SUBROUTINE UEL(RHS,AMATRX,SVARS,ENERGY,NDOFEL,NRHS,NSVARS,PROPS,         
     1 NPROPS,COORDS,MCRD,NNODE,U,DU,V,A,JTYPE,TIME,DTIME,KSTEP,KINC,
     2 JELEM,PARAMS,NDLOAD,JDLTYP,ADLMAG,PREDEF,NPREDF,LFLAGS,
     3 MLVARX,DDLMAG,MDLOAD,PNEWDT,JPROPS,NJPROP,PERIOD)
C
      INCLUDE 'aba_param.inc'
C
      DIMENSION RHS(MLVARX,*),AMATRX(NDOFEL,NDOFEL),SVARS(NSVARS),
     1 ENERGY(8),PROPS(*),COORDS(MCRD,NNODE),
     2 U(NDOFEL),DU(MLVARX,*),V(NDOFEL),A(NDOFEL),TIME(2),
     3 PARAMS(3),JDLTYP(MDLOAD,*),ADLMAG(MDLOAD,*),
     4 DDLMAG(MDLOAD,*),PREDEF(2,NPREDF,NNODE),LFLAGS(*),JPROPS(*)
C
      DIMENSION GPX(9),GPY(9),GWEI(9),PHI(8),PHIX(8),PHIY(8),PHIC(8),
     1 PHIE(8),IFACE(9),GWE(3),AR(3)
C
      PARAMETER(ZERO=0.D0,TWOHUN=200.D0,FIVHUN=500.D0,CONDUC=204.D0)
      DATA IFACE/1,5,2,6,3,7,4,8,1/
C
C
C     MATERIAL PROPERTY DEFINITION
C
      THICK = PROPS(1)
      RHO   = PROPS(2)
      SPEC  = PROPS(3)
C
C     INITIALIZATION  (NRHS=1)
C                                                          
      DO 6 K1=1,NDOFEL                      
      RHS(K1,NRHS)=ZERO
      DO 4 K2=1,NDOFEL
      AMATRX(K2,K1)=ZERO
    4 CONTINUE                                      
    6 CONTINUE                                      
C
      IF (LFLAGS(3).EQ.4) RETURN
C
C     TRANSIENT ANALYSIS
C
      IF (LFLAGS(1).EQ.33) THEN
C
C     DETERMINE GAUSS POINT LOCATIONS
C
      SUBROUTINE GSPT(GPX,GPY)
      INCLUDE 'aba_param.inc'
      DIMENSION AR(3),GPX(9),GPY(9)
C
      PARAMETER(ZERO=0.D0,ONENEG=-1.D0,ONE=1.D0,SIX=6.D0,TEN=10.D0)
C
C     GPX: X COORDINATE OF GAUSS PT
C     GPY: Y COORDINATE OF GAUSS PT
C
      R=SQRT(SIX/TEN)
      AR(1)=-1.
      AR(2)=0.
      AR(3)=1.
      DO 10 I=1,3
      DO 10 J=1,3
      NUMGP=(I-1)*3+J
      GPX(NUMGP)=AR(I)*R
      GPY(NUMGP)=AR(J)*R
 10   CONTINUE
      RETURN
      END
      CALL GSPT(GPX,GPY)
C
C     DETERMINE GAUSS WEIGHTS
C
      CALL GSWT(GWEI,GWE)
C
C     ASSEMBLE AMATRX AND RHS
C
      DO 300 K=1,9
C     LOOP THROUGH GAUSS PTS
      	C=GPX(K)
      	E=GPY(K)
      	CALL DER(C,E,GPX,GPY,GWEI,PHI,PHIX,PHIY,PHIC,PHIE
     1           ,DXDC,DXDE,DYDC,DYDE,AJACOB,COORDS,MCRD,NNODE)  
      	DTDX=ZERO
      	DTDY=ZERO
        T =ZERO
        TOLD=ZERO
      	DO I=1,8
           DTDX=U(I)*PHIX(I)+DTDX
           DTDY=U(I)*PHIY(I)+DTDY
           T =U(I)*PHI(I)+T
           TOLD=(U(I)-DU(I,NRHS))*PHI(I)+TOLD
        END DO
C       CHECK ON TEMPERATURE DEPENDENCE OF THERMAL CONDUCTIVITY
        COND=CONDUC
        DCDT=ZERO
        DTDT=(T-TOLD)/DTIME
        WE=GWEI(K)*AJACOB
        DO KI=1,8
C       LOOP OVER NODES
        RHS(KI,NRHS) = RHS(KI,NRHS) - 
     1                 WE*(PHI(KI)*RHO*SPEC*DTDT + 
     2                 COND*(PHIX(KI)*DTDX + PHIY(KI)*DTDY))

        DO KJ=1,8
        AMATRX(KI,KJ)= AMATRX(KI,KJ) + WE*(PHI(KI)*PHI(KJ)*RHO*
     1                 SPEC/DTIME + COND*(PHIX(KI)*PHIX(KJ) + PHIY(KI)*
     2                 PHIY(KJ)) + DCDT*PHI(KJ)*(PHIX(KI)*DTDX + 
     3                 PHIY(KI)*DTDY))

        END DO
        END DO
  300 CONTINUE
C
      RETURN
      END
C

C
      SUBROUTINE GSWT(GWEI,GWE)
      INCLUDE 'aba_param.inc'
      DIMENSION GWEI(9),GWE(3)
C
      PARAMETER(FIVE=5.D0,EIGHT=8.D0,NINE=9.D0)
C
C     GWEI : GAUSS WEIGHT
C
      GWE(1)=FIVE/NINE
      GWE(2)=EIGHT/NINE
      GWE(3)=FIVE/NINE
      DO 10 I=1,3
      DO 10 J=1,3
      NUMGP=(I-1)*3+J
      GWEI(NUMGP)=GWE(I)*GWE(J)
 10   CONTINUE
      RETURN
      END
C
      SUBROUTINE DER(C,E,GPX,GPY,GWEI,PHI,PHIX,PHIY,PHIC,PHIE,
     1 DXDC,DXDE,DYDC,DYDE,AJACOB,COORDS,MCRD,NNODE)
      INCLUDE 'aba_param.inc'
      DIMENSION PHI(8),PHIX(8),PHIY(8),PHIC(8),PHIE(8),
     1 COORDS(MCRD,NNODE)
C
      PARAMETER(ZERO=0.D0,FOURTH=0.25D0,HALF=0.5D0,ONE=1.D0,TWO=2.D0)
C
C     INTERPOLATION FUNCTIONS
C
      PHI(1) = FOURTH*(ONE-C)*(ONE-E)*(-C-E-ONE)
      PHI(2) = FOURTH*(ONE+C)*(ONE-E)*(C-E-ONE)
      PHI(3) = FOURTH*(ONE+C)*(ONE+E)*(C+E-ONE)
      PHI(4) = FOURTH*(ONE-C)*(ONE+E)*(-C+E-ONE)
      PHI(5) = HALF*(ONE-C*C)*(ONE-E)
      PHI(6) = HALF*(ONE+C)*(ONE-E*E)
      PHI(7) = HALF*(ONE-C*C)*(ONE+E)
      PHI(8) = HALF*(ONE-C)*(ONE-E*E)
C
C     DERIVATIVES WRT TO C
C
      PHIC(1) = FOURTH*(ONE-E)*(TWO*C+E)
      PHIC(2) = FOURTH*(ONE-E)*(TWO*C-E)
      PHIC(3) = FOURTH*(ONE+E)*(TWO*C+E)
      PHIC(4) = FOURTH*(ONE+E)*(TWO*C-E)
      PHIC(5) = -C*(ONE-E)
      PHIC(6) = HALF*(ONE-E*E)
      PHIC(7) = -C*(ONE+E)
      PHIC(8) = -HALF*(ONE-E*E)
C
C     DERIVATIVES WRT TO E
C
      PHIE(1) = FOURTH*(ONE-C)*(TWO*E+C)
      PHIE(2) = FOURTH*(ONE+C)*(TWO*E-C)
      PHIE(3) = FOURTH*(ONE+C)*(TWO*E+C)
      PHIE(4) = FOURTH*(ONE-C)*(TWO*E-C)
      PHIE(5) = -HALF*(ONE-C*C)
      PHIE(6) = -E*(ONE+C)   
      PHIE(7) = HALF*(ONE-C*C)
      PHIE(8) = -E*(ONE-C)    

      DXDC=ZERO
      DXDE=ZERO
      DYDC=ZERO
      DYDE=ZERO

      DO 3 I=1,8
        DXDC=DXDC+COORDS(1,I)*PHIC(I)
        DXDE=DXDE+COORDS(1,I)*PHIE(I)
        DYDC=DYDC+COORDS(2,I)*PHIC(I)
        DYDE=DYDE+COORDS(2,I)*PHIE(I)
    3 CONTINUE
C
C     CALCULATION OF JACOBIAN
C
      AJACOB=(DXDC*DYDE-DXDE*DYDC)
C
C     DERIVATIVES WRT TO X AND Y
C
      DO 5 I=1,8
        PHIX(I)=(PHIC(I)*DYDE-PHIE(I)*DYDC)/AJACOB
        PHIY(I)=(PHIE(I)*DXDC-PHIC(I)*DXDE)/AJACOB
5     CONTINUE
      RETURN
      END