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femutil.for
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cc MODULE FEMUTIL
cc CONTAINS
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C11111111122222222223333333333444444444455555555556666666666777777777777
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C --G E N E R A L F E M S U B R O U T I N E S-- C
C C
C23456789012345678901234567890123456789012345678901234567890123456789012
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C STRAIN DISPLACEMENT INTERPOLATORS C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE STDM4:GENERATES THE STRAIN-DISPLACEMENT MATRIX B C
C AND JACOBIAN DETERMINANT DDET AT THE POINT r ,s C
C i j C
C FOR AN 4-NODED 2D ELEMENT-PLANE STRAIN C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE STDM4(NNE,NDOFEL,NTENS,XX,MCRD,B,DDET,R,S,XBAR)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
PARAMETER (ONE=1.D0,TWO=2.D0,THREE=3.D0,HALF=0.5D0)
C
DIMENSION XX(MCRD,NNE),B(NTENS,NDOFEL),P(2,NNE),AUX1(2,NNE),
1 XJ(2,2),XJI(2,2)
C
C Initialize arrays
C
XBAR=ONE
CALL CLEAR(B,NTENS,NDOFEL)
CALL CLEAR(XJ,2,2)
CALL CLEAR(XJI,2,2)
CALL CLEAR(P,2,NNE)
C
C Shape functions derivatives w.r.t natural coordinates
C
CALL SFDER4(NNE,R,S,P)
C
C Computes the Jacobian operator and its determinant at point (r,s)
C
CALL JACOPER(NNE,XJ,XX,P)
DDET=XJ(1,1)*XJ(2,2)-XJ(1,2)*XJ(2,1)
C
C Computes the inverse of the Jacobiam operator
C
CALL JACINVE(XJ,DDET,XJI)
C
C Jacobian Inverse times Shape Functions derivatives w.r.t natural coordinates
C to produce shape function derivatives w.r.t x,y coordinates.
C
CALL MMULT(XJI,2,2,P,2,NNE,AUX1)
C
C Assembles B matrix for a
C Cosserat element.
C
DO I=1,NNE
II=2*(I-1)+1
B(1,II)=AUX1(1,I)
B(2,II+1)=AUX1(2,I)
B(4,II)=AUX1(2,I)
B(4,II+1)=AUX1(1,I)
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE STDM4SH:GENERATES THE STRAIN-DISPLACEMENT MATRIX B C
C AND JACOBIAN DETERMINANT DDET AT THE POINT r ,s C
C i j C
C FOR AN 4-NODED 2D ELEMENT- SH WAVE C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE STDM4SH(NNE,NDOFEL,NTENS,XX,MCRD,B,DDET,R,S,XBAR)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
PARAMETER (ONE=1.D0,TWO=2.D0,THREE=3.D0,HALF=0.5D0)
C
DIMENSION XX(MCRD,NNE),B(NTENS,NDOFEL),P(2,NNE),AUX1(2,NNE),
1 XJ(2,2),XJI(2,2)
C
C Initialize arrays
C
XBAR=ONE
CALL CLEAR(B,NTENS,NDOFEL)
CALL CLEAR(XJ,2,2)
CALL CLEAR(XJI,2,2)
CALL CLEAR(P,2,NNE)
C
C Shape functions derivatives w.r.t natural coordinates
C
CALL SFDER4(NNE,R,S,P)
C
C Computes the Jacobian operator and its determinant at point (r,s)
C
CALL JACOPER(NNE,XJ,XX,P)
DDET=XJ(1,1)*XJ(2,2)-XJ(1,2)*XJ(2,1)
C
C Computes the inverse of the Jacobiam operator
C
CALL JACINVE(XJ,DDET,XJI)
C
C Jacobian Inverse times Shape Functions derivatives w.r.t natural coordinates
C to produce shape function derivatives w.r.t x,y coordinates.
C
CALL MMULT(XJI,2,2,P,2,NNE,AUX1)
C
C Assembles B matrix for a
C Cosserat element.
C
DO I=1,NNE
B(1,I)=AUX1(1,I)
B(2,I)=AUX1(2,I)
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE STDM6:GENERATES THE STRAIN-DISPLACEMENT MATRIX B C
C AND JACOBIAN DETERMINANT DDET AT THE POINT r ,s C
C i j C
C FOR AN 6-NODED 2D ELEMENT-PLANE STRAIN C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE STDM6(NNE,NDOFEL,NTENS,XX,MCRD,B,DDET,R,S,XBAR)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
PARAMETER (ONE=1.D0,TWO=2.D0,THREE=3.D0,HALF=0.5D0)
C
DIMENSION XX(MCRD,NNE),B(NTENS,NDOFEL),P(2,NNE),AUX1(2,NNE),
1 XJ(2,2),XJI(2,2)
C
C Initialize arrays
C
XBAR=ONE
CALL CLEAR(B,NTENS,NDOFEL)
CALL CLEAR(XJ,2,2)
CALL CLEAR(XJI,2,2)
CALL CLEAR(P,2,NNE)
C
C Shape functions derivatives w.r.t natural coordinates
C
CALL SFDER6(NNE,R,S,P)
C
C Computes the Jacobian operator and its determinant at point (r,s)
C
CALL JACOPER(NNE,XJ,XX,P)
DDET=XJ(1,1)*XJ(2,2)-XJ(1,2)*XJ(2,1)
C
C Computes the inverse of the Jacobiam operator
C
CALL JACINVE(XJ,DDET,XJI)
C
C Jacobian Inverse times Shape Functions derivatives w.r.t natural coordinates
C to produce shape function derivatives w.r.t x,y coordinates.
C
CALL MMULT(XJI,2,2,P,2,NNE,AUX1)
C
C Assembles B matrix for a
C Cosserat element.
C
DO I=1,NNE
II=2*(I-1)+1
B(1,II)=AUX1(1,I)
B(2,II+1)=AUX1(2,I)
B(4,II)=AUX1(2,I)
B(4,II+1)=AUX1(1,I)
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE STDM8:GENERATES THE STRAIN-DISPLACEMENT MATRIX B C
C AND JACOBIAN DETERMINANT DDET AT THE POINT r ,s C
C i j C
C FOR AN 8-NODED 2D ELEMENT-PLANE STRAIN C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE STDM8(NNE,NDOFEL,NTENS,XX,MCRD,B,DDET,R,S,XBAR)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
PARAMETER (ONE=1.D0,TWO=2.D0,THREE=3.D0,HALF=0.5D0)
C
DIMENSION XX(MCRD,NNE),B(NTENS,NDOFEL),P(2,NNE),AUX1(2,NNE),
1 XJ(2,2),XJI(2,2)
C
C Initialize arrays
C
XBAR=ONE
CALL CLEAR(B,NTENS,NDOFEL)
CALL CLEAR(XJ,2,2)
CALL CLEAR(XJI,2,2)
CALL CLEAR(P,2,NNE)
C
C Shape functions derivatives w.r.t natural coordinates
C
CALL SFDER8(NNE,R,S,P)
C
C Computes the Jacobian operator and its determinant at point (r,s)
C
CALL JACOPER(NNE,XJ,XX,P)
DDET=XJ(1,1)*XJ(2,2)-XJ(1,2)*XJ(2,1)
C
C Computes the inverse of the Jacobiam operator
C
CALL JACINVE(XJ,DDET,XJI)
C
C Jacobian Inverse times Shape Functions derivatives w.r.t natural coordinates
C to produce shape function derivatives w.r.t x,y coordinates.
C
CALL MMULT(XJI,2,2,P,2,NNE,AUX1)
C
C Assembles B matrix for a
C Cosserat element.
C
DO I=1,NNE
II=2*(I-1)+1
B(1,II)=AUX1(1,I)
B(2,II+1)=AUX1(2,I)
B(4,II)=AUX1(2,I)
B(4,II+1)=AUX1(1,I)
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE STDM9:GENERATES THE STRAIN-DISPLACEMENT MATRIX B C
C AND JACOBIAN DETERMINANT DDET AT THE POINT r ,s C
C i j C
C FOR AN 9-NODED 2D ELEMENT-PLANE STRAIN C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE STDM9(NNE,NDOFEL,NTENS,XX,MCRD,B,DDET,R,S,XBAR)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
PARAMETER (ONE=1.D0,TWO=2.D0,THREE=3.D0,HALF=0.5D0)
C
DIMENSION XX(MCRD,NNE),B(NTENS,NDOFEL),P(2,NNE),AUX1(2,NNE),
1 XJ(2,2),XJI(2,2)
C
C Initialize arrays
C
XBAR=ONE
CALL CLEAR(B,NTENS,NDOFEL)
CALL CLEAR(XJ,2,2)
CALL CLEAR(XJI,2,2)
CALL CLEAR(P,2,NNE)
C
C Shape functions derivatives w.r.t natural coordinates
C
CALL SFDER9(NNE,R,S,P)
C
C Computes the Jacobian operator and its determinant at point (r,s)
C
CALL JACOPER(NNE,XJ,XX,P)
DDET=XJ(1,1)*XJ(2,2)-XJ(1,2)*XJ(2,1)
C
C Computes the inverse of the Jacobiam operator
C
CALL JACINVE(XJ,DDET,XJI)
C
C Jacobian Inverse times Shape Functions derivatives w.r.t natural coordinates
C to produce shape function derivatives w.r.t x,y coordinates.
C
CALL MMULT(XJI,2,2,P,2,NNE,AUX1)
C
C Assembles B matrix for a
C Cosserat element.
C
DO I=1,NNE
II=2*(I-1)+1
B(1,II)=AUX1(1,I)
B(2,II+1)=AUX1(2,I)
B(4,II)=AUX1(2,I)
B(4,II+1)=AUX1(1,I)
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE STDM9SH:GENERATES THE STRAIN-DISPLACEMENT MATRIX B C
C AND JACOBIAN DETERMINANT DDET AT THE POINT r ,s C
C i j C
C FOR AN 9-NODED 2D ELEMENT- SH WAVE C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE STDM9SH(NNE,NDOFEL,NTENS,XX,MCRD,B,DDET,R,S,XBAR)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
PARAMETER (ONE=1.D0,TWO=2.D0,THREE=3.D0,HALF=0.5D0)
C
DIMENSION XX(MCRD,NNE),B(NTENS,NDOFEL),P(2,NNE),AUX1(2,NNE),
1 XJ(2,2),XJI(2,2)
C
C Initialize arrays
C
XBAR=ONE
CALL CLEAR(B,NTENS,NDOFEL)
CALL CLEAR(XJ,2,2)
CALL CLEAR(XJI,2,2)
CALL CLEAR(P,2,NNE)
C
C Shape functions derivatives w.r.t natural coordinates
C
CALL SFDER9(NNE,R,S,P)
C
C Computes the Jacobian operator and its determinant at point (r,s)
C
CALL JACOPER(NNE,XJ,XX,P)
DDET=XJ(1,1)*XJ(2,2)-XJ(1,2)*XJ(2,1)
C
C Computes the inverse of the Jacobiam operator
C
CALL JACINVE(XJ,DDET,XJI)
C
C Jacobian Inverse times Shape Functions derivatives w.r.t natural coordinates
C to produce shape function derivatives w.r.t x,y coordinates.
C
CALL MMULT(XJI,2,2,P,2,NNE,AUX1)
C
C Assembles B matrix for a
C Cosserat element.
C
DO I=1,NNE
B(1,I)=AUX1(1,I)
B(2,I)=AUX1(2,I)
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SHAPE FUNCTIONS AND THEIR DERIVATIVES C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE SFDER4:GENERATES THE SHAPE FUNCTION DERIVATIVES C
C ACCORDING TO ELEMENT TYPE AT THE POINT r ,s C
C i j C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SFDER4(NNE,R,S,P)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER(ONE=1.D0,TWO=2.D0, HALF=0.5D0,QUARTER=0.25D0,FOUR=4.D0)
C
DIMENSION P(2,NNE)
C
RP= ONE+R
SP= ONE+S
RM= ONE-R
SM= ONE-S
C
C 4-NODED ELEMENT
C
C Derivatives w.r.t the natural coordinates
C w.r.t.r
C
P(1,2)= QUARTER*SM
P(1,1)=-QUARTER*SM
P(1,4)=-QUARTER*SP
P(1,3)= QUARTER*SP
C
C w.r.t.s
C
P(2,2)=-QUARTER*RP
P(2,1)=-QUARTER*RM
P(2,4)= QUARTER*RM
P(2,3)= QUARTER*RP
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE SFDER6:GENERATES THE SHAPE FUNCTION DERIVATIVES C
C ACCORDING TO ELEMENT TYPE AT THE POINT r ,s C
C i j C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SFDER6(NNE,R,S,P)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER(ONE=1.D0,TWO=2.D0,THREE=3.0D0, HALF=0.5D0,
1 QUARTER=0.25D0,FOUR=4.D0,EIGHT=8.0D0, ZERO=0.0D0)
C
DIMENSION P(2,NNE)
C
C 6-NODED ELEMENT
C
C Derivatives w.r.t the natural coordinates
C w.r.t.r
C
P(1,6)=-FOUR*S
P(1,5)= FOUR*S
P(1,4)= FOUR-EIGHT*R-FOUR*S
P(1,3)= ZERO
P(1,2)= FOUR*R-ONE
P(1,1)=-THREE+FOUR*R+FOUR*S
C
C w.r.t.s
C
P(2,6)= FOUR-FOUR*R-EIGHT*S
P(2,5)= FOUR*R
P(2,4)=-FOUR*R
P(2,3)= FOUR*S-ONE
P(2,2)= ZERO
P(2,1)=-THREE+FOUR*R+FOUR*S
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE SFDER8:GENERATES THE SHAPE FUNCTION DERIVATIVES C
C ACCORDING TO ELEMENT TYPE AT THE POINT r ,s C
C i j C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SFDER8(NNE,R,S,P)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER(ONE=1.D0,TWO=2.D0, HALF=0.5D0,QUARTER=0.25D0,FOUR=4.D0)
C
DIMENSION P(2,NNE)
C
RP= ONE+R
SP= ONE+S
RM= ONE-R
SM= ONE-S
RMS=ONE-R**TWO
SMS=ONE-S**TWO
C
C 8-NODED ELEMENT
C
C Derivatives w.r.t the natural coordinates
C w.r.t.r
C
P(1,6)= HALF*SMS
P(1,5)=-R*SM
P(1,8)=-HALF*SMS
P(1,7)=-R*SP
P(1,2)= QUARTER*SM-HALF*P(1,5)-HALF*P(1,6)
P(1,1)=-QUARTER*SM-HALF*P(1,8)-HALF*P(1,5)
P(1,4)=-QUARTER*SP-HALF*P(1,7)-HALF*P(1,8)
P(1,3)= QUARTER*SP-HALF*P(1,7)-HALF*P(1,6)
C
C w.r.t.s
C
P(2,6)=-S*RP
P(2,5)=-HALF*RMS
P(2,8)=-S*RM
P(2,7)= HALF*RMS
P(2,2)=-QUARTER*RP-HALF*P(2,5)-HALF*P(2,6)
P(2,1)=-QUARTER*RM-HALF*P(2,8)-HALF*P(2,5)
P(2,4)= QUARTER*RM-HALF*P(2,7)-HALF*P(2,8)
P(2,3)= QUARTER*RP-HALF*P(2,7)-HALF*P(2,6)
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE SFDER9:GENERATES THE SHAPE FUNCTION DERIVATIVES C
C ACCORDING TO ELEMENT TYPE AT THE POINT r ,s C
C i j C
C B =STRAIN-DISPLACEMENT MATRIX C
C DDET =JACOBIAN DETERMINANT C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SFDER9(NNE,R,S,P)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER(ONE=1.D0,TWO=2.D0, HALF=0.5D0,QUARTER=0.25D0,FOUR=4.D0)
C
DIMENSION P(2,NNE)
C
RP= ONE+R
SP= ONE+S
RM= ONE-R
SM= ONE-S
RMS=ONE-R**TWO
SMS=ONE-S**TWO
C
C 9-NODED ELEMENT
C Derivatives w.r.t the natural coordinates
C w.r.t.r
C
P(1,9)=-TWO*R*SMS
P(1,8)=-HALF*SMS-HALF*P(1,9)
P(1,7)=-R*SP-HALF*P(1,9)
P(1,6)= HALF*SMS-HALF*P(1,9)
P(1,5)=-R*SM-HALF*P(1,9)
P(1,4)=-QUARTER*SP-HALF*P(1,7)-HALF*P(1,8)-QUARTER*P(1,9)
P(1,3)= QUARTER*SP-HALF*P(1,7)-HALF*P(1,6)-QUARTER*P(1,9)
P(1,2)= QUARTER*SM-HALF*P(1,5)-HALF*P(1,6)-QUARTER*P(1,9)
P(1,1)=-QUARTER*SM-HALF*P(1,8)-HALF*P(1,5)-QUARTER*P(1,9)
C
C w.r.t.s
C
P(2,9)=-TWO*S*RMS
P(2,8)=-S*RM-HALF*P(2,9)
P(2,7)= HALF*RMS-HALF*P(2,9)
P(2,6)=-S*RP-HALF*P(2,9)
P(2,5)=-HALF*RMS-HALF*P(2,9)
P(2,4)= QUARTER*RM-HALF*P(2,7)-HALF*P(2,8)-QUARTER*P(2,9)
P(2,3)= QUARTER*RP-HALF*P(2,7)-HALF*P(2,6)-QUARTER*P(2,9)
P(2,2)=-QUARTER*RP-HALF*P(2,5)-HALF*P(2,6)-QUARTER*P(2,9)
P(2,1)=-QUARTER*RM-HALF*P(2,8)-HALF*P(2,5)-QUARTER*P(2,9)
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C SUBROUTINE SHAPEF6(SN,R,S) C
C 6-noded triangular element shape function at point R,S C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SHAPEF6(SN,R,S)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (ONE=1.0D0,HALF=0.5D0,FOUR=4.0D0, TWO=2.0D0)
C
DIMENSION SN(6)
C
CALL CLEARV(SN,6)
C
OMRMS=ONE-R-S
C
SN(6)=FOUR*S*OMRMS
SN(5)=FOUR*R*S
SN(4)=FOUR*R*OMRMS
SN(3)=TWO*S*(S-HALF)
SN(2)=TWO*R*(R-HALF)
SN(1)=TWO*(HALF-R-S)*OMRMS
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C SUBROUTINE SHAPEF8(SN,R,S) C
C 8-noded element shape function at point R,S C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SHAPEF8(SN,R,S)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (ONE=1.0D0,HALF=0.5D0,QUART=0.25D0)
C
DIMENSION SN(8)
C
CALL CLEARV(SN,8)
C
RP =ONE+R
RM =ONE-R
RMS=ONE-R*R
SP =ONE+S
SM =ONE-S
SMS=ONE-S*S
C
SN(8)=HALF*SMS*RM
SN(7)=HALF*RMS*SP
SN(6)=HALF*SMS*RP
SN(5)=HALF*RMS*SM
SN(1)=QUART*RM*SM-HALF*SN(8)-HALF*SN(5)
SN(2)=QUART*RP*SM-HALF*SN(6)-HALF*SN(5)
SN(3)=QUART*RP*SP-HALF*SN(6)-HALF*SN(7)
SN(4)=QUART*RM*SP-HALF*SN(8)-HALF*SN(7)
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C SUBROUTINE SHAPEF9(SN,R,S) C
C 9-noded element shape function at point R,S C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SHAPEF9(SN,R,S)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (ONE=1.0D0,HALF=0.5D0,QUART=0.25D0)
C
DIMENSION SN(9)
C
CALL CLEARV(SN,9)
C
RP =ONE+R
RM =ONE-R
RMS=ONE-R*R
SP =ONE+S
SM =ONE-S
SMS=ONE-S*S
C
SN(9)=RMS*SMS
SN(8)=HALF*SMS*RM-HALF*SN(9)
SN(7)=HALF*RMS*SP-HALF*SN(9)
SN(6)=HALF*SMS*RP-HALF*SN(9)
SN(5)=HALF*RMS*SM-HALF*SN(9)
SN(1)=QUART*RM*SM-HALF*SN(8)-HALF*SN(5)-QUART*SN(9)
SN(2)=QUART*RP*SM-HALF*SN(6)-HALF*SN(5)-QUART*SN(9)
SN(3)=QUART*RP*SP-HALF*SN(6)-HALF*SN(7)-QUART*SN(9)
SN(4)=QUART*RM*SP-HALF*SN(8)-HALF*SN(7)-QUART*SN(9)
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C MASS- MATRICES C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C SUBROUTINE CMASS6(MASS,NDOFEL,RII,SII) C
C Computes the mass matrix for an 6-noded triangular element C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE AMASS6(AMASS,NDOFEL,RII,SII)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (NTENS=2)
C
DIMENSION SF(NTENS,NDOFEL),SFT(NDOFEL,NTENS),SN(6),
1 AUX1(NDOFEL,NDOFEL),AMASS(NDOFEL,NDOFEL)
C
CALL CLEAR(SF,NTENS,NDOFEL)
CALL CLEAR(SFT,NDOFEL,NTENS)
CALL CLEARV(SN,6)
CALL CLEAR(AUX1,NDOFEL,NDOFEL)
CALL CLEAR(AMASS,NDOFEL,NDOFEL)
C
CALL SHAPEF6(SN,RII,SII)
C
DO I=1,6
KK=2*I-1
SF(1, KK)=SN(I)
SF(2,KK+1)=SN(I)
END DO
C
CALL MTRAN(SF,NTENS,NDOFEL,SFT)
CALL MMULT(SFT,NDOFEL,NTENS,SF,NTENS,NDOFEL,AUX1)
C
DO I=1,NDOFEL
DO J=1,NDOFEL
AMASS(I,J)=DCMPLX(AUX1(I,J))
END DO
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C SUBROUTINE CMASS8(MASS,NDOFEL,RII,SII) C
C Computes the mass matrix for an 8-noded element C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE AMASS8(AMASS,NDOFEL,RII,SII)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (NTENS=2)
C
DIMENSION SF(NTENS,NDOFEL),SFT(NDOFEL,NTENS),SN(8),
1 AUX1(NDOFEL,NDOFEL),AMASS(NDOFEL,NDOFEL)
C
CALL CLEAR(SF,NTENS,NDOFEL)
CALL CLEAR(SFT,NDOFEL,NTENS)
CALL CLEARV(SN,8)
CALL CLEAR(AUX1,NDOFEL,NDOFEL)
CALL CLEAR(AMASS,NDOFEL,NDOFEL)
C
CALL SHAPEF8(SN,RII,SII)
C
DO I=1,8
KK=2*I-1
SF(1, KK)=SN(I)
SF(2,KK+1)=SN(I)
END DO
C
CALL MTRAN(SF,NTENS,NDOFEL,SFT)
CALL MMULT(SFT,NDOFEL,NTENS,SF,NTENS,NDOFEL,AUX1)
C
DO I=1,NDOFEL
DO J=1,NDOFEL
AMASS(I,J)=AUX1(I,J)
END DO
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C SUBROUTINE AMASS9(MASS,NDOFEL,RII,SII) C
C Computes the mass matrix for an 8-noded element C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE AMASS9(AMASS,NDOFEL,RII,SII)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (NTENS=2)
C
DIMENSION SF(NTENS,NDOFEL),SFT(NDOFEL,NTENS),SN(9),
1 AUX1(NDOFEL,NDOFEL),AMASS(NDOFEL,NDOFEL)
C
CALL CLEAR(SF,NTENS,NDOFEL)
CALL CLEAR(SFT,NDOFEL,NTENS)
CALL CLEARV(SN,9)
CALL CLEAR(AUX1,NDOFEL,NDOFEL)
CALL CLEAR(AMASS,NDOFEL,NDOFEL)
C
CALL SHAPEF9(SN,RII,SII)
C
DO I=1,9
KK=2*I-1
SF(1, KK)=SN(I)
SF(2,KK+1)=SN(I)
END DO
C
CALL MTRAN(SF,NTENS,NDOFEL,SFT)
CALL MMULT(SFT,NDOFEL,NTENS,SF,NTENS,NDOFEL,AUX1)
C
DO I=1,NDOFEL
DO J=1,NDOFEL
AMASS(I,J)=AUX1(I,J)
END DO
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE KJACOPER C
C C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE JACOPER(NNE,XJA,XCORD,RDER)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
PARAMETER(ZERO=0.0D0)
C
DIMENSION XJA(2,2),XCORD(2,NNE),RDER(2,NNE)
C
CALL CLEAR(XJA,2,2)
C
DUM=ZERO
DO K=1,2
DO J=1,2
DO I=1,NNE
DUM=DUM+RDER(K,I)*XCORD(J,I)
END DO
XJA(K,J)=DUM
DUM=ZERO
END DO
END DO
C
RETURN
C
END
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C C
C 2X2 Jacobian inverse C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE JACINVE(XJA,DD,XJAI)
C
IMPLICIT REAL*8 (A-H,O-Z)
C
DIMENSION XJA(2,2),XJAI(2,2),XADJ(2,2)
C
XADJ(1,1)=XJA(2,2)
XADJ(1,2)=XJA(1,2)
XADJ(2,1)=XJA(2,1)
XADJ(2,2)=XJA(1,1)
DO J=1,2
DO K=1,2
COFA=((-1)**(J+K))*XADJ(J,K)
XJAI(J,K)=COFA/DD
END DO
END DO
C
RETURN
C
END
C
C23456789012345678901234567890123456789012345678901234567890123456789012
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE SHAPE1D C
C C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SHAPE1D(SM,ETA)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (ONE=1.0D0,HALF=0.5D0)
C
DIMENSION SM(6,2)
C
CALL CLEAR(SM,6,2)
C
EP=ONE+ETA
EM=ONE-ETA
EMS=ONE-ETA**2
C
S11=HALF*EM-HALF*EMS
S51=HALF*EP-HALF*EMS
S31=EMS
C
SM(1,1)=S11
SM(2,2)=SM(1,1)
SM(3,1)=S31
SM(4,2)=SM(3,1)
SM(5,1)=S51
SM(6,2)=SM(5,1)
C
RETURN
C
END
C
C23456789012345678901234567890123456789012345678901234567890123456789012
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE SHAPE1D C
C C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SHAPE1DM(SM,ETA)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (ONE=1.0D0,HALF=0.5D0)
C
DIMENSION SM(6,2)
C
CALL CLEAR(SM,6,2)
C
EP=ONE+ETA
EM=ONE-ETA
EMS=ONE-ETA**2
C
S1=HALF*EM-HALF*EMS
S2=HALF*EP-HALF*EMS
S3=EMS
C
SM(1,1)=S1
SM(2,2)=SM(1,1)
SM(3,1)=S2
SM(4,2)=SM(3,1)
SM(5,1)=S3
SM(6,2)=SM(5,1)
C
RETURN
C
END
C
C23456789012345678901234567890123456789012345678901234567890123456789012
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C C
C SUBROUTINE SHAPE1D C
C C
C C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C23456789012345678901234567890123456789012345678901234567890123456789012
C
SUBROUTINE SHAPEF31D(SM,ETA)
C
IMPLICIT REAL*8(A-H,O-Z)
C
PARAMETER (ONE=1.0D0,HALF=0.5D0)
C
DIMENSION SM(3)
C
CALL CLEARV(SM,3)
C
EP=ONE+ETA
EM=ONE-ETA
EMS=ONE-ETA**2
C