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김경종
+821
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<!-- source-page: 421 -->
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```txt
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SUBROUTINE LUMASS (COORD, INTGR, LNODS, MATNO, NCONM, NDIME, NDOFN, NELEM, NGAUM, NMATS, NNODE, NPOIN, NTYPE, PROPS, YMASS)
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```
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```txt
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C
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```
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```txt
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C
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```
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```txt
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C *** CALCULATES LUMPED MASS FOR 4, 8 AND 9 NODED ELEMENT
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```
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```txt
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C
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```
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```txt
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C******************************************************************************************
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```
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```txt
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DIMENSION COORD(NPOIN,1),ELCOD(2,9),DIAGM(9),POSGP(4),
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. LNODS(NELEM,1),CARTD(2,9),SHAPE(9),WEIGP(4),
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. PROPS(NMATS,1),GPCOD(2,9),MATNO(1),YMASS(1),
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. EMASS(171),DERIV(2,9),INTGR(1)
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```
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```txt
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C
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```
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```csv
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REWIND 3
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TWOPI=6.283185307179586
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NEVAB=NNODE*NDOFN
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NTOTV=NPOIN*NDOFN
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DO 500 ITOTV =1,NTOTV
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```
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```txt
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500 YMASS(ITOTV)=0.0
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CALL GAUSSQ (NGAUM, POSGP, WEIGP)
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DO 100 IELEM=1, NELEM
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DO 5 IEVAB=1, 171
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```
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```txt
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5 EMASS(IEVAB)=0.0
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IMASS=INTGR(IELEM)
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KGASP=0
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TAREA=0.0
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LPROP=MATNO(IELEM)
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THICK=PROPS(LPROP,3)
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RHOEL=PROPS(LPROP,4)
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DO 10 INODE=1,NNODE
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DIAGM(INODE)=0.0
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LNODE=LNODS(IELEM,INODE)
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DO 10 IDIME=1,NDIME
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ELCOD(IDIME,INODE)=COORD(LNODE,IDIME)
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```
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```csv
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10 CONTINUE
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DO 70 IGAUS=1,NGAUM
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EXISP=POSGP(IGAUS)
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DO 70 JGAUS=1,NGAUM
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KGASP=KGASP+1
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ETASP=POSGP(JGAUS)
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CALL SFR2 (DERIV,NNODE,SHAPE,EXISP,ETASP)
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CALL JACOB2 (CARTD,DERIV,DJACB,ELCOD,GPCOD,IELEM,KGASP,NNODE,SHAPE)
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```
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```txt
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DVOLU=DJACB*WEIGP(IGAUS)*WEIGP(JGAUS)
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IF(NTYPE.EQ.1) DVOLU=DVOLU*THICK
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IF(NTYPE.EQ.3) DVOLU=DVOLU*TWOPI*GPCOD(1,KGASP)
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IF(IMASS.EQ.1) GO TO 210
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DO 20 INODE=1,NNODE
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SHAPI=SHAPE(INODE)
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```
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```txt
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20 DIAGM(INODE)=DIAGM(INODE)+SHAPI*SHAPI*DVOLU
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TAREA=TAREA+DVOLU
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```
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```matlab
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210 IF(IMASS.EQ.2) GO TO 70
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DVOLU=DVOLU*RHOEL
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IEVAB=1
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KOUNT=NEVAB
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DO 30 INODE=1,NNODE
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SHAPI=SHAPE(INODE)
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DO 60 JNODE=INODE,NNODE
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DMASS=DVOLU*SHAPI*SHAPE(JNODE)
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EMASS(IEVAB)=EMASS(IEVAB)+DMASS
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JEVAB=IEVAB+KOUNT
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EMASS(JEVAB)=EMASS(JEVAB)+DMASS
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60 IEVAB=IEVAB+2
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KOUNT=KOUNT-2
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```
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<!-- source-page: 422 -->
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```fortran
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IEVAB=JEVAB+1 MASS 65
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30 CONTINUE MASS 66
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70 CONTINUE MASS 67
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C MASS 68
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C*** WRITES CONSISTENT MASS MATRIX ON TAPE 3 MASS 69
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C MASS 70
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IF(IMASS.EQ.2) GO TO 200 MASS 71
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WRITE(3) EMASS MASS 72
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WRITE(6,90) (EMASS(I),I=1,171) MASS 73
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200 IF(IMASS.EQ.1) GO TO 100 MASS 74
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C MASS 75
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C *** GENERATES LUMPED MASS MATRIX PROPORTIONAL TO DIAGONAL MASS 76
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C MASS 77
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SUMAS=0. MASS 78
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DO 40 INODE=1,NNODE MASS 79
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40 SUMAS=SUMAS+DIAGM(INODE) MASS 80
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TAREA=TAREA*RHOEL MASS 81
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SUMAS=TAREA/SUMAS MASS 82
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DO 50 INODE=1,NNODE MASS 83
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LNODE=LNODS(IELEM,INODE) MASS 84
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IPOSN=(LNODE-1)*NDOFN MASS 85
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DO 50 IDOFN=1,NDOFN MASS 86
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IPOSN=IPOSN+1 MASS 87
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YMASS(IPOSN)=YMASS(IPOSN)+DIAGM(INODE)*SUMAS MASS 88
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50 CONTINUE MASS 89
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90 FORMAT(2X,9E12.3) MASS 90
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100 CONTINUE MASS 91
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C MASS 92
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C CONCENTRATED MASSES MASS 93
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C MASS 94
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IF(NCONM.EQ.0) RETURN MASS 95
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WRITE(6,900) MASS 96
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DO 520 ICONM=1,NNOM MASS 97
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READ(5,910) IPOIN,XCMAS,YCMAS MASS 98
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900 FORMAT(5X,19HCONCENTRATED MASSES) MASS 99
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WRITE(6,910) IPOIN,XCMAS,YCMAS MASS 100
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NPOSN=(IPOIN-1)*NDOFN+1 MASS 101
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YMASS(NPOSN)=YMASS(NPOSN)+XCMAS MASS 102
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NPOSN=NPOSN+1 MASS 103
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YMASS(NPOSN)=YMASS(NPOSN)+YCMAS MASS 104
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520 CONTINUE MASS 105
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C WRITE(6,90) (YMASS(I),I=1,NTOTV) MASS 106
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910 FORMAT(I5,2F10.3) MASS 107
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RETURN MASS 108
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END MASS 109
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```
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# MASS 24
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Sets indicator for mass matrix evaluation. INTGR(I) = 1 for the consistent mass matrix and INTGR(I) = 2 for the special lumped mass vector.
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# MASS 35-52
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Evaluate the diagonal element of the consistent mass matrix DIAGM.
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# MASS 53-63
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Evaluates the element consistent mass matrix.
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# MASS 72
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Writes element consistent mass matrix on tape 3.
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# MASS 78-80
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Evaluates ELMAS, the sum of the diagonal elements.
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# MASS 81
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Determines the total element mass from the element volume TAREA and mass density RHOEL.
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<!-- source-page: 423 -->
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MASS 83–89 Scales the diagonal terms using the factor TAREA/ELMAS to preserve element mass and assembles the result into diagonal mass vector YMASS.
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MASS 95–107 Reads the concentrated masses and assembles them into YMASS.
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# 10.6.17 Subroutine MODPS
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This subroutine evaluates the elasticity matrix and has been described earlier in Chapter 6. The only changes involved are given below.
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```csv
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SUBROUTINE MODPS (DMATX ,LPROP ,NMATS ,NSTRE ,NTYPE ,PROPS ) MODP 1
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C**************************
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C
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C ** ELASTICITY D MATRIX
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C
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C**************************
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DIMENSION DMATX(4,4),PROPS(NMATS,1)
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```
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# 10.6.18 Subroutine NODXYR
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It calculates $(r, z)$ coordinates from $(R, \Theta)$ coordinates for axisymmetric problems. If coordinates of midside nodes are not read, it evaluates them by linear interpolation. An almost identical subroutine was described in Chapter 6.
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```fortran
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SUBROUTINE NODXYR (COORD, LNODS, NELEM, NNODE, NPOIN, NRADS, NTYPE) NODX 1
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C*************** NODX 2
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C NODX 3
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C*** INTERPOLATION OF MIDSIDE AND CENTER NODES NODX 4
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C NODX 5
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C*************** NODX 6
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DIMENSION COORD(NPOIN, 1), LNODS(NELEM, 1) NODX 7
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C NODX 8
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IF(NTYPE.NE.3.OR.NRADS.EQ.0) GO TO 40 NODX 9
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C NODX 10
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C*** CHANGE POLAR COORDINATES TO CARTISIAN NODX 11
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DO 50 IPOIN=1, NPOIN NODX 12
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RADDI=COORD(IPOIN, 1) NODX 13
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THETA=COORD(IPOIN, 2) NODX 14
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THETA=0.017453292*THETA NODX 15
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COORD(IPOIN, 1)=RADDI*SIN(THETA) NODX 16
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50 COORD(IPOIN, 2)=RADDI*COS(THETA) NODX 17
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C NODX 18
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40 IF(NNODE.EQ.4) RETURN NODX 19
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C NODX 20
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LNODE = NNODE - 1 NODX 21
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DO 30 Ielem=1, NELEM NODX 22
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C*** LOOP OVER EACH ELEMENT EDGE NODX 23
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DO 20 INODE=1, NNODE, 2 NODX 24
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IF(INODE.EQ.9) GO TO 20 NODX 25
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C*** COMPUTE THE NODE NUMBER OF THE FIRST NODE NODX 26
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NODST=LNODS(IELEM, INODE) NODX 27
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IGASH=INODE+2 NODX 28
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IF(IGASH.GT.LNODE) IGASH=1 NODX 29
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C*** COMPUTE THE NODE NUMBER OF THE LAST NODE NODX 30
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NODFN=LNODS(IELEM, IGASH) NODX 31
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MIDPT=INODE+1 NODX 32
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```
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<!-- source-page: 424 -->
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```fortran
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C*** COMPUTE THE NODE NUMBER OF THE INTERMEDIATE NODE NODX 33
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NODMD=LNODS(IELEM,MIDPT) NODX 34
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TOTAL=ABS(COORD(NODMD,1))+ABS(COORD(NODMD,2)) NODX 35
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C*** IF THE COORDINATES OF THE INTERMEDIATE NODE ARE BOTH ZERO NODX 36
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C INTERPOLATE BY A STRAIGHT LINE NODX 37
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IF(TOTAL.GT.0.0) GO TO 20 NODX 38
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KOUNT=1 NODX 39
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10 COORD(NODMD,KOUNT)=(COORD(NODST,KOUNT)+COORD(NODFN,KOUNT))/2.0 NODX 40
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KOUNT=KOUNT+1 NODX 41
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IF(KOUNT.EQ.2) GO TO 10 NODX 42
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20 CONTINUE NODX 43
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30 CONTINUE NODX 44
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RETURN NODX 45
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END NODX 46
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```
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# 10.6.19 Subroutine OUTDYN
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This routine writes out most of the output on the line printer and on various tapes for plotting purposes. It outputs the displacements and stresses every NOUTP steps. It also writes the displacement and stress histories of specified nodal and integration points at every NOUTP steps. The complete state of displacements is also written on tape 13 for a deformation plot. The complete state of the stresses is written on tape 4. The principal stresses and their directions are also calculated and output.
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```txt
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SUBROUTINE OUTDYN (DISPL, DTIME, ISTEP, NDOFN, NELEM, NGAUS, OUTP 1
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NGRQS, NOUTD, NOUTP, NPOIN, NPRQD, NREQD, OUTP 2
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NREQS, NTYPE, STRSG, TDISP, VIVEL) OUTP 3
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C*******************************
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OUTP 4
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C
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C** OUTPUT ROUTINE
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OUTP 5
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C
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C*******************************
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OUTP 6
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OUTP 7
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OUTP 8
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DIMENSION STRSG(4,1), DISPL(1), NPRQD(1), STRSP(3), OUTP 9
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VIVEL(5,1), TDISP(1), NGRQS(1) OUTP 10
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NSTR1=4
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OUTP 11
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KSTEP=ISTEP
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OUTP 12
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MGAUS=NELEM*NGAUS*NGAUS
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OUTP 13
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IF(ISTEP.EQ.1) WRITE(10,925) OUTP 14
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TTIME=TTIME+DTIME OUTP 15
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C
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OUTP 16
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C *** WRITES DISPLACEMENT HISTORY AT REQUESTED NODAL POINTS ON TAPE 10 OUTP 17
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C *** AND STRESS HISTORY AT REQUESTED GAUSS POINTS AT EVERY NOUTD STEPSOUTP 18
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C
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OUTP 19
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KOUNT=0
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OUTP 20
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KOUTD=(ISTEP/NOUTD)*NOUTD
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OUTP 21
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IF(KOUTD.NE.ISTEP) GO TO 510
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OUTP 22
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DO 500 IPOIN=1,NPOIN
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OUTP 23
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DO 500 IREQD=1,NREQD
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OUTP 24
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IF(IPOIN.NE.NPRQD(IREQD)) GO TO 500
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OUTP 25
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NPOSN=(IPOIN-1)*NDOFN+1
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OUTP 26
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NPOSM=NPOSN+1
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OUTP 27
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KOUNT=KOUNT+1
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OUTP 28
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DISPL(KOUNT)=TDISP(NPOSN)
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OUTP 29
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KOUNT=KOUNT+1
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OUTP 30
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DISPL(KOUNT)=TDISP(NPOSM)
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OUTP 31
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500 CONTINUE
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OUTP 32
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WRITE(10,960) (DISPL(IKOUN), IKOUN=1,KOUNT), TTIME OUTP 33
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```
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<!-- source-page: 425 -->
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```csv
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DO 520 IGAUS=1,MGAUS
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DO 520 IREQS=1,NREQS
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IF(IGAUS.NE.NGRQS(IREQS)) GO TO 520
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WRITE(11,950) (STRSG(ISTR1,IGAUS),ISTR1=1,NSTR1)
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520 CONTINUE
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510 KOUTD=(KSTEP/NOUTP)*NOUTP
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IF(KOUTD.NE.KSTEP) RETURN
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XTIME=FLOAT(KSTEP)*DTIME
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WRITE(6,604) KSTEP,XTIME
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604 FORMAT(//5X,28H DISPLACEMENTS AT TIME STEP ,I10,5X,5HTIME ,E20.11)
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C
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C *** REARRANGE DISPLACEMENT VECTOR
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C
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NODEI=0
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DO 550 IPOIN=1,NPOIN
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DO 550 IDOFN=1,NDOFN
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NODEI=NODEI+1
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DISPL(NODEI)=TDISP(NODEI)
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550 CONTINUE
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C
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C*** OUTPUT DISPLACEMENTS
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C
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925 FORMAT(5X,' DISPLACEMENTS ')
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WRITE(6,990)
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990 FORMAT(/3(1X,'NNODE',3X,'X-DISP',6X,'Y-DISP',3X)/)
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DO 560 IPOIN=1,NPOIN,3
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NGASI=NDOFN*IPOIN-1
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NGASJ=NGASI+NDOFN
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NGASK=NGASJ+NDOFN
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MGASI=NGASI+1
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MGASJ=NGASJ+1
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MGASK=NGASK+1
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JPOIN=IPOIN+1
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KPOIN=JPOIN+1
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C
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C *** WRITES DISPLACEMENTS ON TAPE 13 FOR DEFORMATION PLOT
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C
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WRITE(13,910) IPOIN ,(DISPL(IGASI),IGASI=NGASI,MGASI)
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IF(JPOIN.GT.NPOIN) GO TO 200
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WRITE(13,910) JPOIN ,(DISPL(IGASJ),IGASJ=NGASJ,MGASJ)
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IF(KPOIN.GT.NPOIN) GO TO 200
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WRITE(13,910) KPOIN ,(DISPL(IGASK),IGASK=NGASK,MGASK)
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200 CONTINUE
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C
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C *** WRITES DISPLACEMENTS ON OUTPUT FILE
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C
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560 WRITE(6,920) IPOIN,DISPL(NGASI),DISPL(MGASI),
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JPOIN,DISPL(NGASJ),DISPL(MGASJ),
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KPOIN,DISPL(NGASK),DISPL(MGASK)
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C
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C *** WRITES STRESSES ON OUTPUT FILE
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C
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WRITE(6,900)
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IF(NTYPE.NE.3) WRITE(6,970)
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970 FORMAT(1HO,1X,4HG.P.,6X,9HXX-STRESS,5X,9HYY-STRESS,5X,9HXY-STRESS,OUTP
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.5X,9HZZ-STRESS,6X,8HMAX P.S.,6X,8HMIN P.S.,3X,5HANGLE,3X,6H P.S.)OUTP
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IF(NTYPE.EQ.3) WRITE(6,975)
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975 FORMAT(1HO,1X,4HG.P.,6X,9HRR-STRESS,5X,9HZZ-STRESS,5X,9HRZ-STRESS,OUTP
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.5X,9HTT-STRESS,6X,8HMAX P.S.,6X,8HMIN P.S.,3X,5HANGLE,3X,6H P.S.)OUTP
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KGAUS=0
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DO 570 IELEM=1,NELEM
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KELGS=0
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WRITE(6,930) IELEM
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930 FORMAT(1HO,5X,13HELEMENT NO. =,I5)
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||||
```
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<!-- source-page: 426 -->
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||||
```csv
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DO 570 IGAUS=1,NGAUS
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DO 570 JGAUS=1,NGAUS
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KGAUS=KGAUS+1
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KELGS=KELGS+1
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||||
XGASH=(STRSG(1,KGAUS)+STRSG(2,KGAUS))*0.5
|
||||
XGISH=(STRSG(1,KGAUS)-STRSG(2,KGAUS))*0.5
|
||||
XGESH=STRSG(3,KGAUS)
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XGOSH=SQRT(XGISH*XGISH+XGESH*XGESH)
|
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STRSP(1)=XGASH+XGOSH
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||||
STRSP(2)=XGASH-XGOSH
|
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IF(XGISH.EQ.0.0) XGISH=0.1E-20
|
||||
STRSP(3)=ATAN(XGESH/XGISH)*28.647889757
|
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C
|
||||
C *** WRITES COMPLETE STRESS STATE ON TAPE 4
|
||||
C
|
||||
WRITE(4,950) (STRSG(ISTR1,KGAUS),ISTR1=1,NSTR1),
|
||||
.(STRSP(ISTRE),ISTRE=1,3)
|
||||
570 WRITE(6,940) KELGS,(STRSG(ISTR1,KGAUS),ISTR1=1,NSTR1),
|
||||
.(STRSP(ISTRE),ISTRE=1,3),VIVEL(5,KGAUS)
|
||||
980 FORMAT(1X,60I2)
|
||||
960 FORMAT(1X,10E11.4)
|
||||
950 FORMAT(7E10.4)
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||||
940 FORMAT(I5,2X,6E14.6,F8.3,E14.6)
|
||||
900 FORMAT(/,10X,8HSTRESSES,/)
|
||||
920 FORMAT(3(1X,I5,2E12.5))
|
||||
910 FORMAT(I5,2E15.6)
|
||||
RETURN
|
||||
END
|
||||
OUTP 98
|
||||
OUTP 99
|
||||
OUTP 100
|
||||
OUTP 101
|
||||
OUTP 102
|
||||
OUTP 103
|
||||
OUTP 104
|
||||
OUTP 105
|
||||
OUTP 106
|
||||
OUTP 107
|
||||
OUTP 108
|
||||
OUTP 109
|
||||
OUTP 110
|
||||
OUTP 111
|
||||
OUTP 112
|
||||
OUTP 113
|
||||
OUTP 114
|
||||
OUTP 115
|
||||
OUTP 116
|
||||
OUTP 117
|
||||
OUTP 118
|
||||
OUTP 119
|
||||
OUTP 120
|
||||
OUTP 121
|
||||
OUTP 122
|
||||
OUTP 123
|
||||
OUTP 124
|
||||
OUTP 125
|
||||
```
|
||||
|
||||
# 10.6.20 Subroutine PREVOS
|
||||
|
||||
This routine reads and write the initial forces and stresses.
|
||||
|
||||
```csv
|
||||
SUBROUTINE PREVOS (FORCE ,NDOFN ,NELEM ,NGAUS ,NPOIN ,NPREV , STRIN )
|
||||
C*************** PREV 2
|
||||
C
|
||||
C*** GRAVITY LOADS AND STRESSES PREV 3
|
||||
C
|
||||
C*************** PREV 4
|
||||
C
|
||||
DIMENSION FORCE(1) ,STRIN(4,1) PREV 5
|
||||
C
|
||||
IF(NPREV.EQ.0) RETURN PREV 6
|
||||
C
|
||||
NSTR1=4 PREV 7
|
||||
NGAU2=NGAUS*NGAUS PREV 8
|
||||
C
|
||||
C*** READ GRAVITY LOADS PREV 9
|
||||
C
|
||||
WRITE(6,920) PREV 10
|
||||
920 FORMAT(//4X,6H NODE ,17H GRAVITY X-LOAD: ,17H GRAVITY Y-LOAD: /) PREV 11
|
||||
200 READ (5,900) NGASH,XGASH,YGASH PREV 12
|
||||
900 FORMAT(I5,4F10.3) PREV 13
|
||||
910 FORMAT(I10,4E18.5) PREV 14
|
||||
NPOSN=(NGASH-1)*NDOFN+1 PREV 15
|
||||
FORCE(NPOSN)=XGASH PREV 16
|
||||
NPOSN=NPOSN+1 PREV 17
|
||||
FORCE(NPOSN)=YGASH PREV 18
|
||||
WRITE(6,910) NGASH,XGASH,YGASH PREV 19
|
||||
IF (NGASH.NE.NPOIN) GO TO 200 PREV 20
|
||||
C
|
||||
C*** READ GRAVITY STRESS PREV 21
|
||||
C PREV 22
|
||||
PREV 23
|
||||
PREV 24
|
||||
PREV 25
|
||||
PREV 26
|
||||
PREV 27
|
||||
PREV 28
|
||||
PREV 29
|
||||
PREV 30
|
||||
```
|
||||
|
||||
<!-- source-page: 427 -->
|
||||
|
||||
WRITE(6,930) PREV 31
|
||||
930 FORMAT(//2X,9HGAUSS PT.,17H GRAVITY X-STRESS,17H GRAVITY Y-STRESS,PREV 32
|
||||
.18H GRAVITY XY-STRESS,17H GRAVITY Z-STRESS/) PREV 33
|
||||
DO 500 IELEM=1,NELEM PREV 34
|
||||
DO 500 IGAUS=1,NGAU2 PREV 35
|
||||
READ(5,900) KGAUS,(STRIN(ISTRI,KGAUS),ISTRI=1,NSTR1) PREV 36
|
||||
500 WRITE(6,910)KGAUS,(STRIN(ISTRI,KGAUS),ISTRI=1,NSTR1) PREV 37
|
||||
RETURN PREV 38
|
||||
END PREV 39
|
||||
|
||||
# 10.6.21 Subroutine RESVPL
|
||||
|
||||
This routine evaluates the internal resisting force vector
|
||||
|
||||
$$
|
||||
\boldsymbol {p} _ {n} = \int_ {\Omega} [ \boldsymbol {B} ] _ {n} ^ {T} \boldsymbol {\sigma} _ {n} d \Omega .
|
||||
$$
|
||||
|
||||
It is very similar to the routine described in Section 8.8.
|
||||
|
||||
SUBROUTINE RESVPL (COORD, DTIME, LNODS, MATNO, NCRIT, NDIME, RESD 1
|
||||
NDOFN, NELEM, NGAUS, NLAPS, NNODE, NMATS, RESD 2
|
||||
NPOIN, NSTRE, NTYPE, POSGP, PROPS, RESID, RESD 3
|
||||
RLOAD, STRIN, STRSG, TDISP, VISTN, VIVEL, RESD 4
|
||||
WEIGP)
|
||||
C******************************************************************************************
|
||||
C
|
||||
C*** EVALUATION OF INTEGRAL (B)**T*(SIGMA)
|
||||
C
|
||||
C******************************************************************************************
|
||||
DIMENSION COORD(NPOIN,1), DERIV(2,9), DJACM(2,2), AVECT(4), MATNO(1), RESD 11
|
||||
PROPS(NMATS,1), DLCOD(2,9), STRIN(4,1), DEVIA(4), TDISP(1), RESD 12
|
||||
LNODS(NELEM,1), GPCOD(2,9), STRSG(4,1), STRAN(4), POSGP(1), RESD 13
|
||||
RLOAD(NELEM,1), CARTD(2,9), VISTN(4,1), STRES(4), WEIGP(1), RESD 14
|
||||
DMATX(4,4), ELCOD(2,9), VIVEL(5,1), SHAPE(9), RESID(1), RESD 15
|
||||
BMATX(4,18), ELDIS(2,9), DESTN(4) RESD 16
|
||||
KGAUS=0
|
||||
NSTR1=4
|
||||
NEVAB=NNODE*NDOFN
|
||||
NTOTV=NPOIN*NDOFN
|
||||
TWOPI=6.283185307179586
|
||||
DO 530 IELEM=1, NELEM
|
||||
DO 540 IEVAB=1, NEVAB
|
||||
540 RLOAD(IELEM, IEVAB)=0.0
|
||||
530 CONTINUE
|
||||
DO 510 ITOTV=1, NTOTV
|
||||
510 RESID(ITOTV)=0.0
|
||||
C
|
||||
C*** LOOP OVER ALL THE ELEMENTS
|
||||
C
|
||||
DO 20 IELEM=1, NELEM
|
||||
LPROP=MATNO(IELEM)
|
||||
THICK=PROPS(LPROP,3)
|
||||
POISS=PROPS(LPROP,2)
|
||||
FRICT=PROPS(LPROP,8)
|
||||
C
|
||||
C*** COMPUTE NEW COORDINATES AND DISPLACEMENTS OF THE
|
||||
C ELEMENT NODAL POINTS
|
||||
C
|
||||
DO 30 INODE =1, NNODE
|
||||
LNODE=IABS(LNODS(IELEM, INODE))
|
||||
NPOSN=(LNODE-1)*NDOFN
|
||||
RESD 1
|
||||
RESD 2
|
||||
RESD 3
|
||||
RESD 4
|
||||
RESD 5
|
||||
RESD 6
|
||||
RESD 7
|
||||
RESD 8
|
||||
RESD 9
|
||||
RESD 10
|
||||
RESD 11
|
||||
RESD 12
|
||||
RESD 13
|
||||
RESD 14
|
||||
RESD 15
|
||||
RESD 16
|
||||
RESD 17
|
||||
RESD 18
|
||||
RESD 19
|
||||
RESD 20
|
||||
RESD 21
|
||||
RESD 22
|
||||
RESD 23
|
||||
RESD 24
|
||||
RESD 25
|
||||
RESD 26
|
||||
RESD 27
|
||||
RESD 28
|
||||
RESD 29
|
||||
RESD 30
|
||||
RESD 31
|
||||
RESD 32
|
||||
RESD 33
|
||||
RESD 34
|
||||
RESD 35
|
||||
RESD 36
|
||||
RESD 37
|
||||
RESD 38
|
||||
RESD 39
|
||||
RESD 40
|
||||
RESD 41
|
||||
RESD 42
|
||||
|
||||
<!-- source-page: 428 -->
|
||||
|
||||
```csv
|
||||
DO 30 IDOFN=1,NDOFN RESD 43
|
||||
NPOSN=NPOSN+1 RESD 44
|
||||
ELCOD(IDOFN,INODE)=COORD(LNODE,IDOFN) RESD 45
|
||||
DLCOD(IDOFN,INODE)=COORD(LNODE,IDOFN)+TDISP(NPOSN) RESD 46
|
||||
30 ELDIS(IDOFN,INODE)=TDISP(NPOSN) RESD 47
|
||||
CALL MODPS (DMATX,LPROP,NMATS,NSTRE,NTYPE,PROPS) RESD 48
|
||||
KGASP=0 RESD 49
|
||||
DO 40 IGAUS=1,NGAUS RESD 50
|
||||
DO 40 JGAUS=1,NGAUS RESD 51
|
||||
KGAUS=KGAUS+1 RESD 52
|
||||
KGASP=KGASP+1 RESD 53
|
||||
EXISP=POSGP(IGAUS) RESD 54
|
||||
ETASP=POSGP(JGAUS) RESD 55
|
||||
C
|
||||
CALL SFR2 (DERIV,NNODE,SHAPE,EXISP,ETASP) RESD 57
|
||||
CALL JACOB2 (CARTD,DERIV,DJACB,ELCOD,GPCOD, RESD 58
|
||||
IELEM,KGASP,NNODE,SHAPE) RESD 59
|
||||
CALL JACOBD (CARTD,DLCOD,DJACM,NDIME,NLAPS,NNODE) RESD 60
|
||||
DVOLU=DJACB*WEIGP(IGAUS)*WEIGP(JGAUS) RESD 61
|
||||
IF(NTYPE.EQ.1) DVOLU=DVOLU*THICK RESD 62
|
||||
IF(NTYPE.EQ.3) DVOLU=DVOLU*TWOPI*GPCOD(1,KGASP) RESD 63
|
||||
CALL BLARGE (BMATX,CARTD,DJACM,DLCOD,GPCOD, RESD 64
|
||||
KGASP,NLAPS,NNODE,NTYPE,SHAPE) RESD 65
|
||||
CALL LINGNL (CARTD,DJACM,DMATX,ELDIS,GPCOD,KGASP, RESD 66
|
||||
KGAUS,NDOFN,NLAPS,NNODE,NSTRE,NTYPE, RESD 67
|
||||
POISS,SHAPE,STRAN,STRES,VISTN) RESD 68
|
||||
C
|
||||
DO 580 ISTR1=1,NSTR1 RESD 69
|
||||
580 STRES(ISTR1)=STRES(ISTR1)+STRIN(ISTR1,KGAUS) RESD 70
|
||||
DO 570 ISTR1=1,NSTR1 RESD 71
|
||||
570 STRSG(ISTR1,KGAUS)=STRES(ISTR1) RESD 72
|
||||
C
|
||||
IF(NLAPS.EQ.2.OR.NLAPS.EQ.0) GO TO 200 RESD 73
|
||||
C
|
||||
CALL INVAR (DEVIA,LPROP,NCrit,NMATS,PROPS,SINT3,STEFF, RESD 74
|
||||
STRES,THETA,VARJ2,YIELD) RESD 75
|
||||
CALL YIELDF (AVECT,DEVIA,FRICT,NCrit,SINT3,STEFF,THETA,VARJ2) RESD 76
|
||||
CALL FLOWVP (AVECT,KGAUS,LPROP,NCrit,NMATS,PROPS, RESD 77
|
||||
STEFF,VIVEL,YIELD) RESD 78
|
||||
C
|
||||
C*** VISCOPLASTIC STRAIN INCREMENT AND A MEASURE FOR HARDENING RESD 79
|
||||
C
|
||||
DO 60 ISTR1=1,NSTR1 RESD 80
|
||||
DESTN(ISTR1)=VIVEL(ISTR1,KGAUS)*DTIME RESD 81
|
||||
60 VISTN(ISTR1,KGAUS)=VISTN(ISTR1,KGAUS)+DESTN(ISTR1) RESD 82
|
||||
DEBAR=SQRT((2.0*(DESTN(1)*DESTN(1)+DESTN(2)*DESTN(2)+ RESD 83
|
||||
DESTN(4)*DESTN(4))+DESTN(3)*DESTN(3))/3.0) RESD 84
|
||||
VIVEL(5,KGAUS)=DEBAR RESD 85
|
||||
C
|
||||
C*** COMPUT INT(B**T*SICMA) ON ELEMENT LEVEL RESD 86
|
||||
C
|
||||
200 CONTINUE RESD 94
|
||||
KEVAB=0 RESD 95
|
||||
DO 502 INODE=1,NNODE RESD 96
|
||||
DO 502 IDOFN=1,NDOFN RESD 97
|
||||
KEVAB=KEVAB+1 RESD 98
|
||||
DO 501 ISTRE=1,NSTRE RESD 99
|
||||
501 RLOAD(IELEM,KEVAB)=RLOAD(IELEM,KEVAB)+
|
||||
.BMATX(ISTRE,KEVAB)*STRSG(ISTRE,KGAUS)*DVOLU RESD 100
|
||||
502 CONTINUE RESD 101
|
||||
40 CONTINUE RESD 102
|
||||
20 CONTINUE RESD 103
|
||||
C
|
||||
C*** ASSEMBLY OF RESID VECTOR RESD 104
|
||||
C
|
||||
```
|
||||
|
||||
<!-- source-page: 429 -->
|
||||
|
||||
<table><tr><td>C</td><td></td><td>RESD 107</td></tr><tr><td></td><td>DO 500 IELEM=1,NELEM</td><td>RESD 108</td></tr><tr><td></td><td>KEVAB=0</td><td>RESD 109</td></tr><tr><td></td><td>DO 500 INODE=1,NNODE</td><td>RESD 110</td></tr><tr><td></td><td>LNODE=LNODS(IELEM,INODE)</td><td>RESD 111</td></tr><tr><td></td><td>NPOSN=(LNODE-1)*NDOFN</td><td>RESD 112</td></tr><tr><td></td><td>DO 500 IDOFN=1,NDOFN</td><td>RESD 113</td></tr><tr><td></td><td>KEVAB=KEVAB+1</td><td>RESD 114</td></tr><tr><td></td><td>NPOSN=NPOSN+1</td><td>RESD 115</td></tr><tr><td></td><td>RESID(NPOSN)=RESID(NPOSN)+RLOAD(IELEM,KEVAB)</td><td>RESD 116</td></tr><tr><td>500</td><td>CONTINUE</td><td>RESD 117</td></tr><tr><td></td><td>RETURN</td><td>RESD 118</td></tr><tr><td></td><td>END</td><td>RESD 119</td></tr></table>
|
||||
|
||||
<table><tr><td>RESD 66-68</td><td>Call LINGNL to determine the state of stress at the current Gauss point.</td></tr><tr><td>RESD 77-78</td><td>Call INVAR to evaluate stress invariants at the current Gauss point.</td></tr><tr><td>RESD 79</td><td>Call YIELDF to select the yield function and calculate the a vector.</td></tr><tr><td>RESD 80-81</td><td>Call FLOWVP to define the rate of viscoplastic straining VIVEL if the stress point is outside the current yield surface.</td></tr><tr><td>RESD 86</td><td>Evaluate the increments of viscoplastic strains DESTN.</td></tr><tr><td>RESD 87</td><td>Evaluate the viscoplastic strains $(\epsilon_{vp})_{n+1}$ for the next time station $t_n + \Delta t$ , VISTN.</td></tr><tr><td>RESD 88-90</td><td>Determine a measure of hardening for the current yield surface.</td></tr><tr><td>RESD 95-101</td><td>Evaluate $p_n^{(e)}$ at the element level, RLOAD.</td></tr><tr><td>RESD 108-117</td><td>Assemble $p_n$ , RESID.</td></tr></table>
|
||||
|
||||
# 10.6.22 Subroutine YIELDF
|
||||
|
||||
This subroutine selects the yield function and calculates the vector a (AVECT) and is almost identical to the version described in Section 7.8.4.1.
|
||||
|
||||
```fortran
|
||||
SUBROUTINE YIELDF (AVECT, DEVIA, FRICT, NCRIT, SINT3, STEFF, YELD 1
|
||||
THETA, VARJ2) YELD 2
|
||||
C********** YELD 3
|
||||
C YELD 4
|
||||
C *** SELECTS YIELD FUNCTION AND CALCULATES VECTOR 'AVECT' YELD 5
|
||||
C YELD 6
|
||||
C********** YELD 7
|
||||
DIMENSION AVECT(4), DEVIA(4), VECA1(4), VECA2(4), VECA3(4) YELD 8
|
||||
IF(STEFF.EQ.0.0) RETURN YELD 9
|
||||
NSTR1=4 YELD 10
|
||||
TANTH=TAN(THETA) YELD 11
|
||||
SINTH=SIN(THETA) YELD 12
|
||||
COSTH=COS(THETA) YELD 13
|
||||
COST3=COS(3.0*THETA) YELD 14
|
||||
ROOT3=1.73205080757 YELD 15
|
||||
```
|
||||
|
||||
<!-- source-page: 430 -->
|
||||
|
||||
```txt
|
||||
C*** CALCULATE VECTOR A1
|
||||
VECA1(1)=1.0
|
||||
VECA1(2)=1.0
|
||||
VECA1(3)=0.0
|
||||
VECA1(4)=1.0
|
||||
C*** CALCULATE VECTOR A2
|
||||
DO 10 ISTR1=1,NSTR1
|
||||
10 VECA2(ISTR1)=DEVIA(ISTR1)/(2.0*STEFF)
|
||||
VECA2(3)=DEVIA(3)/STEFF
|
||||
C*** CALCULATE VECTOR A3
|
||||
VECA3(1)=DEVIA(2)*DEVIA(4)+VARJ2/3.0
|
||||
VECA3(2)=DEVIA(1)*DEVIA(4)+VARJ2/3.0
|
||||
VECA3(3)=-2.0*DEVIA(3)*DEVIA(4)
|
||||
VECA3(4)=DEVIA(1)*DEVIA(2)-DEVIA(3)*DEVIA(3)+VARJ2/3.0
|
||||
GO TO (1,2,3,4) NCRIT
|
||||
C*** TRESCA
|
||||
1 CONS1=0.0
|
||||
ABTHE=ABS(THETA*57.29577951308)
|
||||
IF(ABTHE.LT.29.0) GO TO 20
|
||||
CONS2=ROOT3
|
||||
CONS3=0.0
|
||||
GO TO 40
|
||||
20 CONS2=2.0*(COSTH+SINTH*TAN(3.0*THETA))
|
||||
CONS3=ROOT3*SINTH/(VARJ2*COST3)
|
||||
GO TO 40
|
||||
C*** VON MISES
|
||||
2 CONS1=0.0
|
||||
CONS2=ROOT3
|
||||
CONS3=0.0
|
||||
GO TO 40
|
||||
C*** MOHR-COULOMB
|
||||
3 CONS1=SIN(FRICT*0.017453292)/3.0
|
||||
ABTHE=ABS(THETA*57.29577951308)
|
||||
IF(ABTHE.LT.29.0) GO TO 30
|
||||
CONS3=0.0
|
||||
PLUMI=1.0
|
||||
IF(THETA.GT.0.0) PLUMI=-1.0
|
||||
CONS2=0.5*(ROOT3+PLUMI*CONS1/ROOT3)
|
||||
GO TO 40
|
||||
30 TANT3=TAN(3.0*THETA)
|
||||
CONS2=COSTH*(1.0+TANTH*TANT3)+CONS1*(TANT3-TANTH)/ROOT3)
|
||||
CONS3=(ROOT3*SINTH+CONS1*COSTH)/(2.0*VARJ2*COST3)
|
||||
GO TO 40
|
||||
C*** DRUCKER-PRAGER
|
||||
4 SNPHI=SIN(FRICT*0.017453292)
|
||||
CONS1=2.0*SNPHI/(ROOT3*(3.0-SNPHI))
|
||||
CONS2=1.0
|
||||
CONS3=0.0
|
||||
40 CONTINUE
|
||||
DO 50 ISTR1=1,NSTR1
|
||||
50 AVECT(ISTR1)=CONS1*VECA1(ISTR1)+CONS2*
|
||||
.VECA2(ISTR1)+CONS3*VECA3(ISTR1)
|
||||
RETURN
|
||||
END
|
||||
YELD 16
|
||||
YELD 17
|
||||
YELD 18
|
||||
YELD 19
|
||||
YELD 20
|
||||
YELD 21
|
||||
YELD 22
|
||||
YELD 23
|
||||
YELD 24
|
||||
YELD 25
|
||||
YELD 26
|
||||
YELD 27
|
||||
YELD 28
|
||||
YELD 29
|
||||
YELD 30
|
||||
YELD 31
|
||||
YELD 32
|
||||
YELD 33
|
||||
YELD 34
|
||||
YELD 35
|
||||
YELD 36
|
||||
YELD 37
|
||||
YELD 38
|
||||
YELD 39
|
||||
YELD 40
|
||||
YELD 41
|
||||
YELD 42
|
||||
YELD 43
|
||||
YELD 44
|
||||
YELD 45
|
||||
YELD 46
|
||||
YELD 47
|
||||
YELD 48
|
||||
YELD 49
|
||||
YELD 50
|
||||
YELD 51
|
||||
YELD 52
|
||||
YELD 53
|
||||
YELD 54
|
||||
YELD 55
|
||||
YELD 56
|
||||
YELD 57
|
||||
YELD 58
|
||||
YELD 59
|
||||
YELD 60
|
||||
YELD 61
|
||||
YELD 62
|
||||
YELD 63
|
||||
YELD 64
|
||||
YELD 65
|
||||
YELD 66
|
||||
YELD 67
|
||||
YELD 68
|
||||
YELD 69
|
||||
```
|
||||
|
||||
# 10.7 Examples
|
||||
|
||||
# 10.7.1 Introduction
|
||||
|
||||
To illustrate the use of DYNPAK we now describe the nonlinear transient dynamic analysis of (i) a spherical shell and (ii) a concrete gravity dam.
|
||||
Reference in New Issue
Block a user