISPLACEMENTS OUTP 15
|
||||
C
|
||||
IF(KOUTP.LT.1) GO TO 10 OUTP 17
|
||||
WRITE(6,900) OUTP 18
|
||||
900 FORMAT(1H0,5X,13HDISPLACEMENTS) OUTP 19
|
||||
WRITE(6,950) OUTP 20
|
||||
950 FORMAT(1H0,6X,4HNODE,6X,5HDISP.,8X,7HXZ-ROT.,7X,7HYZ-ROT.) OUTP 21
|
||||
DO 20 IPOIN=1,NPOIN OUTP 22
|
||||
NGASH=IPOIN*3 OUTP 23
|
||||
NGISH=NGASH-3+1 OUTP 24
|
||||
20 WRITE(6,910) IPOIN,(TDISP(IGASH),IGASH=NGISH,NGASH) OUTP 25
|
||||
910 FORMAT(I10,3E14.6) OUTP 26
|
||||
10 CONTINUE OUTP 27
|
||||
C
|
||||
C*** OUTPUT REACTIONS OUTP 28
|
||||
C
|
||||
IF(KOUTP.LT.2) GO TO 30 OUTP 30
|
||||
WRITE(6,920) OUTP 31
|
||||
920 FORMAT(1H0,5X,9HREACTIONS) OUTP 32
|
||||
WRITE(6,960) OUTP 33
|
||||
960 FORMAT(1H0,6X,4HNODE,6X,5HFORCE,3X,9HXZ-MOMENT,5X,9HYZ-MOMENT) OUTP 34
|
||||
DO 40 IVFIX=1,NVFIX OUTP 35
|
||||
40 WRITE(6,910) NOFIX(IVFIX),(TREAC(IVFIX,IDOFN),IDOFN=1,3) OUTP 36
|
||||
30 CONTINUE OUTP 37
|
||||
C
|
||||
C*** OUTPUT STRESSES OUTP 38
|
||||
C
|
||||
IF(KOUTP.LT.3) GO TO 50 OUTP 39
|
||||
REWIND 3 OUTP 40
|
||||
WRITE(6,970) OUTP 41
|
||||
970 FORMAT(1H0,5X,8HSTRESSES) OUTP 42
|
||||
WRITE(6,980) OUTP 43
|
||||
980 FORMAT(1H0,4HG.P.,2X,8HX-COORD.,2X,8HY-COORD.,3X,8HX-MOMENT,4X,OUTP 44
|
||||
.8HY-MOMENT,3X,9HXY-MOMENT,3X,OUTP 45
|
||||
.13HEFF.PL.STRAIN) OUTP 46
|
||||
KGAUS=0 OUTP 47
|
||||
DO 60 IELEM=1,NELEM OUTP 48
|
||||
READ(3)GPCOD OUTP 49
|
||||
KELGS=0 OUTP 50
|
||||
WRITE(6,930)IELEM OUTP 51
|
||||
930 FORMAT(1H0,5X,13HELEMENT NO. =,I5) OUTP 52
|
||||
DO 60 IGAUS=1,NGAUS OUTP 53
|
||||
DO 60 JGAUS=1,NGAUS OUTP 54
|
||||
KGAUS=KGAUS+1 OUTP 55
|
||||
KELGS=KELGS+1 OUTP 56
|
||||
WRITE(6,940)KELGS,(GPCOD(IDIME,KELGS),IDIME=1,2), OUTP 57
|
||||
.(STRSG(ISTRE,KGAUS),ISTRE=1,3),EPSTN(KGAUS) OUTP 58
|
||||
940 FORMAT(I5,2F10.4,6E12.5) OUTP 59
|
||||
60 CONTINUE OUTP 60
|
||||
50 CONTINUE OUTP 61
|
||||
RETURN OUTP 62
|
||||
END OUTP 63
|
||||
OUTP 64
|
||||
OUTP 65
|
||||
OUTP 66
|
||||
```
|
||||
|
||||
<!-- source-page: 354 -->
|
||||
|
||||
# 9.5.11 Subroutine RESMP
|
||||
|
||||
This subroutine evaluates the residual nodal forces. The structure of this routine is similar to that given in Chapter 7 for the other two dimensional elasto-plastic applications and it is illustrated in Fig. 9.3.
|
||||
|
||||
```fortran
|
||||
SUBROUTINE RESMP (ASDIS,COORD,EFFST,ELOAD,EPSTN,LNODS, RESP 1
|
||||
MATNO,MELEM,MMATS,MPOIN,MTOTG,MTOTV, RESP 2
|
||||
NCRIT,NELEM,NEVAB,NGAUS,NNODE,PROPS, RESP 3
|
||||
STRSG) RESP 4
|
||||
C**************************RESP 5
|
||||
C
|
||||
C*** EVALUATES EQUIVALENT NODAL FORCES FOR THE STRESS RESULTANTS RESP 7
|
||||
C*** IN MINDLIN PLATES DURING EP ANALYSIS RESP 8
|
||||
C
|
||||
C**************************RESP 9
|
||||
DIMENSION ASDIS(MTOTV),AVECT(5),CARTD(2,9), RESP 11
|
||||
COORD(MPOIN,2),DERIV(2,9),DESIG(5),DEVIA(4), RESP 12
|
||||
DVECT(5), RESP 13
|
||||
EFFST(MTOTG),ELCOD(2,9), RESP 14
|
||||
ELDIS(3,9),ELOAD(MELEM,27),EPSTN(MTOTG),GPCOD(2,9), RESP 15
|
||||
LNODS(MELEM,9),MATNO(MELEM),POSGP(4), RESP 16
|
||||
PROPS(MMATS,8),SGTOT(5),SHAPE(9),SIGMA(5), RESP 17
|
||||
STRES(5),STRSG(5,MTOTG),WEIGP(4), RESP 18
|
||||
DFLEX(3,3),DSHER(2,2),BFLEI(3,3),BSHEI(2,3), RESP 19
|
||||
DUMMY(3,3),FORCE(3),DGRAD(6) RESP 20
|
||||
NTIME=1 RESP 21
|
||||
DO 10 IELEM=1,NELEM RESP 22
|
||||
DO 10 IEVAB=1,NEVAB RESP 23
|
||||
10 ELOAD(IELEM,IEVAB)=0.0 RESP 24
|
||||
KGAUS=0 RESP 25
|
||||
LGAUS=0 RESP 26
|
||||
DO 20 IELEM=1,NELEM RESP 27
|
||||
LPROP=MATNO(IELEM) RESP 28
|
||||
C
|
||||
C*** COMPUTE COORDINATE AND INCREMENTAL DISPLACEMENTS OF THE RESP 30
|
||||
ELEMENT NODAL POINTS RESP 31
|
||||
C
|
||||
DO 190 INODE =1,NNODE RESP 32
|
||||
LNODE=IABS(LNODS(IELEM,INODE)) RESP 33
|
||||
NPOSN=(LNODE-1)*3 RESP 34
|
||||
DO 30 IDOFN=1,3 RESP 35
|
||||
NPOSN=NPOSN+1 RESP 36
|
||||
30 ELDIS(IDOFN,INODE)=ASDIS(NPOSN) RESP 37
|
||||
DO 180 IDIME=1,2 RESP 38
|
||||
180 ELCOD(IDIME,INODE)=COORD(LNODE,IDIME) RESP 39
|
||||
190 CONTINUE RESP 40
|
||||
KGASP=0 RESP 41
|
||||
CALL MODPB (DFLEX,DUMMY,DSHER,LPROP,MMATS,PROPS, RESP 42
|
||||
0, 1, 1) RESP 43
|
||||
CALL GAUSSQ (NGAUS,POSGP,WEIGP) RESP 44
|
||||
DO 40 IGAUS=1,NGAUS RESP 45
|
||||
DO 40 JGAUS=1,NGAUS RESP 46
|
||||
BRING=1.0 RESP 47
|
||||
KGAUS=KGAUS+1 RESP 48
|
||||
EXISP=POSGP(IGAUS) RESP 49
|
||||
ETASP=POSGP(JGAUS) RESP 50
|
||||
CALL SFR2 (DERIV,ETASP,EXISP,NNODE,SHAPE) RESP 51
|
||||
KGASP=KGASP+1 RESP 52
|
||||
CALL JACOB2 (CARTD,DERIV,DJACB,ELCOD,GPCOD,IELEM, RESP 53
|
||||
KGASP,NNODE,SHAPE) RESP 54
|
||||
C
|
||||
```
|
||||
|
||||
<!-- source-page: 355 -->
|
||||
|
||||
```csv
|
||||
DAREA=DJACB*WEIGP(IGAUS)*WEIGP(JGAUS)
|
||||
CALL GRADMP (CARTD,DGRAD,ELDIS, 3,NNODE)
|
||||
CALL STRMP (CARTD,DFLEX,DGRAD,DSHER,ELDIS,NNODE, SHAPE,STRES, 1, 0)
|
||||
PREYS=PROPS(LPROP,6)+EPSTN(KGAUS)*PROPS(LPROP,7)
|
||||
DO 150 ISTRE=1,3
|
||||
DESIG(ISTRE)=STRES(ISTRE)
|
||||
150 SIGMA(ISTRE)=STRSG(ISTRE,KGAUS)+STRES(ISTRE)
|
||||
CALL INVMP (DEVIA,NCRIT,SINT3,STEFF,SIGMA,THETA, VARJ2,YIELD)
|
||||
ESPRE=EFFST(KGAUS)-PREYS
|
||||
IF(ESPRE.GE.0.0) GO TO 50
|
||||
ESCUR=YIELD-PREYS
|
||||
IF(ESCUR.LE.0.0) GO TO 60
|
||||
RFACT=ESCUR/(YIELD-EFFST(KGAUS))
|
||||
GO TO 70
|
||||
50 ESCUR=YIELD-EFFST(KGAUS)
|
||||
IF(ESCUR.LE.0.0) GO TO 60
|
||||
RFACT=1.0
|
||||
70 MSTEP=ESCUR*8.0/PROPS(LPROP,6)+1.0
|
||||
ASTEP=MSTEP
|
||||
REDUC=1.0-RFACT
|
||||
DO 80 ISTRE=1,3
|
||||
SGTOT(ISTRE)=STRSG(ISTRE,KGAUS)+REDUC*STRES(ISTRE)
|
||||
80 STRES(ISTRE)=RFACT*STRES(ISTRE)/ASTEP
|
||||
DO 90 ISTEP=1,MSTEP
|
||||
CALL INVMP (DEVIA,NCRIT,SINT3,STEFF,SGTOT,THETA, VARJ2,YIELD)
|
||||
HARDS=PROPS(LPROP,7)
|
||||
CALL FLOWMP (ABETA,AVECT,DEVIA,DFLEX,DVECT,HARDS, NCRIT,SINT3,STEFF,THETA,VARJ2)
|
||||
AGASH=0.0
|
||||
DO 100 ISTRE=1,3
|
||||
100 AGASH=AGASH+AVECT(ISTRE)*STRES(ISTRE)
|
||||
DLAMD=AGASH*ABETA
|
||||
IF(DLAMD.LT.0.0) DLAMD=0.0
|
||||
BGASH=0.0
|
||||
DO 110 ISTRE=1,3
|
||||
BGASH=BGASH+AVECT(ISTRE)*SGTOT(ISTRE)
|
||||
110 SGTOT(ISTRE)=SGTOT(ISTRE)+STRES(ISTRE)-DLAMD*DVECT(ISTRE)
|
||||
90 EPSTN(KGAUS)=EPSTN(KGAUS)+DLAMD*BGASH/YIELD
|
||||
DO 120 ISTRE=1,3
|
||||
120 DESIG(ISTRE)=SGTOT(ISTRE)-STRSG(ISTRE,KGAUS)
|
||||
CALL INVMP (DEVIA,NCRIT,SINT3,STEFF,SGTOT,THETA, VARJ2,YIELD)
|
||||
CURYS=PROPS(LPROP,6)+EPSTN(KGAUS)*PROPS(LPROP,7)
|
||||
IF(YIELD.GT.CURYS) BRING=CURYS/YIELD
|
||||
60 DO 130 ISTRE=1,3
|
||||
SGTOT(ISTRE)=BRING*(STRSG(ISTRE,KGAUS)+DESIG(ISTRE))
|
||||
130 STRSG(ISTRE,KGAUS)=SGTOT(ISTRE)
|
||||
EFFST(KGAUS)=BRING*YIELD
|
||||
*** CALCULATE THE EQUIVALENT NODAL FORCES AND ASSOCIATE WITH THE ELEMENT NODES
|
||||
DO 140 INODE=1,NNODE
|
||||
*** ZERO FORCE VECTOR
|
||||
CALL VZERO (3,FORCE)
|
||||
CALL BMATPB (BFLEI,DUMMY,BSHEI,CARTD,INODE,SHAPE, 0, 1, 0)
|
||||
FORCE(2)=(BFLEI(1,2)*SGTOT(1)+BFLEI(3,2)*SGTOT(3))*DAREA
|
||||
+FORCE(2)
|
||||
FORCE(3)=(BFLEI(2,3)*SGTOT(2)+BFLEI(3,3)*SGTOT(3))*DAREA
|
||||
+FORCE(3)
|
||||
IPOSN=(INODE-1)*3+1
|
||||
RESP 56
|
||||
RESP 57
|
||||
RESP 58
|
||||
RESP 59
|
||||
RESP 60
|
||||
RESP 61
|
||||
RESP 62
|
||||
RESP 63
|
||||
RESP 64
|
||||
RESP 65
|
||||
RESP 66
|
||||
RESP 67
|
||||
RESP 68
|
||||
RESP 69
|
||||
RESP 70
|
||||
RESP 71
|
||||
RESP 72
|
||||
RESP 73
|
||||
RESP 74
|
||||
RESP 75
|
||||
RESP 76
|
||||
RESP 77
|
||||
RESP 78
|
||||
RESP 79
|
||||
RESP 80
|
||||
RESP 81
|
||||
RESP 82
|
||||
RESP 83
|
||||
RESP 84
|
||||
RESP 85
|
||||
RESP 86
|
||||
RESP 87
|
||||
RESP 88
|
||||
RESP 89
|
||||
RESP 90
|
||||
RESP 91
|
||||
RESP 92
|
||||
RESP 93
|
||||
RESP 94
|
||||
RESP 95
|
||||
RESP 96
|
||||
RESP 97
|
||||
RESP 98
|
||||
RESP 99
|
||||
RESP 100
|
||||
RESP 101
|
||||
RESP 102
|
||||
RESP 103
|
||||
RESP 104
|
||||
RESP 105
|
||||
RESP 106
|
||||
RESP 107
|
||||
RESP 108
|
||||
RESP 109
|
||||
RESP 110
|
||||
RESP 111
|
||||
RESP 112
|
||||
RESP 113
|
||||
RESP 114
|
||||
RESP 115
|
||||
RESP 116
|
||||
RESP 117
|
||||
RESP 118
|
||||
RESP 119
|
||||
```
|
||||
|
||||
<!-- source-page: 356 -->
|
||||
|
||||
```csv
|
||||
DO 135 IDOFN=2,3
|
||||
IPOSN=IPOSN+1
|
||||
135 ELOAD(IELEM,IPOSN)=ELOAD(IELEM,IPOSN)+FORCE(IDOFN)
|
||||
140 CONTINUE
|
||||
40 CONTINUE
|
||||
C
|
||||
C*** CALCULATE FORCES ASSOCIATED WITH SHEAR DEFORMATION
|
||||
C
|
||||
NGAUM=NGAUS-1
|
||||
CALL GAUSSQ (NGAUM,POSGP,WEIGP)
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
C
|
||||
KGASP=0
|
||||
DO 300 IGAUS=1,NGAUM
|
||||
DO 300 JGAUS=1,NGAUM
|
||||
LGAUS=LGAUS+1
|
||||
EXISP=POSGP(IGAUS)
|
||||
ETASP=POSGP(JGAUS)
|
||||
CALL SFR2 (DERIV,ETASP,EXISP,NNODE,SHAPE)
|
||||
KGASP=KGASP+1
|
||||
CALL JACOB2 (CARTD,DERIV,DJACB,ELCOD,GPCOD,IELEM, KGASP,NNODE,SHAPE)
|
||||
DAREA=DJACB*WEIGP(IGAUS)*WEIGP(JGAUS)
|
||||
CALL GRADMP (CARTD,DGRAD,ELDIS, 3,NNODE)
|
||||
CALL STRMP (CARTD,DFLEX,DGRAD,DSHER,ELDIS,NNODE, SHAPE,STRES, 0, 1)
|
||||
DO 310 ISTRE=4,5
|
||||
SGTOT(ISTRE)=STRSG(ISTRE,LGAUS)+STRES(ISTRE)
|
||||
310 STRSG(ISTRE,LGAUS)=SGTOT(ISTRE)
|
||||
C
|
||||
C*** CALCULATE THE EQUIVALENT NODAL FORCES
|
||||
C
|
||||
DO 320 INODE=1,NNODE
|
||||
C*** ZERO FORCE VECTOR
|
||||
CALL VZERO(3,FORCE)
|
||||
CALL BMATPB (BFLEI,DUMMY,BSHEI,CARTD,INODE,SHAPE, 0, 0, 1)
|
||||
FORCE(1)=(BSHEI(1,1)*SGTOT(4)+BSHEI(2,1)*SGTOT(5))*DAREA
|
||||
+FORCE(1)
|
||||
FORCE(2)=(BSHEI(1,2)*SGTOT(4))*DAREA+FORCE(2)
|
||||
FORCE(3)=(BSHEI(2,3)*SGTOT(5))*DAREA+FORCE(3)
|
||||
IPOSN=(INODE-1)*3
|
||||
DO 315 IDOFN=1,3
|
||||
IPOSN=IPOSN+1
|
||||
315 ELOAD(IELEM,IPOSN)=ELOAD(IELEM,IPOSN)+FORCE(IDOFN)
|
||||
320 CONTINUE
|
||||
300 CONTINUE
|
||||
20 CONTINUE
|
||||
RETURN
|
||||
END
|
||||
RESP 120
|
||||
RESP 121
|
||||
RESP 122
|
||||
RESP 123
|
||||
RESP 124
|
||||
RESP 125
|
||||
RESP 126
|
||||
RESP 127
|
||||
RESP 128
|
||||
RESP 129
|
||||
RESP 130
|
||||
RESP 131
|
||||
RESP 132
|
||||
RESP 133
|
||||
RESP 134
|
||||
RESP 135
|
||||
RESP 136
|
||||
RESP 137
|
||||
RESP 138
|
||||
RESP 139
|
||||
RESP 140
|
||||
RESP 141
|
||||
RESP 142
|
||||
RESP 143
|
||||
RESP 144
|
||||
RESP 145
|
||||
RESP 146
|
||||
RESP 147
|
||||
RESP 148
|
||||
RESP 149
|
||||
RESP 150
|
||||
RESP 151
|
||||
RESP 152
|
||||
RESP 153
|
||||
RESP 154
|
||||
RESP 155
|
||||
RESP 156
|
||||
RESP 157
|
||||
RESP 158
|
||||
RESP 159
|
||||
RESP 160
|
||||
RESP 161
|
||||
RESP 162
|
||||
RESP 163
|
||||
RESP 164
|
||||
RESP 165
|
||||
RESP 166
|
||||
RESP 167
|
||||
RESP 168
|
||||
RESP 169
|
||||
RESP 170
|
||||
```
|
||||
|
||||
# 9.5.12 Subroutine SFR2
|
||||
|
||||
This subroutine evaluates the shape functions and their derivatives for 4, 8 and 9-node quadrilateral isoparametric elements. The 9-node element is treated as a hierarchical element as described in Section 9.3.2. This enables the Heterosis element to be easily incorporated.
|
||||
|
||||
<!-- source-page: 357 -->
|
||||
|
||||
|
||||
|
||||
<details>
|
||||
<summary>flowchart</summary>
|
||||
|
||||
```mermaid
|
||||
graph TD
|
||||
A["START"] --> B["Set to zero ELOAD ( . . . )"]
|
||||
B --> C["Extract local element material property set number, displacements and coordinates"]
|
||||
C --> D["Call MODPB to evaluate Df, Ds"]
|
||||
D --> E["Call GAUSSQ to evaluate n-point Gauss-Legendre sampling positions and weights"]
|
||||
E --> F["Call SFR2, JACOB2, GRADMP and STRMP to evaluate elastic stress increment dσf"]
|
||||
F --> G["Calculate the effective stress necessary for yielding to occur"]
|
||||
G --> H["Calculate the total bending moments at the current Gauss points"]
|
||||
H --> I["If the current bending moments are outside of the yield surface bring them back to the yield surface taking into account unloading if it has taken place"]
|
||||
I --> J["A"]
|
||||
K["ELEMENT LOOP"] --> L["GAUSS LOOPS"]
|
||||
L --> M["Calculate the effective stress necessary for yielding to occur"]
|
||||
M --> N["Calculate the total bending moments at the current Gauss points"]
|
||||
N --> O["If the current bending moments are outside of the yield surface bring them back to the yield surface taking into account unloading if it has taken place"]
|
||||
```
|
||||
</details>
|
||||
|
||||
Fig. 9.3 Overall structure of subroutine RESMP.
|
||||
|
||||
<!-- source-page: 358 -->
|
||||
|
||||
|
||||
|
||||
<details>
|
||||
<summary>flowchart</summary>
|
||||
|
||||
```mermaid
|
||||
graph TD
|
||||
A["A"] --> B["Evaluate [Bf"]T σ̂f × Gauss weights × det J and add into ELOAD ( , ). Use routines VZERO and BMATPB]
|
||||
B --> C["Call GAUSSQ to evaluate (n - 1) point Gauss-Legendre sampling positions and weights"]
|
||||
C --> D["Call SFR2, JACOB2, GRADMP and STRMP to evaluate elastic stress increment dσ̂s"]
|
||||
D --> E["Evaluate [Bs"]T σ̂s × Gauss weights × det J and add into ELOAD ( , ). Use routines VZERO and BMATPB]
|
||||
E --> F["RETURN"]
|
||||
G["GAUSS LOOPS"] --> D
|
||||
G --> E
|
||||
```
|
||||
</details>
|
||||
|
||||
Fig. 9.3 Overall structure of subroutine RESMP (continued).
|
||||
|
||||
Subroutine SFR2 is identical to its namesake given earlier in Section 6.4.3 except that SFR2 72–118 are replaced by SFRH 67–73.
|
||||
|
||||
<table><tr><td>IF(NNODE.EQ.8) RETURN</td><td>SFR2</td><td>67</td></tr><tr><td>C*** BUBBLE FUNCTION FOR HIERARCHICAL AND HETEROSIS ELEMENTS</td><td>SFRH</td><td>68</td></tr><tr><td>SHAPE(9)=(1.0-SS)*(1.0-TT)</td><td>SFRH</td><td>69</td></tr><tr><td>DERIV(1,9)=-S2*(1.0-TT)</td><td>SFRH</td><td>70</td></tr><tr><td>DERIV(2,9)=-T2*(1.0-SS)</td><td>SFRH</td><td>71</td></tr><tr><td>RETURN</td><td>SFRH</td><td>72</td></tr><tr><td>END</td><td>SFRH</td><td>73</td></tr></table>
|
||||
|
||||
# 9.5.13 Subroutine STIFMP
|
||||
|
||||
This routine evaluates the stiffness matrix for the nonlayered elasto-plastic Mindlin plate elements. The overall structure is shown in Fig. 9.4.
|
||||
|
||||
<!-- source-page: 359 -->
|
||||
|
||||
|
||||
|
||||
<details>
|
||||
<summary>flowchart</summary>
|
||||
|
||||
```mermaid
|
||||
graph TD
|
||||
A["START"] --> B["Rewind tapes 1 and 3"]
|
||||
B --> C["Extract local element material property set number and coordinates"]
|
||||
C --> D["Initialise array used to store element stiffness matrices"]
|
||||
D --> E["Call GAUSSQ to evaluate n-point Gauss-Legendre sampling positions and weights"]
|
||||
E --> F["Call SFR2 and JACOB2 to evaluate N_i^(e) / ∂N_i^(e)/∂x, ∂N_i^(e)/∂y and det J^(e)"]
|
||||
F --> G["Call MODPB to evaluate D_f"]
|
||||
G --> H{Is this the first load increment?}
|
||||
H -->|Yes| I["GAUSS LOOPS"]
|
||||
H -->|No| J{Was this Gauss point plastic in the last load increment?}
|
||||
J -->|No| I
|
||||
J -->|Yes| K["A"]
|
||||
```
|
||||
</details>
|
||||
|
||||
<!-- source-page: 360 -->
|
||||
|
||||
|
||||
|
||||
<details>
|
||||
<summary>flowchart</summary>
|
||||
|
||||
```mermaid
|
||||
graph TD
|
||||
A["A"] --> B["Call INVMP and FLOWMP to evaluate a' and d_D and hence calculate D_ep"]
|
||||
B --> C["Call BMATPB and SUBMP to add [B_f^(e)"]^T D_f B_f^(e) det J^(e) × Gauss weights into K_ij^(e)]
|
||||
C --> D["Call GAUSSQ to evaluate (n-1)-point Gauss-Legendre sampling positions and weights"]
|
||||
D --> E["Call SFR2 and JACOB2 to evaluate N_i^(e), ∂N_i^(e)/∂x, ∂N_i^(e)/∂y and det J^(e)"]
|
||||
E --> F["Call MODPB to evaluate D_s"]
|
||||
F --> G["Call BMATPB and SUBMP to add [B_δi^(e)"]^T D_δ B_δj^(e) det J × Gauss weights into K_ij^(e)]
|
||||
G --> H["Store stiffness matrix K^(e) and Gauss point coordinates on files 1 and 3 respectively"]
|
||||
H --> I["RETURN"]
|
||||
I --> J["GAUSS LOOPS"]
|
||||
```
|
||||
</details>
|
||||
|
||||
Fig. 9.4 Overall structure of subroutine STIFMP (continued).
|
||||
Reference in New Issue
Block a user