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김경종
+975
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<!-- source-page: 371 -->
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```csv
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DO 30 ILAYR=1,NLAYR
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KGAUS=KGAUS+1
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JLAYR=ILAYR+1
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C
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C*** EVALUATE Z-COORDINATES FOR CURRENT LAYER
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C
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DEPT1=DEPTH(ILAYR)
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DEPT2=DEPTH(JLAYR)
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CONS3=(DEPT2+DEPT1)*(DEPT2**2-DEPT1**2)/4.0
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C
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C*** EVALUATE ELASTO-PLASTIC D MATRIX FOR CURRENT LAYER
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C
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CALL MDMPA(DPLAN,DSHER,LPROP,MMATS,PROPS,1,0)
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IF(IINCS.EQ.1)GO TO 40
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IF(EPSTN(KGAUS).EQ.0.0)GO TO 40
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DO 50 ISTRE=1,5
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50 SGTOT(ISTRE)=STRSG(ISTRE,KGAUS)
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CALL INVMP(DEVIA,NCrit,SINT3,STEFF,SGTOT,THETA,VARJ2,YIELD)
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CALL FLOWMP(ABETA,AVECT,DEVIA,DPLAN,DVECT,HARDS,NCrit,SINT3,
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STEFF,THETA,VARJ2)
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DO 60 ISTRE=1,3
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DO 60 JSTRE=1,3
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60 DPLAN(ISTRE,JSTRE)=DPLAN(ISTRE,JSTRE)-ABETA*DVECT(ISTRE)*
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.DVECT(JSTRE)
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40 CONTINUE
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C
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C*** SUM D MATRIX OVER ELEMENT DEPTH
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C
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DO 70 ISTRE=1,3
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DO 70 JSTRE=1,3
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70 DFLEF(ISTRE,JSTRE)=DFLEF(ISTRE,JSTRE)+CONS3*DPLAN(ISTRE,JSTRE)
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30 CONTINUE
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GO TO 200
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C
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C*** ZERO D MATRIX FOR SHEAR
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C
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100 DO 80 ISTRE=1,2
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DO 80 JSTRE=1,2
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80 DSHES(ISTRE,JSTRE)=0.0
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C
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C*** EVALUATE ELASTIC D MATRIX
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C
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CALL MDMPA(DPLAN,DSHER,LPROP,MMATS,PROPS,0,1)
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C
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C*** LOOP AROUND LAYERS
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C
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DO 90 ILAYR=1,NLAYR
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JLAYR=ILAYR+1
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C
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C*** EVALUATE Z-COORDINATES FOR CURRENT LAYER
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C
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DEPT1=DEPTH(ILAYR)
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DEPT2=DEPTH(JLAYR)
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CONS4=DEPT2-DEPT1
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C
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C*** SUM D MATRIX OVER ELEMENT DEPTH
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C
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DO 110 ISTRE=1,2
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DO 110 JSTRE=1,2
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110 DSHES(ISTRE,JSTRE)=DSHES(ISTRE,JSTRE)+CONS4*Dsher(ISTRE,JSTRE)
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90 CONTINUE
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200 CONTINUE
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RETURN
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END
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LAYR 27
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LAYR 28
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LAYR 29
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LAYR 30
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LAYR 31
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LAYR 32
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LAYR 33
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LAYR 34
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LAYR 35
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LAYR 36
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LAYR 37
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LAYR 38
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LAYR 39
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LAYR 40
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LAYR 41
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LAYR 42
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LAYR 43
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LAYR 44
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LAYR 45
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LAYR 46
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LAYR 47
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LAYR 48
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LAYR 49
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LAYR 50
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LAYR 51
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LAYR 52
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LAYR 53
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LAYR 54
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LAYR 55
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LAYR 56
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LAYR 57
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LAYR 58
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LAYR 59
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LAYR 60
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LAYR 61
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LAYR 62
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LAYR 63
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LAYR 64
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LAYR 65
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LAYR 66
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LAYR 67
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LAYR 68
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LAYR 69
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LAYR 70
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LAYR 71
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LAYR 72
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LAYR 73
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LAYR 74
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LAYR 75
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LAYR 76
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LAYR 77
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LAYR 78
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LAYR 79
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LAYR 80
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LAYR 81
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LAYR 82
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LAYR 83
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LAYR 84
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LAYR 85
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LAYR 86
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LAYR 87
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LAYR 88
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LAYR 89
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LAYR 90
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```
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<!-- source-page: 372 -->
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LAYR 10 If JFFLE is zero $D_f'$ is not evaluated. If it is one $D_s'$ is not evaluated.
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LAYR 15-17 Initializes $D_{f}'$ .
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LAYR 21 Starts the summation loop to form DFLEF, i.e.
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$$
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\hat {D} _ {f} = \sum_ {i = 1} ^ {n} \frac {1}{4} (z _ {i + 1} + z _ {i}) (z _ {i + 1} ^ {2} - z _ {i} ^ {2}) D _ {f} ^ {\prime}.
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$$
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LAYR 22 Increases the counter for Gauss points in each layer by 1. It is needed to use the effective plastic strain (EPSTN) stresses (STRSG) calculated in RESMPA.
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LAYR 27-29 Forms $\frac{1}{4} (z_{i + 1} + z_i)(z_{i + 1}^2 -z_i^2)$ .
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LAYR 33-45 Calls MDMPA to get DPLAN and $D_{ep'}$ is formed using INVMP and FLOWMP.
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LAYR 49–51 DFLEF is formed.
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LAYR 57-59 DSHES is initialised.
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LAYR 63 Calls MDMPA to form DSHER.
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LAYR 67–74 Starts the summation loop and the integrating constant for DSHES is evaluated, i.e.
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$$
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\hat {\boldsymbol {D}} _ {s} = \sum_ {i = 1} ^ {n} (z _ {i + 1} - z _ {i}) \boldsymbol {D} _ {s}.
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$$
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LAYR 78-81 DSHES is formed.
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# 9.6.6 Subroutine MDMPA
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This subroutine evaluates $D_{f}'$ and $D_{s}'$ .
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```txt
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SUBROUTINE MDMPA (DPLAN,DSHER,LPROP,MMATS,PROPS, MODL 1
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IFPLA,IFSHE) MODL 2
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C**************************MODL 3
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C
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C*** CALCULATES MATRIX OF ELASTIC RIGIDITIES FOR EACH LAYER
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C*** OF MINDLIN PLATE
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C
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C**************************MODL 8
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DIMENSION DPLAN(3,3),DSHER(2,2), MODL 9
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PROPS(MMATS,8) MODL 10
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YOUNG=PROPS(LPROP,1) MODL 11
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POISS=PROPS(LPROP,2) MODL 12
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THICK=PROPS(LPROP,3) MODL 13
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C*** FORM DPLAN
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IF(IFPLA.EQ.0) GO TO 10
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DO 1 IROWS=1,3
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DO 1 JCOLS=1,3
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1 DPLAN(IROWS,JCOLS)=0.0
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CONST=YOUNG/(1.0-POISS*POISS) MODL 18
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DPLAN(1,1)=CONST
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DPLAN(2,2)=CONST
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DPLAN(1,2)=CONST*POISS
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MODL 20
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MODL 21
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MODL .22
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```
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<!-- source-page: 373 -->
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```csv
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DPLAN(2,1)=CONST*POISS
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DPLAN(3,3)=CONST*(1.0-POISS)/2.0
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C*** FORM DSHER
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10 IF(IFSHE.EQ.0) RETURN
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DO 3 IROWS=1,2
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DO 3 JCOLS=1,2
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3 DSHER(IROWS,JCOLS)=0.0
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DSHER(1,1)=YOUNG/(2.4+2.4*POISS)
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DSHER(2,2)=YOUNG/(2.4+2.4*POISS)
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RETURN
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END
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MODL 23
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MODL 24
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MODL 25
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MODL 26
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MODL 27
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MODL 28
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MODL 29
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MODL 30
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MODL 31
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MODL 32
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MODL 33
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```
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# 9.6.7 Subroutine OUTMPA
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This subroutine outputs nodal displacements and reactions and also the Gauss point stress resultants and the stresses within each layer. It is very similar to subroutine OUTMP which was described in Section 9.5.7. Statements OUTP 1-3 are replaced by OUTL 1-3 and statements OUTP 56-66 are replaced by statements OUTL 56-67.
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```fortran
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SUBROUTINE OUTMPA (EPSTN,IITER,MTOTG,MTOTV,MVFIX,NELEM, OUTL 1
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. NGAUS,NLAPS,NOFIX,NUOTP,NPOIN,NVFIX, OUTL 2
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. STRSG,TDISP,TREAC) OUTL 3
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C******************************************************************************************OUTL 4
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C OUTL 5
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C*** OUTPUT DISPLACEMENTS,REACTIONS AND GAUSS POINT STRESSES OUTL 6
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C*** IN EACH LAYER FOR EP MINDLIN PLATE ANALYSIS OUTL 7
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C OUTL 8
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C******************************************************************************************OUTL 9
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DIMENSION EPSTN(MTOTG),GPCOD(2,9),NOFIX(MVFIX),NUOTP(2), OUTL 10
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. STRSG(5,MTOTG),TDISP(MTOTV),TREAC(MVFIX,3) OUTL 11
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KOUTP=NOUTP(1) OUTL 12
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IF(IITER.GT.1) KOUTP=NOUTP(2) OUTL 13
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C OUTL 14
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C*** OUTPUT DISPLACEMENTS OUTL 15
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C OUTL 16
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IF(KOUTP.LT.1) GO TO 10 OUTL 17
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WRITE(6,900) OUTL 18
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900 FORMAT(1H0,5X,13HDISPLACEMENTS) OUTL 19
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WRITE(6,950) OUTL 20
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950 FORMAT(1H0,6X,4HNODE,6X,5HDISP.,8X,7HXZ-ROT.,7X,7HYZ-ROT.) OUTL 21
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DO 20 IPOIN=1,NPOIN OUTL 22
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NGASH=IPOIN*3 OUTL 23
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NGISH=NGASH-3+1 OUTL 24
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20 WRITE(6,910) IPOIN,(TDISP(IGASH),IGASH=NGISH,NGASH) OUTL 25
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910 FORMAT(I10,3E14.6) OUTL 26
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10 CONTINUE OUTL 27
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C OUTL 28
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C*** OUTPUT REACTIONS OUTL 29
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C OUTL 30
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IF(KOUTP.LT.2) GO TO 30 OUTL 31
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WRITE(6,920) OUTL 32
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920 FORMAT(1H0,5X,9HREACTIONS) OUTL 33
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WRITE(6,960) OUTL 34
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960 FORMAT(1H0,6X,4HNODE,6X,5HFORCE,3X,9HXZ-MOMENT,5X,9HYZ-MOMENT) OUTL 35
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DO 40 IVFIX=1,NVFIX OUTL 36
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40 WRITE(6,910) NOFIX(IVFIX),(TREAC(IVFIX,IDOFN),IDOFN=1,3) OUTL 37
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30 CONTINUE OUTL 38
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C OUTL 39
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C*** OUTPUT STRESSES OUTL 40
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```
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<!-- source-page: 374 -->
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```csv
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C
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IF(KOUTP.LT.3) GO TO 50
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REWIND 3
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WRITE(6,970)
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970 FORMAT(1H0,5X,8HSTRESSES)
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WRITE(6,980)
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980 FORMAT(1H0,4HG.P.,2X,8HX-COORD.,2X,8HY-COORD.,3X,8HX-MOMENT,4X,
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.8HY-MOMENT,3X,9HXY-MOMENT,3X,
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.13HEFF.PL.STRAIN)
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KGAUS=0
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DO 60 IELEM=1,NELEM
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READ(3)GPCOD
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KELGS=0
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WRITE(6,930)IELEM
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930 FORMAT(1H0,5X,13HELEMENT NO. =,I5)
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DO 60 IGAUS=1,NGAUS
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DO 60 JGAUS=1,NGAUS
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KELGS=KELGS+1
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DO 60 ILAYR=1,NLAPS
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KGAUS=KGAUS+1
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WRITE(6,940)KELGS,(GPCOD(IDIME,KELGS),IDIME=1,2),
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.(STRSG(ISTRE,KGAUS),ISTRE=1,3),EPSTN(KGAUS)
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940 FORMAT(I5,2F10.4,6E12.5)
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60 CONTINUE
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50 CONTINUE
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RETURN
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END
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OUTL 41
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OUTL 42
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OUTL 43
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OUTL 44
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OUTL 45
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OUTL 46
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OUTL 47
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OUTL 48
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OUTL 49
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OUTL 50
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OUTL 51
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OUTL 52
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OUTL 53
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OUTL 54
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OUTL 55
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OUTL 56
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OUTL 57
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OUTL 58
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OUTL 59
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OUTL 60
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OUTL 61
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OUTL 62
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OUTL 63
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OUTL 64
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OUTL 65
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OUTL 66
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OUTL 67
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```
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# 9.6.8 Subroutine RESMPA
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This routine evaluates the residual forces for the layered Mindlin plate. It is very similar to RESMP described in Section 9.5.10.
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```csv
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SUBROUTINE RESMPA (ASDIS,COORD,EFFST,ELOAD,EPSTN,LNODS, RESL 1
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. MATNO,MELEM,MMATS,MPOIN,MTOTG,MTOTV, RESL 2
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. NCRIT,NELEM,NEVAB,NGAUS,NNODE,NLAPS, RESL 3
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. PROPS,STRSG) RESL 4
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C************************** RESL 5
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C RESL 6
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C*** EVALUATES EQUIVALENT NODAL FORCES FOR THE STRESSES RESL 7
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C*** IN LAYERED MINDLIN PLATES DURING EP ANALYSIS RESL 8
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C RESL 9
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C************************** RESL 10
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DIMENSION ASDIS(MTOTV),AVECT(5),CARTD(2,9), RESL 11
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. COORD(MPOIN,2),DERIV(2,9),DESIG(5),DEVIA(4), RESL 12
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. DEPTH(26),DVECT(5), RESL 13
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. EFFST(MTOTG),ELCOD(2,9), RESL 14
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. ELDIS(3,9),ELOAD(MELEM,27),EPSTN(MTOTG),GPCOD(2,9), RESL 15
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. LNODS(MELEM,9),MATNO(MELEM),POSGP(4), RESL 16
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. PROPS(MMATS,8),SGTOT(5),SHAPE(9),SIEMA(5), RESL 17
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||||
. STRES(5),STRSG(5,MTOTG),TOSPB(5),WEIGP(4), RESL 18
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||||
. DPLAN(3,3),DSHER(2,2),BFLEI(3,3),BSHEI(2,3), RESL 19
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||||
. DUMMY(3,3),FORCE(3),DGRAD(6) RESL 20
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NTIME=1 RESL 21
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DO 10 IELEM=1,NELEM RESL 22
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DO 10 IEVAB=1,NEVAB RESL 23
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10 ELOAD(IELEM,IEVAB)=0.0 RESL 24
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KGAUS=0 RESL 25
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LGAUS=0 RESL 26
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DO 20 IELEM=1,NELEM RESL 27
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LPROP=MATNO(IELEM) RESL 28
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```
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||||
<!-- source-page: 375 -->
|
||||
|
||||
```txt
|
||||
C
|
||||
C*** COMPUTE COORDINATE AND INCREMENTAL DISPLACEMENTS OF THE
|
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C ELEMENT NODAL POINTS
|
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C
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DO 190 INODE =1, NNODE
|
||||
LNODE=IABS(LNODS(IELEM, INODE))
|
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NPOSN=(LNODE-1)*3
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DO 30 IDOFN=1,3
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NPOSN=NPOSN+1
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30 ELDIS(IDOFN, INODE)=ASDIS(NPOSN)
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DO 180 IDIME=1,2
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180 ELCOD(IDIME, INODE)=COORD(LNODE, IDIME)
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||||
190 CONTINUE
|
||||
KGASP=0
|
||||
CALL DEMPA(DEPTH, LPROP, MMATS, NLAPS, PROPS)
|
||||
CALL MDMPA (DPLAN, DSHER, LPROP, MMATS, PROPS, 1, 1)
|
||||
CALL GAUSSQ (NGAUS, POSGP, WEIGP)
|
||||
DO 40 IGAUS=1, NGAUS
|
||||
DO 40 JGAUS=1, NGAUS
|
||||
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)
|
||||
DO 400 ISTRE=1,3
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400 TOSPB(ISTRE)=0.0
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||||
DO 410 ILAYR=1, NLAPS
|
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BRING=1.0
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||||
KGAUS=KGAUS+1
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||||
JLAYR=ILAYR+1
|
||||
DEPT1=DEPTH(ILAYR)
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||||
DEPT2=DEPTH(JLAYR)
|
||||
CONST=0.5*(DEPT2+DEPT1)
|
||||
CALL GRADMP (CARTD, DGRAD, ELDIS, 3, NNODE)
|
||||
CALL STRMPA (CARTD, CONST, DPLAN, 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, DPLAN, DVECT, HARDS,
|
||||
```
|
||||
|
||||
<!-- source-page: 376 -->
|
||||
|
||||
```csv
|
||||
NCRIT,SINT3,STEFF,THETA,VARJ2) RESL 94
|
||||
AGASH=0.0 RESL 95
|
||||
DO 100 ISTRE=1,3 RESL 96
|
||||
100 AGASH=AGASH+AVECT(ISTRE)*STRES(ISTRE) RESL 97
|
||||
DLAMD=AGASH*ABETA RESL 98
|
||||
IF(DLAMD.LT.0.0) DLAMD=0.0 RESL 99
|
||||
BGASH=0.0 RESL 100
|
||||
DO 110 ISTRE=1,3 RESL 101
|
||||
BGASH=BGASH+AVECT(ISTRE)*SGTOT(ISTRE) RESL 102
|
||||
110 SGTOT(ISTRE)=SGTOT(ISTRE)+STRES(ISTRE)-DLAMD*DVECT(ISTRE) RESL 103
|
||||
90 EPSTN(KGAUS)=EPSTN(KGAUS)+DLAMD*BGASH/YIELD RESL 104
|
||||
DO 120 ISTRE=1,3 RESL 105
|
||||
120 DESIG(ISTRE)=SGTOT(ISTRE)-STRSG(ISTRE,KGAUS) RESL 106
|
||||
CALL INVMP (DEVIA,NCRIT,SINT3,STEFF,SGTOT,THETA,VARJ2,YIELD) RESL 107
|
||||
CURYS=PROPS(LPROP,6)+EPSTN(KGAUS)*PROPS(LPROP,7) RESL 108
|
||||
IF(YIELD.GT.CURYS) BRING=CURYS/YIELD RESL 109
|
||||
60 DO 130 ISTRE=1,3 RESL 110
|
||||
SGTOT(ISTRE)=BRING*(STRSG(ISTRE,KGAUS)+DESIG(ISTRE)) RESL 111
|
||||
130 STRSG(ISTRE,KGAUS)=SGTOT(ISTRE) RESL 112
|
||||
EFFST(KGAUS)=BRING*YIELD RESL 113
|
||||
CONSA=(DEPT2**2-DEPT1**2)/2.0 RESL 114
|
||||
DO 440 ISTRE=1,3 RESL 115
|
||||
440 TOSPB(ISTRE)=TOSPB(ISTRE)+SGTOT(ISTRE)*CONSA RESL 116
|
||||
410 CONTINUE RESL 117
|
||||
DO 430 ISTRE=1,3 RESL 118
|
||||
430 SGTOT(ISTRE)=TOSPB(ISTRE) RESL 119
|
||||
C RESL 120
|
||||
C*** CALCULATE THE EQUIVALENT NODAL FORCES AND ASSOCIATE WITH THE RESL 121
|
||||
C ELEMENT NODES RESL 122
|
||||
DO 140 INODE=1,NNODE RESL 123
|
||||
C*** ZERO FORCE VECTOR RESL 124
|
||||
CALL VZERO (3,FORCE) RESL 125
|
||||
CALL BMATPB (BFLEI,DUMMY,BSHEI,CARTD,INODE,SHAPE, RESL 126
|
||||
0, 1, 0) RESL 127
|
||||
FORCE(2)=(BFLEI(1,2)*SGTOT(1)+BFLEI(3,2)*SGTOT(3))*DAREA RESL 128
|
||||
+FORCE(2) RESL 129
|
||||
FORCE(3)=(BFLEI(2,3)*SGTOT(2)+BFLEI(3,3)*SGTOT(3))*DAREA RESL 130
|
||||
+FORCE(3) RESL 131
|
||||
IPOSN=(INODE-1)*3+1 RESL 132
|
||||
DO 135 IDOFN=2,3 RESL 133
|
||||
IPOSN=IPOSN+1 RESL 134
|
||||
135 ELOAD(IELEM,IPOSN)=ELOAD(IELEM,IPOSN)+FORCE(IDOFN) RESL 135
|
||||
140 CONTINUE RESL 136
|
||||
40 CONTINUE RESL 137
|
||||
C RESL 138
|
||||
C*** CALCULATE FORCES ASSOCIATED WITH SHEAR DEFORMATION RESL 139
|
||||
C RESL 140
|
||||
NGAUM=NGAUS-1 RESL 141
|
||||
CALL GAUSSQ (NGAUM,POSGP,WEIGP) RESL 142
|
||||
C RESL 143
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION RESL 144
|
||||
C RESL 145
|
||||
KGASP=0 RESL 146
|
||||
DO 300 IGAUS=1,NGAUM RESL 147
|
||||
DO 300 JGAUS=1,NGAUM RESL 148
|
||||
EXISP=POSGP(IGAUS) RESL 149
|
||||
ETASP=POSGP(JGAUS) RESL 150
|
||||
CALL SFR2 (DERIV,ETASP,EXISP,NNODE,SHAPE) RESL 151
|
||||
KGASP=KGASP+1 RESL 152
|
||||
CALL JACOB2 (CARTD,DERIV,DJACB,ELCOD,GPCOD,IELEM, RESL 153
|
||||
KGASP,NNODE,SHAPE) RESL 154
|
||||
DAREA=DJACB*WEIGP(IGAUS)*WEIGP(JGAUS) RESL 155
|
||||
DO 610 ISTRE=4,5 RESL 156
|
||||
610 TOSPB(ISTRE)=0.0 RESL 157
|
||||
RESL 158
|
||||
```
|
||||
|
||||
<!-- source-page: 377 -->
|
||||
|
||||
```csv
|
||||
C
|
||||
C*** LOOP AROUND LAYRS
|
||||
C
|
||||
DO 600 ILAYR=1,NLAPS
|
||||
LGAUS=LGAUS+1
|
||||
JLAYR=ILAYR+1
|
||||
DEPT1=DEPTH(ILAYR)
|
||||
DEPT2=DEPTH(JLAYR)
|
||||
CONST=1.0
|
||||
CALL GRADMP (CARTD,DGRAD,ELDIS, 3,NNODE)
|
||||
CALL STRMPA (CARTD,CONST,DPLAN,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)
|
||||
CONSB=DEPT2-DEPT1
|
||||
DO 620 ISTRE=4,5
|
||||
620 TOSPB(ISTRE)=TOSPB(ISTRE)+SGTOT(ISTRE)*CONSB
|
||||
600 CONTINUE
|
||||
DO 605 ISTRE=4,5
|
||||
605 SGTOT(ISTRE)=TOSPB(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
|
||||
RESL 159
|
||||
RESL 160
|
||||
RESL 161
|
||||
RESL 162
|
||||
RESL 163
|
||||
RESL 164
|
||||
RESL 165
|
||||
RESL 166
|
||||
RESL 167
|
||||
RESL 168
|
||||
RESL 169
|
||||
RESL 170
|
||||
RESL 171
|
||||
RESL 172
|
||||
RESL 173
|
||||
RESL 174
|
||||
RESL 175
|
||||
RESL 176
|
||||
RESL 177
|
||||
RESL 178
|
||||
RESL 179
|
||||
RESL 180
|
||||
RESL 181
|
||||
RESL 182
|
||||
RESL 183
|
||||
RESL 184
|
||||
RESL 185
|
||||
RESL 186
|
||||
RESL 187
|
||||
RESL 188
|
||||
RESL 189
|
||||
RESL 190
|
||||
RESL 191
|
||||
RESL 192
|
||||
RESL 193
|
||||
RESL 194
|
||||
RESL 195
|
||||
RESL 196
|
||||
RESL 197
|
||||
RESL 198
|
||||
RESL 199
|
||||
RESL 200
|
||||
```
|
||||
|
||||
# 9.6.9 Subroutine STIFMPA
|
||||
|
||||
This routine evaluates the stiffness matrices for layered elasto-plastic Mindlin plate elements.
|
||||
|
||||
```csv
|
||||
SUBROUTINE STIMPA (COORD, EPSTN, IINCS, LNODS, MATNO, MELEM, STFL 1
|
||||
. MEVAB, MMATS, MPOIN, MTOTG, NCRIT, NELEM, STFL 2
|
||||
. NEVAB, NGAUS, NNODE, NLAPS, PROPS, STRSG) STFL 3
|
||||
C**************************STFL 4
|
||||
C STFL 5
|
||||
C*** EVALUATE STIFFNESS MATRICES FOR LAYREED ELASTO-PLASTIC STFL 6
|
||||
C*** MINDLIN PLATE ELEMENTS STFL 7
|
||||
C STFL 8
|
||||
C**************************STFL 9
|
||||
DIMENSION CARTD(2,9), COORD(MPOIN,2), STFL 10
|
||||
. DERIV(2,9), DEPTH(26), ELCOD(2,9), STFL 11
|
||||
. EPSTN(MTOTG), ESTIF(27,27), GPCOD(2,9), LNODS(MELEM,9), STFL 12
|
||||
. MATNO(MELEM), POSGP(4), PROPS(MMATS,8), SHAPE(9), STFL 13
|
||||
. STRSG(5, MTOTG), WEIGP(4), STFL 14
|
||||
. DFLEX(3,3), DSHER(2,2), BFLEI(3,3), BFLEJ(3,3), STFL 15
|
||||
```
|
||||
|
||||
<!-- source-page: 378 -->
|
||||
|
||||
```asm
|
||||
BSHEI(2,3),BSHEJ(2,3),DUMMY(3,3)
|
||||
STFL 16
|
||||
REWIND 1
|
||||
STFL 17
|
||||
REWIND 3
|
||||
STFL 18
|
||||
KGAUS=0
|
||||
STFL 19
|
||||
C
|
||||
C*** LOOP OVER EACH ELEMENT
|
||||
STFL 20
|
||||
C
|
||||
DO 70 IELEM=1,NELEM
|
||||
STFL 21
|
||||
LPROP=MATNO(IELEM)
|
||||
STFL 22
|
||||
C
|
||||
C*** EVALUATE THE COORDINATES OF THE ELEMENT NODAL POINTS
|
||||
STFL 23
|
||||
C
|
||||
DO 10 INODE=1,NNODE
|
||||
STFL 24
|
||||
LNODE=LNODS(IELEM,INODE)
|
||||
STFL 25
|
||||
LNODE=IABS(LNODE)
|
||||
STFL 26
|
||||
DO 10 IDIME=1,2
|
||||
STFL 27
|
||||
10 ELCOD(IDIME,INODE)=COORD(LNODE,IDIME)
|
||||
STFL 28
|
||||
C
|
||||
C*** INITIALIZE THE ELEMENT STIFFNESS MATRIX
|
||||
STFL 29
|
||||
C
|
||||
DO 20 IEVAB=1,NEVAB
|
||||
STFL 30
|
||||
DO 20 JEVAB=1,NEVAB
|
||||
STFL 31
|
||||
20 ESTIF(IEVAB,JEVAB)=0.0
|
||||
STFL 32
|
||||
CALL DEMPA(DEPTH,LPROP,MMATS,NLAPS,PROPS)
|
||||
STFL 33
|
||||
C
|
||||
C*** EVALUATE PART OF STIFFNESS MATRIX
|
||||
STFL 34
|
||||
C
|
||||
ASSOCIATED WITH BENDING DEFORMATION
|
||||
STFL 35
|
||||
C
|
||||
KGASP=0
|
||||
STFL 36
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 37
|
||||
C
|
||||
C
|
||||
C*** SET UP GAUSSIAN INTEGRATION CONSTANTS
|
||||
STFL 38
|
||||
C
|
||||
STFL 39
|
||||
C
|
||||
STFL 40
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 41
|
||||
C
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 42
|
||||
C
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 43
|
||||
C
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 44
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 45
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 46
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 47
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 48
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 49
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA NUMERICAL INTEGRATION
|
||||
STFL 50
|
||||
C
|
||||
CALL GAUSSQ (NGAUS,POSGP,WEIGP)
|
||||
STFL 51
|
||||
C
|
||||
DO 50 IGAUS=1,NGAUS
|
||||
STFL 52
|
||||
DO 50 JGAUS=1,NGAUS
|
||||
STFL 53
|
||||
KGASP=KGASP+1
|
||||
STFL 54
|
||||
EXISP=POSGP(IGAUS)
|
||||
STFL 55
|
||||
ETASP=POSGP(JGAUS)
|
||||
STFL 56
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 57
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 58
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 59
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 60
|
||||
C
|
||||
CALL SFR2 (DERIV,ETASP,EXISP,NNODE,SHAPE)
|
||||
STFL 61
|
||||
CALL JACOB2 (CARTD,DERIV,DJACB,ELCOD,GPCOD,IELEM,
|
||||
KGASP,NNODE,SHAPE)
|
||||
STFL 62
|
||||
DAREA=DJACB*WEIGP(IGAUS)*WEIGP(JGAUS)
|
||||
STFL 63
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 64
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 65
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 66
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 67
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 68
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 69
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 70
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 71
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 72
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 73
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 74
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 75
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 76
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 77
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 78
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 79
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS,ELEMENTAL AREA,ETC
|
||||
STFL 80
|
||||
```
|
||||
|
||||
<!-- source-page: 379 -->
|
||||
|
||||
```txt
|
||||
50 CONTINUE
|
||||
C
|
||||
C*** EVALUATE PART OF STIFFNESS MATRIX
|
||||
C ASSOCIATED WITH SHEAR DEFORMATION
|
||||
C
|
||||
KGASP=0
|
||||
NGAUM=NGAUS-1
|
||||
C
|
||||
C*** ENTER LOOPS FOR AREA INTEGRATION
|
||||
C
|
||||
C
|
||||
C*** SET UP GAUSSIAN INTEGRATION CONSTANTS
|
||||
C
|
||||
CALL GAUSSQ (NGAUM,POSGP,WEIGP)
|
||||
DO 51 IGAUS=1,NGAUM
|
||||
DO 51 JGAUS=1,NGAUM
|
||||
KGASP=KGASP+1
|
||||
EXISP=POSGP(IGAUS)
|
||||
ETASP=POSGP(JGAUS)
|
||||
C
|
||||
C*** EVALUATE THE SHAPE FUNCTIONS, ELEMENTAL AREA,ETC
|
||||
C
|
||||
CALL SFR2 (DERIV,ETASP,EXISP,NNODE,SHAPE)
|
||||
CALL JACOB2 (CARTD,DERIV,DJACB,ELCOD,GPCOD,IELEM,
|
||||
KGASP,NNODE,SHAPE)
|
||||
DAREA=DJACB*WEIGP(IGAUS)*WEIGP(JGAUS)
|
||||
C
|
||||
C*** EVALUATE THE B AND DB MATRICES
|
||||
C
|
||||
CALL LAYMPA (DEPTH,DFLEX,DSHER,EPSTN,IINCS,KGAUS,LPROP,
|
||||
MMATS,MTOTG,NCRIT,NLAPS,PROPS,STRSG,0)
|
||||
C
|
||||
C*** EVALUATE ELEMENT STIFFNESSES
|
||||
C
|
||||
DO 31 INODE=1,NNODE
|
||||
CALL BMATPB (BFLEI,DUMMY,BSHEI,CARTD,INODE,SHAPE,
|
||||
0, 0, 1)
|
||||
DO 31 JNODE=INODE,NNODE
|
||||
CALL BMATPB (BFLEJ,DUMMY,BSHEJ,CARTD,JNODE,SHAPE,
|
||||
0, 0, 1)
|
||||
31 CALL SUBMP (BSHEI,BSHEJ,DAREA,DSHER,ESTIF,INODE,
|
||||
JNODE, 3, 2, 3)
|
||||
51 CONTINUE
|
||||
C
|
||||
C*** CONSTRUCT THE LOWER TRIANGLE OF THE STIFFNESS MATRIX
|
||||
C
|
||||
DO 60 IEVAB=1,NEVAB
|
||||
DO 60 JEVAB=IEVAB,NEVAB
|
||||
60 ESTIF(JEVAB,IEVAB)=ESTIF(IEVAB,JEVAB)
|
||||
C
|
||||
C*** STORE THE STIFFNESS MATRIX,STRESS MATRIX AND SAMPLING POINT
|
||||
C COORDINATES FOR EACH ELEMENT ON DISC FILE
|
||||
C
|
||||
WRITE(1) ESTIF
|
||||
WRITE(3) GPCOD
|
||||
70 CONTINUE
|
||||
RETURN
|
||||
END
|
||||
STFL 81
|
||||
STFL 82
|
||||
STFL 83
|
||||
STFL 84
|
||||
STFL 85
|
||||
STFL 86
|
||||
STFL 87
|
||||
STFL 88
|
||||
STFL 89
|
||||
STFL 90
|
||||
STFL 91
|
||||
STFL 92
|
||||
STFL 93
|
||||
STFL 94
|
||||
STFL 95
|
||||
STFL 96
|
||||
STFL 97
|
||||
STFL 98
|
||||
STFL 99
|
||||
STFL 100
|
||||
STFL 101
|
||||
STFL 102
|
||||
STFL 103
|
||||
STFL 104
|
||||
STFL 105
|
||||
STFL 106
|
||||
STFL 107
|
||||
STFL 108
|
||||
STFL 109
|
||||
STFL 110
|
||||
STFL 111
|
||||
STFL 112
|
||||
STFL 113
|
||||
STFL 114
|
||||
STFL 115
|
||||
STFL 116
|
||||
STFL 117
|
||||
STFL 118
|
||||
STFL 119
|
||||
STFL 120
|
||||
STFL 121
|
||||
STFL 122
|
||||
STFL 123
|
||||
STFL 124
|
||||
STFL 125
|
||||
STFL 126
|
||||
STFL 127
|
||||
STFL 128
|
||||
STFL 129
|
||||
STFL 130
|
||||
STFL 131
|
||||
STFL 132
|
||||
STFL 133
|
||||
STFL 134
|
||||
STFL 135
|
||||
STFL 136
|
||||
STFL 137
|
||||
STFL 138
|
||||
STFL 139
|
||||
```
|
||||
|
||||
# 9.6.10 Subroutine STRMPA
|
||||
|
||||
This subroutine evaluates the stresses within each layer.
|
||||
|
||||
<!-- source-page: 380 -->
|
||||
|
||||
```csv
|
||||
SUBROUTINE STRMPA (CARTD,CONST,DFLEX,DGRAD,DSHER,ELDIS,NNODE, STRL 1
|
||||
SHAPE,STRES,IFFLE,IFSHE) STRL 2
|
||||
C**********STRRL 3
|
||||
C STRL 4
|
||||
C*** EVALUATES STRESSES FOR MINDLIN PLATE STRL 5
|
||||
C STRL 6
|
||||
C**********STRRL 7
|
||||
DIMENSION CARTD(2,9),DFLEX(3,3),DGRAD(6),DSHER(2,2), STRL 8
|
||||
ELDIS(3,9),SHAPE(9),STRES(5) STRL 9
|
||||
C*** ZERO STRESS VECTOR STRL 10
|
||||
CALL VZERO (5,STRES) STRL 11
|
||||
C*** EVALUATE ROTATIONS AT GAUSS POINT, IF NEEDED STRL 12
|
||||
IF(IFSHE.EQ.0) GOTO 50 STRL 13
|
||||
XZROT=0.0 STRL 14
|
||||
YZROT=0.0 STRL 15
|
||||
DO 30 INODE=1,NNODE STRL 16
|
||||
XZROT=XZROT+SHAPE(INODE)*ELDIS(2,INODE) STRL 17
|
||||
30 YZROT=YZROT+SHAPE(INODE)*ELDIS(3,INODE) STRL 18
|
||||
C*** EVALUATE BENDING STRESS RESULTANTS STRL 19
|
||||
50 IF(IFFLE.EQ.0) GOTO 60 STRL 20
|
||||
EFLXX=-DGRAD(2)*CONST STRL 21
|
||||
EFLYY=-DGRAD(6)*CONST STRL 22
|
||||
EFLXY=-(DGRAD(3)+DGRAD(5))*CONST STRL 23
|
||||
STRES(1)=DFLEX(1,1)*EFLXX+DFLEX(1,2)*EFLYY STRL 24
|
||||
STRES(2)=DFLEX(2,1)*EFLXX+DFLEX(2,2)*EFLYY STRL 25
|
||||
STRES(3)=DFLEX(3,3)*EFLXY STRL 26
|
||||
C*** EVALUATE SHEAR STRESS RESULTANTS STRL 27
|
||||
60 IF(IFSHE.EQ.0) RETURN STRL 28
|
||||
ESHXX=DGRAD(1)-XZROT STRL 29
|
||||
ESHYY=DGRAD(4)-YZROT STRL 30
|
||||
STRES(4)=DSHER(1,1)*ESHXX STRL 31
|
||||
STRES(5)=DSHER(2,2)*ESHYY STRL 32
|
||||
RETURN STRL 33
|
||||
END STRL 34
|
||||
```
|
||||
|
||||
# 9.7 Examples
|
||||
|
||||
To test the program, the elasto-plastic analysis of a simply supported plate is performed and 9 noded and Heterosis elements are used. The geometry, material properties of the plate are shown in Fig. 9.6.
|
||||
|
||||
|
||||
|
||||
<details>
|
||||
<summary>text_image</summary>
|
||||
|
||||
y
|
||||
L
|
||||
x
|
||||
L
|
||||
= 1.0, E = 10.92, ν = 0.3, t = 0.01, q = 1.0, σ₀ = 1600.0
|
||||
</details>
|
||||
|
||||
Fig. 9.6 Geometry and material properties of simply supported square plate.
|
||||
Reference in New Issue
Block a user