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Cloned SEACAS for EXODUS library with extra build files for internal package management.
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EXODUS/packages/seacas/libraries/mapvarlib/jacobn.f

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C Copyright(C) 1999-2020 National Technology & Engineering Solutions
C of Sandia, LLC (NTESS). Under the terms of Contract DE-NA0003525 with
C NTESS, the U.S. Government retains certain rights in this software.
C
C See packages/seacas/LICENSE for details
C=======================================================================
*DECK,JACOBN
SUBROUTINE JACOBN (ITYPE,XX,YY,ZZ,SP,TP,RP,A11,A12,A13,A21,A22,
1A23,A31,A32,A33,F1,F2,F3)
C ******************************************************************
C SUBROUTINE TO EVALUATE ELEMENT SHAPE FUNCTIONS AND DERIVATIVES
C (JACOBIAN) AT A SPECIFIED POINT (SP,TP,RP)
C Called by SRCH2D & SRCH3D
C ******************************************************************
DIMENSION XX(*), YY(*), ZZ(*)
C ******************************************************************
F1=0.
F2=0.
F3=0.
A11=0.
A12=0.
A13=0.
A21=0.
A22=0.
A23=0.
A31=0.
A32=0.
A33=0.
C SELECT ELEMENT
GO TO (100, 110, 120, 130, 140, 150, 160, 170, 180, 190,
& 200, 210), ITYPE
C 3-NODE TRIANGLE
100 CONTINUE
PP=1.-SP-TP
F1=XX(1)*SP+XX(2)*TP+XX(3)*PP
F2=YY(1)*SP+YY(2)*TP+YY(3)*PP
A11=XX(1)-XX(3)
A12=XX(2)-XX(3)
A21=YY(1)-YY(3)
A22=YY(2)-YY(3)
RETURN
C 6-NODE TRIANGLE
110 CONTINUE
PP=1.-SP-TP
F1=XX(1)*SP*(2.*SP-1.)+XX(2)*TP*(2.*TP-1.)+
1 XX(3)*PP*(2.*PP-1.)+XX(4)*4.*SP*TP+
2 XX(5)*4.*TP*PP+XX(6)*4.*SP*PP
F2=YY(1)*SP*(2.*SP-1.)+YY(2)*TP*(2.*TP-1.)+
1 YY(3)*PP*(2.*PP-1.)+YY(4)*4.*SP*TP+
2 YY(5)*4.*TP*PP+YY(6)*4.*SP*PP
A11=XX(1)*(4.*SP-1.)-XX(3)*(4.*PP-1.)+(XX(4)-XX(5))*4.*TP+
1 XX(6)*4.*(PP-SP)
A12=XX(2)*(4.*TP-1.)-XX(3)*(4.*PP-1.)+(XX(4)-XX(6))*4.*SP+
1 XX(5)*4.*(PP-TP)
A21=YY(1)*(4.*SP-1.)-YY(3)*(4.*PP-1.)+(YY(4)-YY(5))*4.*TP+
1 YY(6)*4.*(PP-SP)
A22=YY(2)*(4.*TP-1.)-YY(3)*(4.*PP-1.)+(YY(4)-YY(6))*4.*SP+
1 YY(5)*4.*(PP-TP)
RETURN
C 4-NODE QUADRILATERAL
120 CONTINUE
F1=.25*(XX(1)*(1.-SP)*(1.-TP)+XX(2)*(1.+SP)*(1.-TP)+
1 XX(3)*(1.+SP)*(1.+TP)+XX(4)*(1.-SP)*(1.+TP))
F2=.25*(YY(1)*(1.-SP)*(1.-TP)+YY(2)*(1.+SP)*(1.-TP)+
1 YY(3)*(1.+SP)*(1.+TP)+YY(4)*(1.-SP)*(1.+TP))
A11=.25*((XX(2)-XX(1))*(1.-TP)+(XX(3)-XX(4))*(1.+TP))
A12=.25*((XX(4)-XX(1))*(1.-SP)+(XX(3)-XX(2))*(1.+SP))
A21=.25*((YY(2)-YY(1))*(1.-TP)+(YY(3)-YY(4))*(1.+TP))
A22=.25*((YY(4)-YY(1))*(1.-SP)+(YY(3)-YY(2))*(1.+SP))
RETURN
C 8-NODE QUADRILATERAL
130 CONTINUE
F1=.25*(XX(1)*(1.-SP)*(1.-TP)*(-SP-TP-1.)+
1 XX(2)*(1.+SP)*(1.-TP)*(SP-TP-1.)+
2 XX(3)*(1.+SP)*(1.+TP)*(SP+TP-1.)+
3 XX(4)*(1.-SP)*(1.+TP)*(-SP+TP-1.))+
4 .50*(XX(5)*(1.-SP*SP)*(1.-TP)+XX(6)*(1.+SP)*(1.-TP*TP)+
5 XX(7)*(1.-SP*SP)*(1.+TP)+XX(8)*(1.-SP)*(1.-TP*TP))
F2=.25*(YY(1)*(1.-SP)*(1.-TP)*(-SP-TP-1.)+
1 YY(2)*(1.+SP)*(1.-TP)*(SP-TP-1.)+
2 YY(3)*(1.+SP)*(1.+TP)*(SP+TP-1.)+
3 YY(4)*(1.-SP)*(1.+TP)*(-SP+TP-1.))+
4 .50*(YY(5)*(1.-SP*SP)*(1.-TP)+YY(6)*(1.+SP)*(1.-TP*TP)+
5 YY(7)*(1.-SP*SP)*(1.+TP)+YY(8)*(1.-SP)*(1.-TP*TP))
A11=.25*(XX(1)*(1.-TP)*(TP+2.*SP)+XX(2)*(1.-TP)*(-TP+2.*SP)+
1 XX(3)*(1.+TP)*(TP+2.*SP)+XX(4)*(1.+TP)*(-TP+2.*SP))+
2 .50*(XX(5)*(1.-TP)*(-2.*SP)+(XX(6)-XX(8))*(1.-TP*TP)+
3 XX(7)*(1.+TP)*(-2.*SP))
A12=.25*(XX(1)*(1.-SP)*(SP+2.*TP)+XX(2)*(1.+SP)*(-SP+2.*TP)+
1 XX(3)*(1.+SP)*(SP+2.*TP)+XX(4)*(1.-SP)*(-SP+2.*TP))+
2 .50*(XX(6)*(1.+SP)*(-2.*TP)+(XX(7)-XX(5))*(1.-SP*SP)+
3 XX(8)*(1.-SP)*(-2.*TP))
A21=.25*(YY(1)*(1.-TP)*(TP+2.*SP)+YY(2)*(1.-TP)*(-TP+2.*SP)+
1 YY(3)*(1.+TP)*(TP+2.*SP)+YY(4)*(1.+TP)*(-TP+2.*SP))+
2 .50*(YY(5)*(1.-TP)*(-2.*SP)+(YY(6)-YY(8))*(1.-TP*TP)+
3 YY(7)*(1.+TP)*(-2.*SP))
A22=.25*(YY(1)*(1.-SP)*(SP+2.*TP)+YY(2)*(1.+SP)*(-SP+2.*TP)+
1 YY(3)*(1.+SP)*(SP+2.*TP)+YY(4)*(1.-SP)*(-SP+2.*TP))+
2 .50*(YY(6)*(1.+SP)*(-2.*TP)+(YY(7)-YY(5))*(1.-SP*SP)+
3 YY(8)*(1.-SP)*(-2.*TP))
RETURN
C 9-NODE QUADRILATERAL
140 CONTINUE
F1=.25*(XX(1)*(1.-SP)*(1.-TP)*(SP*TP)+
1 XX(2)*(1.+SP)*(1.-TP)*(-SP*TP)+
2 XX(3)*(1.+SP)*(1.+TP)*(SP*TP)+
3 XX(4)*(1.-SP)*(1.+TP)*(-SP*TP))+
4 .50*(XX(5)*(1.-SP*SP)*(1.-TP)*(-TP)+
5 XX(6)*(1.+SP)*(1.-TP*TP)*SP+
6 XX(7)*(1.-SP*SP)*(1.+TP)*TP+
7 XX(8)*(1.-SP)*(1.-TP*TP)*(-SP))+
8 XX(9)*(1.-SP*SP)*(1.-TP*TP)
F2=.25*(YY(1)*(1.-SP)*(1.-TP)*(SP*TP)+
1 YY(2)*(1.+SP)*(1.-TP)*(-SP*TP)+
2 YY(3)*(1.+SP)*(1.+TP)*(SP*TP)+
3 YY(4)*(1.-SP)*(1.+TP)*(-SP*TP))+
4 .50*(YY(5)*(1.-SP*SP)*(1.-TP)*(-TP)+
5 YY(6)*(1.+SP)*(1.-TP*TP)*SP+
6 YY(7)*(1.-SP*SP)*(1.+TP)*TP+
7 YY(8)*(1.-SP)*(1.-TP*TP)*(-SP))+
8 YY(9)*(1.-SP*SP)*(1.-TP*TP)
A11=.25*(XX(1)*(1.-TP)*(TP-2.*SP*TP)+
1 XX(2)*(1.-TP)*(-TP-2.*SP*TP)+
2 XX(3)*(1.+TP)*(TP+2.*SP*TP)+
3 XX(4)*(1.+TP)*(-TP+2.*SP*TP))+
4 .50*(XX(5)*(-TP+TP*TP)*(-2.*SP)+XX(6)*(1.-TP*TP)*(1.+2*SP)+
5 XX(7)*(TP+TP*TP)*(-2.*SP)+XX(8)*(1.-TP*TP)*(-1.+2.*SP))+
6 XX(9)*(1.-TP*TP)*(-2.*SP)
A12=.25*(XX(1)*(1.-SP)*(SP-2.*SP*TP)+
1 XX(2)*(1.+SP)*(-SP+2.*SP*TP)+
2 XX(3)*(1.+SP)*(SP+2.*SP*TP)+
3 XX(4)*(1.-SP)*(-SP-2.*SP*TP))+
4 .50*(XX(5)*(1.-SP*SP)*(-1.+2.*TP)+XX(6)*(SP+SP*SP)*(-2.*TP)+
5 XX(7)*(1.-SP*SP)*(1.+2.*TP)+XX(8)*(-SP+SP*SP)*(-2.*TP))+
6 XX(9)*(1.-SP*SP)*(-2.*TP)
A21=.25*(YY(1)*(1.-TP)*(TP-2.*SP*TP)+
1 YY(2)*(1.-TP)*(-TP-2.*SP*TP)+
2 YY(3)*(1.+TP)*(TP+2.*SP*TP)+
3 YY(4)*(1.+TP)*(-TP+2.*SP*TP))+
4 .50*(YY(5)*(-TP+TP*TP)*(-2.*SP)+YY(6)*(1.-TP*TP)*(1.+2*SP)+
5 YY(7)*(TP+TP*TP)*(-2.*SP)+YY(8)*(1.-TP*TP)*(-1.+2.*SP))+
6 YY(9)*(1.-TP*TP)*(-2.*SP)
A22=.25*(YY(1)*(1.-SP)*(SP-2.*SP*TP)+
1 YY(2)*(1.+SP)*(-SP+2.*SP*TP)+
2 YY(3)*(1.+SP)*(SP+2.*SP*TP)+
3 YY(4)*(1.-SP)*(-SP-2.*SP*TP))+
4 .50*(YY(5)*(1.-SP*SP)*(-1.+2.*TP)+YY(6)*(SP+SP*SP)*(-2.*TP)+
5 YY(7)*(1.-SP*SP)*(1.+2.*TP)+YY(8)*(-SP+SP*SP)*(-2.*TP))+
6 YY(9)*(1.-SP*SP)*(-2.*TP)
RETURN
C 4-NODE TETRAHEDRON
150 CONTINUE
PP=1.-SP-TP-RP
C F1=XX(1)*SP+XX(2)*TP+XX(3)*RP+XX(4)*PP
C F2=YY(1)*SP+YY(2)*TP+YY(3)*RP+YY(4)*PP
C F3=ZZ(1)*SP+ZZ(2)*TP+ZZ(3)*RP+ZZ(4)*PP
C A11=XX(1)-XX(4)
C A12=XX(2)-XX(4)
C A13=XX(3)-XX(4)
C A21=YY(1)-YY(4)
C A22=YY(2)-YY(4)
C A23=YY(3)-YY(4)
C A31=ZZ(1)-ZZ(4)
C A32=ZZ(2)-ZZ(4)
C A33=ZZ(3)-ZZ(4)
C fix gww 8/24/00 - need same fix for 10-node tet??
C merlin had opposite nodal order (left hand rule for + volume)
F1=XX(1)*SP+XX(2)*TP+XX(3)*PP+XX(4)*RP
F2=YY(1)*SP+YY(2)*TP+YY(3)*PP+YY(4)*RP
F3=ZZ(1)*SP+ZZ(2)*TP+ZZ(3)*PP+ZZ(4)*RP
A11=XX(1)-XX(3)
A12=XX(2)-XX(3)
A13=XX(4)-XX(3)
A21=YY(1)-YY(3)
A22=YY(2)-YY(3)
A23=YY(4)-YY(3)
A31=ZZ(1)-ZZ(3)
A32=ZZ(2)-ZZ(3)
A33=ZZ(4)-ZZ(3)
RETURN
C 10-NODE TETRAHEDRON
160 CONTINUE
PP=1.-SP-TP-RP
F1= XX(1)*SP*(2.*SP-1.)+XX(2)*TP*(2.*TP-1.)+
1 XX(3)*RP*(2.*RP-1.)+XX(4)*PP*(2.*PP-1.)+
2 4.*(XX(5)*SP*TP+XX(6)*TP*RP+XX(7)*RP*SP+
3 XX(8)*SP*PP+XX(9)*TP*PP+XX(10)*RP*PP)
F2= YY(1)*SP*(2.*SP-1.)+YY(2)*TP*(2.*TP-1.)+
1 YY(3)*RP*(2.*RP-1.)+YY(4)*PP*(2.*PP-1.)+
2 4.*(YY(5)*SP*TP+YY(6)*TP*RP+YY(7)*RP*SP+
3 YY(8)*SP*PP+YY(9)*TP*PP+YY(10)*RP*PP)
F3= ZZ(1)*SP*(2.*SP-1.)+ZZ(2)*TP*(2.*TP-1.)+
1 ZZ(3)*RP*(2.*RP-1.)+ZZ(4)*PP*(2.*PP-1.)+
2 4.*(ZZ(5)*SP*TP+ZZ(6)*TP*RP+ZZ(7)*RP*SP+
3 ZZ(8)*SP*PP+ZZ(9)*TP*PP+ZZ(10)*RP*PP)
A11=XX(1)*(4.*SP-1.)-XX(4)*(4.*PP-1.)+XX(5)*4.*TP+XX(7)*4.*RP+
1 XX(8)*4.*(PP-SP)-XX(9)*4.*TP-XX(10)*4.*(RP+TP)
A12=XX(2)*(4.*TP-1.)-XX(4)*(4.*PP-1.)+XX(5)*4.*SP+XX(6)*4.*RP-
1 XX(8)*4.*SP+XX(9)*4.*(PP-TP)-XX(10)*4.*(RP+SP)
A13=XX(3)*(4.*RP-1.)-XX(4)*(4.*PP-1.)+XX(6)*4.*TP+XX(7)*4.*SP-
1 XX(8)*4.*SP-XX(9)*4.*TP+XX(10)*(4.*PP-RP)
A21=YY(1)*(4.*SP-1.)-YY(4)*(4.*PP-1.)+YY(5)*4.*TP+YY(7)*4.*RP+
1 YY(8)*4.*(PP-SP)-YY(9)*4.*TP-YY(10)*4.*(RP+TP)
A22=YY(2)*(4.*TP-1.)-YY(4)*(4.*PP-1.)+YY(5)*4.*SP+YY(6)*4.*RP-
1 YY(8)*4.*SP+YY(9)*4.*(PP-TP)-YY(10)*4.*(RP+SP)
A23=YY(3)*(4.*RP-1.)-YY(4)*(4.*PP-1.)+YY(6)*4.*TP+YY(7)*4.*SP-
1 YY(8)*4.*SP-YY(9)*4.*TP+YY(10)*(4.*PP-RP)
A31=ZZ(1)*(4.*SP-1.)-ZZ(4)*(4.*PP-1.)+ZZ(5)*4.*TP+ZZ(7)*4.*RP+
1 ZZ(8)*4.*(PP-SP)-ZZ(9)*4.*TP-ZZ(10)*4.*(RP+TP)
A32=ZZ(2)*(4.*TP-1.)-ZZ(4)*(4.*PP-1.)+ZZ(5)*4.*SP+ZZ(6)*4.*RP-
1 ZZ(8)*4.*SP+ZZ(9)*4.*(PP-TP)-ZZ(10)*4.*(RP+SP)
A33=ZZ(3)*(4.*RP-1.)-ZZ(4)*(4.*PP-1.)+ZZ(6)*4.*TP+ZZ(7)*4.*SP-
1 ZZ(8)*4.*SP-ZZ(9)*4.*TP+ZZ(10)*(4.*PP-RP)
RETURN
C 6-NODE PRISM
170 CONTINUE
PP=1.-SP-TP
F1=(XX(1)*SP+XX(2)*TP+XX(3)*PP)*.5*(1.-RP)+
1 (XX(4)*SP+XX(5)*TP+XX(6)*PP)*.5*(1.+RP)
F2=(YY(1)*SP+YY(2)*TP+YY(3)*PP)*.5*(1.-RP)+
1 (YY(4)*SP+YY(5)*TP+YY(6)*PP)*.5*(1.+RP)
F3=(ZZ(1)*SP+ZZ(2)*TP+ZZ(3)*PP)*.5*(1.-RP)+
1 (ZZ(4)*SP+ZZ(5)*TP+ZZ(6)*PP)*.5*(1.+RP)
A11=(XX(1)-XX(3))*.5*(1.-RP)+
1 (XX(4)-XX(6))*.5*(1.+RP)
A12=(XX(2)-XX(3))*.5*(1.-RP)+
1 (XX(5)-XX(6))*.5*(1.+RP)
A13=(XX(4)-XX(1))*.5*SP+
1 (XX(5)-XX(2))*.5*TP+
2 (XX(6)-XX(3))*.5*PP
A21=(YY(1)-YY(3))*.5*(1.-RP)+
1 (YY(4)-YY(6))*.5*(1.+RP)
A22=(YY(2)-YY(3))*.5*(1.-RP)+
1 (YY(5)-YY(6))*.5*(1.+RP)
A23=(YY(4)-YY(1))*.5*SP+
1 (YY(5)-YY(2))*.5*TP+
2 (YY(6)-YY(3))*.5*PP
A31=(ZZ(1)-ZZ(3))*.5*(1.-RP)+
1 (ZZ(4)-ZZ(6))*.5*(1.+RP)
A32=(ZZ(2)-ZZ(3))*.5*(1.-RP)+
1 (ZZ(5)-ZZ(6))*.5*(1.+RP)
A33=(ZZ(4)-ZZ(1))*.5*SP+
1 (ZZ(5)-ZZ(2))*.5*TP+
2 (ZZ(6)-ZZ(3))*.5*PP
RETURN
C 15-NODE PRISM
180 CONTINUE
PP=1.-SP-TP
AA=1.-RP
BB=1.+RP
CC=1.-RP**2
F1=.50*(XX(1)*SP*((2.*SP-1.)*AA-CC)+XX(2)*TP*((2.*TP-1.)*AA-CC)+
1 XX(3)*PP*((2.*PP-1.)*AA-CC)+
2 XX(4)*SP*((2.*SP-1.)*BB-CC)+XX(5)*TP*((2.*TP-1.)*BB-CC)+
3 XX(6)*PP*((2.*PP-1.)*BB-CC))+
4 2.*AA*(XX(7)*SP*TP+XX(8)*TP*PP+XX(9)*PP*SP)+
5 (XX(10)*SP+XX(11)*TP+XX(12)*PP)*CC+
6 2.*BB*(XX(13)*SP*TP+XX(14)*TP*PP+XX(15)*PP*SP)
F2=.50*(YY(1)*SP*((2.*SP-1.)*AA-CC)+YY(2)*TP*((2.*TP-1.)*AA-CC)+
1 YY(3)*PP*((2.*PP-1.)*AA-CC)+
2 YY(4)*SP*((2.*SP-1.)*BB-CC)+YY(5)*TP*((2.*TP-1.)*BB-CC)+
3 YY(6)*PP*((2.*PP-1.)*BB-CC))+
4 2.*AA*(YY(7)*SP*TP+YY(8)*TP*PP+YY(9)*PP*SP)+
5 (YY(10)*SP+YY(11)*TP+YY(12)*PP)*CC+
6 2.*BB*(YY(13)*SP*TP+YY(14)*TP*PP+YY(15)*PP*SP)
F3=.50*(ZZ(1)*SP*((2.*SP-1.)*AA-CC)+ZZ(2)*TP*((2.*TP-1.)*AA-CC)+
1 ZZ(3)*PP*((2.*PP-1.)*AA-CC)+
2 ZZ(4)*SP*((2.*SP-1.)*BB-CC)+ZZ(5)*TP*((2.*TP-1.)*BB-CC)+
3 ZZ(6)*PP*((2.*PP-1.)*BB-CC))+
4 2.*AA*(ZZ(7)*SP*TP+ZZ(8)*TP*PP+ZZ(9)*PP*SP)+
5 (ZZ(10)*SP+ZZ(11)*TP+ZZ(12)*PP)*CC+
6 2.*BB*(ZZ(13)*SP*TP+ZZ(14)*TP*PP+ZZ(15)*PP*SP)
A11=.5*(XX(1)*((4.*SP-1.)*AA-CC)-XX(3)*((4.*PP-1.)*AA+CC)+
1 XX(4)*((4.*SP-1.)*BB-CC)-XX(6)*((4.*PP-1.)*BB+CC))+
2 2.*AA*(XX(7)*TP-XX(8)*TP+XX(9)*(PP-SP))+
3 (XX(10)-XX(12))*CC+
4 2.*BB*(XX(13)*TP-XX(14)*TP+XX(15)*(PP-SP))
A12=.5*(XX(2)*((4.*TP-1.)*AA-CC)-XX(3)*((4.*PP-1.)*AA+CC)+
1 XX(5)*((4.*TP-1.)*BB-CC)-XX(6)*((4.*PP-1.)*BB+CC))+
2 2.*AA*(XX(7)*TP+XX(8)*(PP-TP)-XX(9)*SP)+
3 (XX(11)-XX(12))*CC+
4 2.*BB*(XX(13)*SP+XX(14)*(PP-TP)-XX(15)*SP)
A13= (XX(4)-XX(1))*.5*SP*(2.*SP-1.+RP)+
1 (XX(5)-XX(2))*.5*TP*(2.*TP-1.+RP)+
2 (XX(6)-XX(3))*.5*PP*(2.*PP-1.+RP)-
3 2.*(XX(7)*SP*TP+XX(8)*TP*PP+XX(9)*PP*SP)-
4 2.*(XX(10)*SP+XX(11)*TP+XX(12)*PP)*RP+
5 2.*(XX(13)*SP*TP+XX(14)*TP*PP+XX(15)*PP*SP)
A21=.5*(YY(1)*((4.*SP-1.)*AA-CC)-YY(3)*((4.*PP-1.)*AA+CC)+
1 YY(4)*((4.*SP-1.)*BB-CC)-YY(6)*((4.*PP-1.)*BB+CC))+
2 2.*AA*(YY(7)*TP-YY(8)*TP+YY(9)*(PP-SP))+
3 (YY(10)-YY(12))*CC+
4 2.*BB*(YY(13)*TP-YY(14)*TP+YY(15)*(PP-SP))
A22=.5*(YY(2)*((4.*TP-1.)*AA-CC)-YY(3)*((4.*PP-1.)*AA+CC)+
1 YY(5)*((4.*TP-1.)*BB-CC)-YY(6)*((4.*PP-1.)*BB+CC))+
2 2.*AA*(YY(7)*TP+YY(8)*(PP-TP)-YY(9)*SP)+
3 (YY(11)-YY(12))*CC+
4 2.*BB*(YY(13)*SP+YY(14)*(PP-TP)-YY(15)*SP)
A23= (YY(4)-YY(1))*.5*SP*(2.*SP-1.+RP)+
1 (YY(5)-YY(2))*.5*TP*(2.*TP-1.+RP)+
2 (YY(6)-YY(3))*.5*PP*(2.*PP-1.+RP)-
3 2.*(YY(7)*SP*TP+YY(8)*TP*PP+YY(9)*PP*SP)-
4 2.*(YY(10)*SP+YY(11)*TP+YY(12)*PP)*RP+
5 2.*(YY(13)*SP*TP+YY(14)*TP*PP+YY(15)*PP*SP)
A31=.5*(ZZ(1)*((4.*SP-1.)*AA-CC)-ZZ(3)*((4.*PP-1.)*AA+CC)+
1 ZZ(4)*((4.*SP-1.)*BB-CC)-ZZ(6)*((4.*PP-1.)*BB+CC))+
2 2.*AA*(ZZ(7)*TP-ZZ(8)*TP+ZZ(9)*(PP-SP))+
3 (ZZ(10)-ZZ(12))*CC+
4 2.*BB*(ZZ(13)*TP-ZZ(14)*TP+ZZ(15)*(PP-SP))
A32=.5*(ZZ(2)*((4.*TP-1.)*AA-CC)-ZZ(3)*((4.*PP-1.)*AA+CC)+
1 ZZ(5)*((4.*TP-1.)*BB-CC)-ZZ(6)*((4.*PP-1.)*BB+CC))+
2 2.*AA*(ZZ(7)*TP+ZZ(8)*(PP-TP)-ZZ(9)*SP)+
3 (ZZ(11)-ZZ(12))*CC+
4 2.*BB*(ZZ(13)*SP+ZZ(14)*(PP-TP)-ZZ(15)*SP)
A33= (ZZ(4)-ZZ(1))*.5*SP*(2.*SP-1.+RP)+
1 (ZZ(5)-ZZ(2))*.5*TP*(2.*TP-1.+RP)+
2 (ZZ(6)-ZZ(3))*.5*PP*(2.*PP-1.+RP)-
3 2.*(ZZ(7)*SP*TP+ZZ(8)*TP*PP+ZZ(9)*PP*SP)-
4 2.*(ZZ(10)*SP+ZZ(11)*TP+ZZ(12)*PP)*RP+
5 2.*(ZZ(13)*SP*TP+ZZ(14)*TP*PP+ZZ(15)*PP*SP)
RETURN
C 8-NODE HEX
190 CONTINUE
F1=.125*(XX(1)*(1.-SP)*(1.-TP)*(1.-RP)+
1 XX(2)*(1.+SP)*(1.-TP)*(1.-RP)+
2 XX(3)*(1.+SP)*(1.+TP)*(1.-RP)+
3 XX(4)*(1.-SP)*(1.+TP)*(1.-RP)+
4 XX(5)*(1.-SP)*(1.-TP)*(1.+RP)+
5 XX(6)*(1.+SP)*(1.-TP)*(1.+RP)+
6 XX(7)*(1.+SP)*(1.+TP)*(1.+RP)+
7 XX(8)*(1.-SP)*(1.+TP)*(1.+RP))
F2=.125*(YY(1)*(1.-SP)*(1.-TP)*(1.-RP)+
1 YY(2)*(1.+SP)*(1.-TP)*(1.-RP)+
2 YY(3)*(1.+SP)*(1.+TP)*(1.-RP)+
3 YY(4)*(1.-SP)*(1.+TP)*(1.-RP)+
4 YY(5)*(1.-SP)*(1.-TP)*(1.+RP)+
5 YY(6)*(1.+SP)*(1.-TP)*(1.+RP)+
6 YY(7)*(1.+SP)*(1.+TP)*(1.+RP)+
7 YY(8)*(1.-SP)*(1.+TP)*(1.+RP))
F3=.125*(ZZ(1)*(1.-SP)*(1.-TP)*(1.-RP)+
1 ZZ(2)*(1.+SP)*(1.-TP)*(1.-RP)+
2 ZZ(3)*(1.+SP)*(1.+TP)*(1.-RP)+
3 ZZ(4)*(1.-SP)*(1.+TP)*(1.-RP)+
4 ZZ(5)*(1.-SP)*(1.-TP)*(1.+RP)+
5 ZZ(6)*(1.+SP)*(1.-TP)*(1.+RP)+
6 ZZ(7)*(1.+SP)*(1.+TP)*(1.+RP)+
7 ZZ(8)*(1.-SP)*(1.+TP)*(1.+RP))
A11=.125*((XX(2)-XX(1))*(1.-TP)*(1.-RP)+
1 (XX(3)-XX(4))*(1.+TP)*(1.-RP)+
2 (XX(6)-XX(5))*(1.-TP)*(1.+RP)+
3 (XX(7)-XX(8))*(1.+TP)*(1.+RP))
A12=.125*((XX(4)-XX(1))*(1.-SP)*(1.-RP)+
1 (XX(3)-XX(2))*(1.+SP)*(1.-RP)+
2 (XX(8)-XX(5))*(1.-SP)*(1.+RP)+
3 (XX(7)-XX(6))*(1.+SP)*(1.+RP))
A13=.125*((XX(5)-XX(1))*(1.-SP)*(1.-TP)+
1 (XX(6)-XX(2))*(1.+SP)*(1.-TP)+
2 (XX(7)-XX(3))*(1.+SP)*(1.+TP)+
3 (XX(8)-XX(4))*(1.-SP)*(1.+TP))
A21=.125*((YY(2)-YY(1))*(1.-TP)*(1.-RP)+
1 (YY(3)-YY(4))*(1.+TP)*(1.-RP)+
2 (YY(6)-YY(5))*(1.-TP)*(1.+RP)+
3 (YY(7)-YY(8))*(1.+TP)*(1.+RP))
A22=.125*((YY(4)-YY(1))*(1.-SP)*(1.-RP)+
1 (YY(3)-YY(2))*(1.+SP)*(1.-RP)+
2 (YY(8)-YY(5))*(1.-SP)*(1.+RP)+
3 (YY(7)-YY(6))*(1.+SP)*(1.+RP))
A23=.125*((YY(5)-YY(1))*(1.-SP)*(1.-TP)+
1 (YY(6)-YY(2))*(1.+SP)*(1.-TP)+
2 (YY(7)-YY(3))*(1.+SP)*(1.+TP)+
3 (YY(8)-YY(4))*(1.-SP)*(1.+TP))
A31=.125*((ZZ(2)-ZZ(1))*(1.-TP)*(1.-RP)+
1 (ZZ(3)-ZZ(4))*(1.+TP)*(1.-RP)+
2 (ZZ(6)-ZZ(5))*(1.-TP)*(1.+RP)+
3 (ZZ(7)-ZZ(8))*(1.+TP)*(1.+RP))
A32=.125*((ZZ(4)-ZZ(1))*(1.-SP)*(1.-RP)+
1 (ZZ(3)-ZZ(2))*(1.+SP)*(1.-RP)+
2 (ZZ(8)-ZZ(5))*(1.-SP)*(1.+RP)+
3 (ZZ(7)-ZZ(6))*(1.+SP)*(1.+RP))
A33=.125*((ZZ(5)-ZZ(1))*(1.-SP)*(1.-TP)+
1 (ZZ(6)-ZZ(2))*(1.+SP)*(1.-TP)+
2 (ZZ(7)-ZZ(3))*(1.+SP)*(1.+TP)+
3 (ZZ(8)-ZZ(4))*(1.-SP)*(1.+TP))
RETURN
C 20-NODE HEX
200 CONTINUE
AA=.125*(XX(1)*(1.-SP)*(1.-TP)*(1.-RP)*(-SP-TP-RP-2.)+
1 XX(2)*(1.+SP)*(1.-TP)*(1.-RP)*(SP-TP-RP-2.)+
2 XX(3)*(1.+SP)*(1.+TP)*(1.-RP)*(SP+TP-RP-2.)+
3 XX(4)*(1.-SP)*(1.+TP)*(1.-RP)*(-SP+TP-RP-2.)+
4 XX(5)*(1.-SP)*(1.-TP)*(1.+RP)*(-SP-TP+RP-2.)+
5 XX(6)*(1.+SP)*(1.-TP)*(1.+RP)*(SP-TP+RP-2.)+
6 XX(7)*(1.+SP)*(1.+TP)*(1.+RP)*(SP+TP+RP-2.)+
7 XX(8)*(1.-SP)*(1.+TP)*(1.+RP)*(-SP+TP+RP-2.))
BB=.250*(XX(9)*(1.-SP**2)*(1.-TP)*(1.-RP)+
1 XX(10)*(1.+SP)*(1.-TP**2)*(1.-RP)+
2 XX(11)*(1.-SP**2)*(1.+TP)*(1.-RP)+
3 XX(12)*(1.-SP)*(1.-TP**2)*(1.-RP)+
4 XX(13)*(1.-SP)*(1.-TP)*(1.-RP**2)+
5 XX(14)*(1.+SP)*(1.-TP)*(1.-RP**2)+
6 XX(15)*(1.+SP)*(1.+TP)*(1.-RP**2)+
7 XX(16)*(1.-SP)*(1.+TP)*(1.-RP**2)+
8 XX(17)*(1.-SP**2)*(1.-TP)*(1.+RP)+
9 XX(18)*(1.+SP)*(1.-TP**2)*(1.+RP)+
# XX(19)*(1.-SP**2)*(1.+TP)*(1.+RP)+
1 XX(20)*(1.-SP)*(1.-TP**2)*(1.+RP))
F1=AA+BB
AA=.125*(YY(1)*(1.-SP)*(1.-TP)*(1.-RP)*(-SP-TP-RP-2.)+
1 YY(2)*(1.+SP)*(1.-TP)*(1.-RP)*(SP-TP-RP-2.)+
2 YY(3)*(1.+SP)*(1.+TP)*(1.-RP)*(SP+TP-RP-2.)+
3 YY(4)*(1.-SP)*(1.+TP)*(1.-RP)*(-SP+TP-RP-2.)+
4 YY(5)*(1.-SP)*(1.-TP)*(1.+RP)*(-SP-TP+RP-2.)+
5 YY(6)*(1.+SP)*(1.-TP)*(1.+RP)*(SP-TP+RP-2.)+
6 YY(7)*(1.+SP)*(1.+TP)*(1.+RP)*(SP+TP+RP-2.)+
7 YY(8)*(1.-SP)*(1.+TP)*(1.+RP)*(-SP+TP+RP-2.))
BB=.250*(YY(9)*(1.-SP**2)*(1.-TP)*(1.-RP)+
1 YY(10)*(1.+SP)*(1.-TP**2)*(1.-RP)+
2 YY(11)*(1.-SP**2)*(1.+TP)*(1.-RP)+
3 YY(12)*(1.-SP)*(1.-TP**2)*(1.-RP)+
4 YY(13)*(1.-SP)*(1.-TP)*(1.-RP**2)+
5 YY(14)*(1.+SP)*(1.-TP)*(1.-RP**2)+
6 YY(15)*(1.+SP)*(1.+TP)*(1.-RP**2)+
7 YY(16)*(1.-SP)*(1.+TP)*(1.-RP**2)+
8 YY(17)*(1.-SP**2)*(1.-TP)*(1.+RP)+
9 YY(18)*(1.+SP)*(1.-TP**2)*(1.+RP)+
# YY(19)*(1.-SP**2)*(1.+TP)*(1.+RP)+
1 YY(20)*(1.-SP)*(1.-TP**2)*(1.+RP))
F2=AA+BB
AA=.125*(ZZ(1)*(1.-SP)*(1.-TP)*(1.-RP)*(-SP-TP-RP-2.)+
1 ZZ(2)*(1.+SP)*(1.-TP)*(1.-RP)*(SP-TP-RP-2.)+
2 ZZ(3)*(1.+SP)*(1.+TP)*(1.-RP)*(SP+TP-RP-2.)+
3 ZZ(4)*(1.-SP)*(1.+TP)*(1.-RP)*(-SP+TP-RP-2.)+
4 ZZ(5)*(1.-SP)*(1.-TP)*(1.+RP)*(-SP-TP+RP-2.)+
5 ZZ(6)*(1.+SP)*(1.-TP)*(1.+RP)*(SP-TP+RP-2.)+
6 ZZ(7)*(1.+SP)*(1.+TP)*(1.+RP)*(SP+TP+RP-2.)+
7 ZZ(8)*(1.-SP)*(1.+TP)*(1.+RP)*(-SP+TP+RP-2.))
BB=.250*(ZZ(9)*(1.-SP**2)*(1.-TP)*(1.-RP)+
1 ZZ(10)*(1.+SP)*(1.-TP**2)*(1.-RP)+
2 ZZ(11)*(1.-SP**2)*(1.+TP)*(1.-RP)+
3 ZZ(12)*(1.-SP)*(1.-TP**2)*(1.-RP)+
4 ZZ(13)*(1.-SP)*(1.-TP)*(1.-RP**2)+
5 ZZ(14)*(1.+SP)*(1.-TP)*(1.-RP**2)+
6 ZZ(15)*(1.+SP)*(1.+TP)*(1.-RP**2)+
7 ZZ(16)*(1.-SP)*(1.+TP)*(1.-RP**2)+
8 ZZ(17)*(1.-SP**2)*(1.-TP)*(1.+RP)+
9 ZZ(18)*(1.+SP)*(1.-TP**2)*(1.+RP)+
# ZZ(19)*(1.-SP**2)*(1.+TP)*(1.+RP)+
1 ZZ(20)*(1.-SP)*(1.-TP**2)*(1.+RP))
F3=AA+BB
AA=.125*(-XX(1)*(1.-TP)*(1.-RP)*(-2.*SP-TP-RP-1.)
1 +XX(2)*(1.-TP)*(1.-RP)*(2.*SP-TP-RP-1.)
2 +XX(3)*(1.+TP)*(1.-RP)*(-2.*SP+TP-RP-1.)
3 -XX(4)*(1.+TP)*(1.-RP)*(-2.*SP+TP-RP-1.)
4 -XX(5)*(1.-TP)*(1.+RP)*(-2.*SP-TP+RP-1.)
5 +XX(6)*(1.-TP)*(1.+RP)*(2.*SP-TP+RP-1.)
6 +XX(7)*(1.+TP)*(1.+RP)*(2.*SP+TP+RP-1.)
7 -XX(8)*(1.+TP)*(1.+RP)*(-2.*SP+TP+RP-1.))
BB=.250*(+XX(9)*(-2.*SP)*(1.-TP)*(1.-RP)
1 +XX(10)*(1.-TP**2)*(1.-RP)
2 +XX(11)*(-2.*SP)*(1.+TP)*(1.-RP)
3 -XX(12)*(1.-TP**2)*(1.-RP)
4 -XX(13)*(1.-TP)*(1.-RP**2)
5 +XX(14)*(1.-TP)*(1.-RP**2)
6 +XX(15)*(1.+TP)*(1.-RP**2)
7 -XX(16)*(1.+TP)*(1.-RP**2)
8 +XX(17)*(-2.*SP)*(1.-TP)*(1.+RP)
9 +XX(18)*(1.-TP**2)*(1.+RP)
# +XX(19)*(-2.*SP)*(1.+TP)*(1.+RP)
1 -XX(20)*(1.-TP**2)*(1.+RP))
A11=AA+BB
AA=.125*(-XX(1)*(1.-SP)*(1.-RP)*(-SP-2.*TP-RP-1.)
1 -XX(2)*(1.+SP)*(1.-RP)*(SP-2.*TP-RP-1.)
2 +XX(3)*(1.+SP)*(1.-RP)*(SP+2.*TP-RP-1.)
3 +XX(4)*(1.-SP)*(1.-RP)*(-SP+2.*TP-RP-1.)
4 -XX(5)*(1.-SP)*(1.+RP)*(-SP-2.*TP+RP-1.)
5 -XX(6)*(1.+SP)*(1.+RP)*(SP-2.*TP+RP-1.)
6 +XX(7)*(1.+SP)*(1.+RP)*(SP+2.*TP+RP-1.)
7 +XX(8)*(1.-SP)*(1.+RP)*(-SP+2.*TP+RP-1.))
BB=.250*(-XX(9)*(1.-SP**2)*(1.-RP)
1 +XX(10)*(1.+SP)*(-2.*TP)*(1.-RP)
2 +XX(11)*(1.-SP**2)*(1.-RP)
3 +XX(12)*(1.-SP)*(-2.*TP)*(1.-RP)
4 -XX(13)*(1.-SP)*(1.-RP**2)
5 -XX(14)*(1.+SP)*(1.-RP**2)
6 +XX(15)*(1.+SP)*(1.-RP**2)
7 +XX(16)*(1.-SP)*(1.-RP**2)
8 -XX(17)*(1.-SP**2)*(1.+RP)
9 +XX(18)*(1.+SP)*(-2.*TP)*(1.+RP)
# +XX(19)*(1.-SP**2)*(1.+RP)
1 +XX(20)*(1.-SP)*(-2.*TP)*(1.+RP))
A12=AA+BB
AA=.125*(-XX(1)*(1.-SP)*(1.-TP)*(-SP-TP-2.*RP-1.)
1 -XX(2)*(1.+SP)*(1.-TP)*(SP-TP-2.*RP-1.)
2 -XX(3)*(1.+SP)*(1.+TP)*(SP+TP-2.*RP-1.)
3 -XX(4)*(1.-SP)*(1.+TP)*(-SP+TP-2.*RP-1.)
4 +XX(5)*(1.-SP)*(1.-TP)*(-SP-TP+2.*RP-1.)
5 +XX(6)*(1.+SP)*(1.-TP)*(SP-TP+2.*RP-1.)
6 +XX(7)*(1.+SP)*(1.+TP)*(SP+TP+2.*RP-1.)
7 +XX(8)*(1.-SP)*(1.+TP)*(-SP+TP+2.*RP-1.))
BB=.250*(-XX(9)*(1.-SP**2)*(1.-TP)
1 -XX(10)*(1.+SP)*(1.-TP**2)
2 -XX(11)*(1.-SP**2)*(1.+TP)
3 -XX(12)*(1.-SP)*(1.-TP**2)
4 +XX(13)*(1.-SP)*(1.-TP)*(-2.*RP)
5 +XX(14)*(1.+SP)*(1.-TP)*(-2.*RP)
6 +XX(15)*(1.+SP)*(1.+TP)*(-2.*RP)
7 +XX(16)*(1.-SP)*(1.+TP)*(-2.*RP)
8 +XX(17)*(1.-SP**2)*(1.-TP)
9 +XX(18)*(1.+SP)*(1.-TP**2)
# +XX(19)*(1.-SP**2)*(1.+TP)
1 +XX(20)*(1.-SP)*(1.-TP**2))
A13=AA+BB
AA=.125*(-YY(1)*(1.-TP)*(1.-RP)*(-2.*SP-TP-RP-1.)
1 +YY(2)*(1.-TP)*(1.-RP)*(2.*SP-TP-RP-1.)
2 +YY(3)*(1.+TP)*(1.-RP)*(-2.*SP+TP-RP-1.)
3 -YY(4)*(1.+TP)*(1.-RP)*(-2.*SP+TP-RP-1.)
4 -YY(5)*(1.-TP)*(1.+RP)*(-2.*SP-TP+RP-1.)
5 +YY(6)*(1.-TP)*(1.+RP)*(2.*SP-TP+RP-1.)
6 +YY(7)*(1.+TP)*(1.+RP)*(2.*SP+TP+RP-1.)
7 -YY(8)*(1.+TP)*(1.+RP)*(-2.*SP+TP+RP-1.))
BB=.250*(+YY(9)*(-2.*SP)*(1.-TP)*(1.-RP)
1 +YY(10)*(1.-TP**2)*(1.-RP)
2 +YY(11)*(-2.*SP)*(1.+TP)*(1.-RP)
3 -YY(12)*(1.-TP**2)*(1.-RP)
4 -YY(13)*(1.-TP)*(1.-RP**2)
5 +YY(14)*(1.-TP)*(1.-RP**2)
6 +YY(15)*(1.+TP)*(1.-RP**2)
7 -YY(16)*(1.+TP)*(1.-RP**2)
8 +YY(17)*(-2.*SP)*(1.-TP)*(1.+RP)
9 +YY(18)*(1.-TP**2)*(1.+RP)
# +YY(19)*(-2.*SP)*(1.+TP)*(1.+RP)
1 -YY(20)*(1.-TP**2)*(1.+RP))
A21=AA+BB
AA=.125*(-YY(1)*(1.-SP)*(1.-RP)*(-SP-2.*TP-RP-1.)
1 -YY(2)*(1.+SP)*(1.-RP)*(SP-2.*TP-RP-1.)
2 +YY(3)*(1.+SP)*(1.-RP)*(SP+2.*TP-RP-1.)
3 +YY(4)*(1.-SP)*(1.-RP)*(-SP+2.*TP-RP-1.)
4 -YY(5)*(1.-SP)*(1.+RP)*(-SP-2.*TP+RP-1.)
5 -YY(6)*(1.+SP)*(1.+RP)*(SP-2.*TP+RP-1.)
6 +YY(7)*(1.+SP)*(1.+RP)*(SP+2.*TP+RP-1.)
7 +YY(8)*(1.-SP)*(1.+RP)*(-SP+2.*TP+RP-1.))
BB=.250*(-YY(9)*(1.-SP**2)*(1.-RP)
1 +YY(10)*(1.+SP)*(-2.*TP)*(1.-RP)
2 +YY(11)*(1.-SP**2)*(1.-RP)
3 +YY(12)*(1.-SP)*(-2.*TP)*(1.-RP)
4 -YY(13)*(1.-SP)*(1.-RP**2)
5 -YY(14)*(1.+SP)*(1.-RP**2)
6 +YY(15)*(1.+SP)*(1.-RP**2)
7 +YY(16)*(1.-SP)*(1.-RP**2)
8 -YY(17)*(1.-SP**2)*(1.+RP)
9 +YY(18)*(1.+SP)*(-2.*TP)*(1.+RP)
# +YY(19)*(1.-SP**2)*(1.+RP)
1 +YY(20)*(1.-SP)*(-2.*TP)*(1.+RP))
A22=AA+BB
AA=.125*(-YY(1)*(1.-SP)*(1.-TP)*(-SP-TP-2.*RP-1.)
1 -YY(2)*(1.+SP)*(1.-TP)*(SP-TP-2.*RP-1.)
2 -YY(3)*(1.+SP)*(1.+TP)*(SP+TP-2.*RP-1.)
3 -YY(4)*(1.-SP)*(1.+TP)*(-SP+TP-2.*RP-1.)
4 +YY(5)*(1.-SP)*(1.-TP)*(-SP-TP+2.*RP-1.)
5 +YY(6)*(1.+SP)*(1.-TP)*(SP-TP+2.*RP-1.)
6 +YY(7)*(1.+SP)*(1.+TP)*(SP+TP+2.*RP-1.)
7 +YY(8)*(1.-SP)*(1.+TP)*(-SP+TP+2.*RP-1.))
BB=.250*(-YY(9)*(1.-SP**2)*(1.-TP)
1 -YY(10)*(1.+SP)*(1.-TP**2)
2 -YY(11)*(1.-SP**2)*(1.+TP)
3 -YY(12)*(1.-SP)*(1.-TP**2)
4 +YY(13)*(1.-SP)*(1.-TP)*(-2.*RP)
5 +YY(14)*(1.+SP)*(1.-TP)*(-2.*RP)
6 +YY(15)*(1.+SP)*(1.+TP)*(-2.*RP)
7 +YY(16)*(1.-SP)*(1.+TP)*(-2.*RP)
8 +YY(17)*(1.-SP**2)*(1.-TP)
9 +YY(18)*(1.+SP)*(1.-TP**2)
# +YY(19)*(1.-SP**2)*(1.+TP)
1 +YY(20)*(1.-SP)*(1.-TP**2))
A23=AA+BB
AA=.125*(-ZZ(1)*(1.-TP)*(1.-RP)*(-2.*SP-TP-RP-1.)
1 +ZZ(2)*(1.-TP)*(1.-RP)*(2.*SP-TP-RP-1.)
2 +ZZ(3)*(1.+TP)*(1.-RP)*(-2.*SP+TP-RP-1.)
3 -ZZ(4)*(1.+TP)*(1.-RP)*(-2.*SP+TP-RP-1.)
4 -ZZ(5)*(1.-TP)*(1.+RP)*(-2.*SP-TP+RP-1.)
5 +ZZ(6)*(1.-TP)*(1.+RP)*(2.*SP-TP+RP-1.)
6 +ZZ(7)*(1.+TP)*(1.+RP)*(2.*SP+TP+RP-1.)
7 -ZZ(8)*(1.+TP)*(1.+RP)*(-2.*SP+TP+RP-1.))
BB=.250*(+ZZ(9)*(-2.*SP)*(1.-TP)*(1.-RP)
1 +ZZ(10)*(1.-TP**2)*(1.-RP)
2 +ZZ(11)*(-2.*SP)*(1.+TP)*(1.-RP)
3 -ZZ(12)*(1.-TP**2)*(1.-RP)
4 -ZZ(13)*(1.-TP)*(1.-RP**2)
5 +ZZ(14)*(1.-TP)*(1.-RP**2)
6 +ZZ(15)*(1.+TP)*(1.-RP**2)
7 -ZZ(16)*(1.+TP)*(1.-RP**2)
8 +ZZ(17)*(-2.*SP)*(1.-TP)*(1.+RP)
9 +ZZ(18)*(1.-TP**2)*(1.+RP)
# +ZZ(19)*(-2.*SP)*(1.+TP)*(1.+RP)
1 -ZZ(20)*(1.-TP**2)*(1.+RP))
A31=AA+BB
AA=.125*(-ZZ(1)*(1.-SP)*(1.-RP)*(-SP-2.*TP-RP-1.)
1 -ZZ(2)*(1.+SP)*(1.-RP)*(SP-2.*TP-RP-1.)
2 +ZZ(3)*(1.+SP)*(1.-RP)*(SP+2.*TP-RP-1.)
3 +ZZ(4)*(1.-SP)*(1.-RP)*(-SP+2.*TP-RP-1.)
4 -ZZ(5)*(1.-SP)*(1.+RP)*(-SP-2.*TP+RP-1.)
5 -ZZ(6)*(1.+SP)*(1.+RP)*(SP-2.*TP+RP-1.)
6 +ZZ(7)*(1.+SP)*(1.+RP)*(SP+2.*TP+RP-1.)
7 +ZZ(8)*(1.-SP)*(1.+RP)*(-SP+2.*TP+RP-1.))
BB=.250*(-ZZ(9)*(1.-SP**2)*(1.-RP)
1 +ZZ(10)*(1.+SP)*(-2.*TP)*(1.-RP)
2 +ZZ(11)*(1.-SP**2)*(1.-RP)
3 +ZZ(12)*(1.-SP)*(-2.*TP)*(1.-RP)
4 -ZZ(13)*(1.-SP)*(1.-RP**2)
5 -ZZ(14)*(1.+SP)*(1.-RP**2)
6 +ZZ(15)*(1.+SP)*(1.-RP**2)
7 +ZZ(16)*(1.-SP)*(1.-RP**2)
8 -ZZ(17)*(1.-SP**2)*(1.+RP)
9 +ZZ(18)*(1.+SP)*(-2.*TP)*(1.+RP)
# +ZZ(19)*(1.-SP**2)*(1.+RP)
1 +ZZ(20)*(1.-SP)*(-2.*TP)*(1.+RP))
A32=AA+BB
AA=.125*(-ZZ(1)*(1.-SP)*(1.-TP)*(-SP-TP-2.*RP-1.)
1 -ZZ(2)*(1.+SP)*(1.-TP)*(SP-TP-2.*RP-1.)
2 -ZZ(3)*(1.+SP)*(1.+TP)*(SP+TP-2.*RP-1.)
3 -ZZ(4)*(1.-SP)*(1.+TP)*(-SP+TP-2.*RP-1.)
4 +ZZ(5)*(1.-SP)*(1.-TP)*(-SP-TP+2.*RP-1.)
5 +ZZ(6)*(1.+SP)*(1.-TP)*(SP-TP+2.*RP-1.)
6 +ZZ(7)*(1.+SP)*(1.+TP)*(SP+TP+2.*RP-1.)
7 +ZZ(8)*(1.-SP)*(1.+TP)*(-SP+TP+2.*RP-1.))
BB=.250*(-ZZ(9)*(1.-SP**2)*(1.-TP)
1 -ZZ(10)*(1.+SP)*(1.-TP**2)
2 -ZZ(11)*(1.-SP**2)*(1.+TP)
3 -ZZ(12)*(1.-SP)*(1.-TP**2)
4 +ZZ(13)*(1.-SP)*(1.-TP)*(-2.*RP)
5 +ZZ(14)*(1.+SP)*(1.-TP)*(-2.*RP)
6 +ZZ(15)*(1.+SP)*(1.+TP)*(-2.*RP)
7 +ZZ(16)*(1.-SP)*(1.+TP)*(-2.*RP)
8 +ZZ(17)*(1.-SP**2)*(1.-TP)
9 +ZZ(18)*(1.+SP)*(1.-TP**2)
# +ZZ(19)*(1.-SP**2)*(1.+TP)
1 +ZZ(20)*(1.-SP)*(1.-TP**2))
A33=AA+BB
RETURN
C 27-NODE HEX
210 CONTINUE
AA=.125*(-XX(1)*SP*TP*RP*(1.-SP)*(1.-TP)*(1.-RP)
1 +XX(2)*SP*TP*RP*(1.+SP)*(1.-TP)*(1.-RP)
2 -XX(3)*SP*TP*RP*(1.+SP)*(1.+TP)*(1.-RP)
3 +XX(4)*SP*TP*RP*(1.-SP)*(1.+TP)*(1.-RP)
4 +XX(5)*SP*TP*RP*(1.-SP)*(1.-TP)*(1.+RP)
5 -XX(6)*SP*TP*RP*(1.+SP)*(1.-TP)*(1.+RP)
6 +XX(7)*SP*TP*RP*(1.+SP)*(1.+TP)*(1.+RP)
7 -XX(8)*SP*TP*RP*(1.-SP)*(1.+TP)*(1.+RP))
BB=.250*(+XX (9)*TP*RP*(1.-SP**2)*(1.-TP)*(1.-RP)
1 -XX(10)*SP*RP*(1.+SP)*(1.-TP**2)*(1.-RP)
2 -XX(11)*TP*RP*(1.-SP**2)*(1.+TP)*(1.-RP)
3 +XX(12)*SP*RP*(1.-SP)*(1.-TP**2)*(1.-RP)
4 +XX(13)*SP*TP*(1.-SP)*(1.-TP)*(1.-RP**2)
5 -XX(14)*SP*TP*(1.+SP)*(1.-TP)*(1.-RP**2)
6 +XX(15)*SP*TP*(1.+SP)*(1.+TP)*(1.-RP**2)
7 -XX(16)*SP*TP*(1.-SP)*(1.+TP)*(1.-RP**2))
CC=.250*(-XX(17)*TP*RP*(1.-SP**2)*(1.-TP)*(1.+RP)
1 +XX(18)*SP*RP*(1.+SP)*(1.-TP**2)*(1.+RP)
2 +XX(19)*TP*RP*(1.-SP**2)*(1.+TP)*(1.+RP)
3 -XX(20)*SP*RP*(1.-SP)*(1.-TP**2)*(1.+RP))+
& .500*(-XX(21)*TP*(1.-SP**2)*(1.-TP)*(1.-RP**2) +
& XX(22)*SP*(1.+SP)*(1.-TP**2)*(1.-RP**2) +
& XX(23)*TP*(1.-SP**2)*(1.+TP)*(1.-RP**2) -
& XX(24)*SP*(1.-SP)*(1.-TP**2)*(1.-RP**2) -
& XX(25)*RP*(1.-SP**2)*(1.-TP**2)*(1.-RP) +
& XX(26)*RP*(1.-SP**2)*(1.-TP**2)*(1.+RP))+
& XX(27)*(1.-SP**2)*(1.-TP**2)*(1.-RP**2)
F1=AA+BB+CC
AA=.125*(-YY(1)*SP*TP*RP*(1.-SP)*(1.-TP)*(1.-RP)
1 +YY(2)*SP*TP*RP*(1.+SP)*(1.-TP)*(1.-RP)
2 -YY(3)*SP*TP*RP*(1.+SP)*(1.+TP)*(1.-RP)
3 +YY(4)*SP*TP*RP*(1.-SP)*(1.+TP)*(1.-RP)
4 +YY(5)*SP*TP*RP*(1.-SP)*(1.-TP)*(1.+RP)
5 -YY(6)*SP*TP*RP*(1.+SP)*(1.-TP)*(1.+RP)
6 +YY(7)*SP*TP*RP*(1.+SP)*(1.+TP)*(1.+RP)
7 -YY(8)*SP*TP*RP*(1.-SP)*(1.+TP)*(1.+RP))
BB=.250*(+YY (9)*TP*RP*(1.-SP**2)*(1.-TP)*(1.-RP)
1 -YY(10)*SP*RP*(1.+SP)*(1.-TP**2)*(1.-RP)
2 -YY(11)*TP*RP*(1.-SP**2)*(1.+TP)*(1.-RP)
3 +YY(12)*SP*RP*(1.-SP)*(1.-TP**2)*(1.-RP)
4 +YY(13)*SP*TP*(1.-SP)*(1.-TP)*(1.-RP**2)
5 -YY(14)*SP*TP*(1.+SP)*(1.-TP)*(1.-RP**2)
6 +YY(15)*SP*TP*(1.+SP)*(1.+TP)*(1.-RP**2)
7 -YY(16)*SP*TP*(1.-SP)*(1.+TP)*(1.-RP**2))
CC=.250*(-YY(17)*TP*RP*(1.-SP**2)*(1.-TP)*(1.+RP)
1 +YY(18)*SP*RP*(1.+SP)*(1.-TP**2)*(1.+RP)
2 +YY(19)*TP*RP*(1.-SP**2)*(1.+TP)*(1.+RP)
3 -YY(20)*SP*RP*(1.-SP)*(1.-TP**2)*(1.+RP))+
& .500*(-YY(21)*TP*(1.-SP**2)*(1.-TP)*(1.-RP**2) +
& YY(22)*SP*(1.+SP)*(1.-TP**2)*(1.-RP**2) +
& YY(23)*TP*(1.-SP**2)*(1.+TP)*(1.-RP**2) -
& YY(24)*SP*(1.-SP)*(1.-TP**2)*(1.-RP**2) -
& YY(25)*RP*(1.-SP**2)*(1.-TP**2)*(1.-RP) +
& YY(26)*RP*(1.-SP**2)*(1.-TP**2)*(1.+RP))+
& YY(27)*(1.-SP**2)*(1.-TP**2)*(1.-RP**2)
F2=AA+BB+CC
AA=.125*(-ZZ(1)*SP*TP*RP*(1.-SP)*(1.-TP)*(1.-RP)
1 +ZZ(2)*SP*TP*RP*(1.+SP)*(1.-TP)*(1.-RP)
2 -ZZ(3)*SP*TP*RP*(1.+SP)*(1.+TP)*(1.-RP)
3 +ZZ(4)*SP*TP*RP*(1.-SP)*(1.+TP)*(1.-RP)
4 +ZZ(5)*SP*TP*RP*(1.-SP)*(1.-TP)*(1.+RP)
5 -ZZ(6)*SP*TP*RP*(1.+SP)*(1.-TP)*(1.+RP)
6 +ZZ(7)*SP*TP*RP*(1.+SP)*(1.+TP)*(1.+RP)
7 -ZZ(8)*SP*TP*RP*(1.-SP)*(1.+TP)*(1.+RP))
BB=.250*(+ZZ (9)*TP*RP*(1.-SP**2)*(1.-TP)*(1.-RP)
1 -ZZ(10)*SP*RP*(1.+SP)*(1.-TP**2)*(1.-RP)
2 -ZZ(11)*TP*RP*(1.-SP**2)*(1.+TP)*(1.-RP)
3 +ZZ(12)*SP*RP*(1.-SP)*(1.-TP**2)*(1.-RP)
4 +ZZ(13)*SP*TP*(1.-SP)*(1.-TP)*(1.-RP**2)
5 -ZZ(14)*SP*TP*(1.+SP)*(1.-TP)*(1.-RP**2)
6 +ZZ(15)*SP*TP*(1.+SP)*(1.+TP)*(1.-RP**2)
7 -ZZ(16)*SP*TP*(1.-SP)*(1.+TP)*(1.-RP**2))
CC=.250*(-ZZ(17)*TP*RP*(1.-SP**2)*(1.-TP)*(1.+RP)
1 +ZZ(18)*SP*RP*(1.+SP)*(1.-TP**2)*(1.+RP)
2 +ZZ(19)*TP*RP*(1.-SP**2)*(1.+TP)*(1.+RP)
3 -ZZ(20)*SP*RP*(1.-SP)*(1.-TP**2)*(1.+RP))+
& .500*(-ZZ(21)*TP*(1.-SP**2)*(1.-TP)*(1.-RP**2) +
& ZZ(22)*SP*(1.+SP)*(1.-TP**2)*(1.-RP**2) +
& ZZ(23)*TP*(1.-SP**2)*(1.+TP)*(1.-RP**2) -
& ZZ(24)*SP*(1.-SP)*(1.-TP**2)*(1.-RP**2) -
& ZZ(25)*RP*(1.-SP**2)*(1.-TP**2)*(1.-RP) +
& ZZ(26)*RP*(1.-SP**2)*(1.-TP**2)*(1.+RP))+
& ZZ(27)*(1.-SP**2)*(1.-TP**2)*(1.-RP**2)
F3=AA+BB+CC
C **** SHAPE FUNCTION DERIVATIVES FOR 27 NODE HEX GO HERE
RETURN
END