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!
! CalculiX - A 3-dimensional finite element program
! Copyright (C) 1998-2015 Guido Dhondt
!
! This program is free software; you can redistribute it and/or
! modify it under the terms of the GNU General Public License as
! published by the Free Software Foundation(version 2);
!
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program; if not, write to the Free Software
! Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
!
subroutine beamextscheme(yil,ndim,nfield,lakonl,npropstart,prop,
& field,mi)
!
! provides the extrapolation scheme for beams with a cross section
! which is not rectangular nor elliptical
!
implicit none
!
character*8 lakonl
!
integer npropstart,mi(*),ndim,nfield,j,k,l
!
real*8 prop(*),ratio,ratio2,yil(ndim,mi(1)),yig(nfield,mi(1)),
& field(999,20*mi(3)),r,scal,a8(8,8),pmean1(nfield),
& pmean2(nfield),t1,t2,t3,t4,a,b,dummy,shp(4,20),xis(8,3)
!
! extrapolation from a 2x2x2=8 integration point scheme in a hex to
! the vertex nodes
!
data a8 /2.549,-.683,.183,-.683,-.683,.183,
& -.04904,.183,-.683,2.549,-.683,.183,
& .183,-.683,.183,-.04904,-.683,.183,
& -.683,2.549,.183,-.04904,.183,-.683,
& .183,-.683,2.549,-.683,-.04904,.183,
& -.683,.183,-.683,.183,-.04904,.183,
& 2.549,-.683,.183,-.683,.183,-.683,
& .183,-.04904,-.683,2.549,-.683,.183,
& .183,-.04904,.183,-.683,-.683,.183,
& -.683,2.549,-.04904,.183,-.683,.183,
& .183,-.683,2.549,-.683/
!
if(lakonl(8:8).eq.'P') then
!
! pipe cross section
!
! the axis of the pipe is along the local xi-direction
! the integration points are at positions +-0.57 along
! the xi-axis. At each of these positions there are 8
! integration points in the eta-zeta plane at one radial
! position and
! equally spaced along the circumferential direction
!
! ratio of inner radius to outer radius
!
ratio=(prop(npropstart+1)-prop(npropstart+2))/
& prop(npropstart+1)
ratio2=ratio*ratio
!
! radial location of integration points
!
r=dsqrt((ratio2+1.d0)/2.d0)
!
! scaling factor between the radial location of the integration
! points and the regular location of C3D20R integration points
!
scal=dsqrt(2.d0/3.d0)/r
!
! calculating the mean values at each of the two xi-positions
!
do k=1,nfield
pmean1(k)=(yil(k,2)+yil(k,4)+yil(k,6)+yil(k,8))/4.d0
pmean2(k)=(yil(k,10)+yil(k,12)+yil(k,14)+yil(k,16))/4.d0
enddo
!
! translating the results from the integration points of the
! pipe section to the integration points of the C3D20R element
!
do k=1,nfield
yig(k,1)=pmean1(k)+(yil(k,6)-pmean1(k))*scal
yig(k,2)=pmean2(k)+(yil(k,14)-pmean2(k))*scal
yig(k,3)=pmean1(k)+(yil(k,8)-pmean1(k))*scal
yig(k,4)=pmean2(k)+(yil(k,16)-pmean2(k))*scal
yig(k,5)=pmean1(k)+(yil(k,4)-pmean1(k))*scal
yig(k,6)=pmean2(k)+(yil(k,12)-pmean2(k))*scal
yig(k,7)=pmean1(k)+(yil(k,2)-pmean1(k))*scal
yig(k,8)=pmean2(k)+(yil(k,10)-pmean2(k))*scal
enddo
!
! standard extrapolation for the C3D20R element
!
do j=1,8
do k=1,nfield
field(k,j)=0.d0
do l=1,8
field(k,j)=field(k,j)+a8(j,l)*yig(k,l)
enddo
enddo
enddo
!
elseif(lakonl(8:8).eq.'B') then
!
! BOX cross section
a=prop(npropstart+1)
b=prop(npropstart+2)
t1=prop(npropstart+3)
t2=prop(npropstart+4)
t3=prop(npropstart+5)
t4=prop(npropstart+6)
c
c new local coordinates for node points of element
c
xis(1,1) = -1/sqrt(3.0d0)
xis(1,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(1,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(2,1) = 1/sqrt(3.0d0)
xis(2,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(2,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(3,1) = 1/sqrt(3.0d0)
xis(3,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(3,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(4,1) = -1/sqrt(3.0d0)
xis(4,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(4,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(5,1) = -1/sqrt(3.0d0)
xis(5,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(5,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
xis(6,1) = 1/sqrt(3.0d0)
xis(6,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(6,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
xis(7,1) = 1/sqrt(3.0d0)
xis(7,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(7,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
!
elseif(lakonl(8:8).eq.'B') then
!
! BOX cross section
a=prop(npropstart+1)
b=prop(npropstart+2)
t1=prop(npropstart+3)
t2=prop(npropstart+4)
t3=prop(npropstart+5)
t4=prop(npropstart+6)
c
c new local coordinates for node points of element
c
xis(1,1) = -1/sqrt(3.0d0)
xis(1,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(1,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(2,1) = 1/sqrt(3.0d0)
xis(2,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(2,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(3,1) = 1/sqrt(3.0d0)
xis(3,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(3,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(4,1) = -1/sqrt(3.0d0)
xis(4,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(4,3) = (t3-t1+2*a)/((-2*a)+t1+t3)
xis(5,1) = -1/sqrt(3.0d0)
xis(5,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(5,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
xis(6,1) = 1/sqrt(3.0d0)
xis(6,2) = -(t4-t2-2*b)/((-2*b)+t2+t4)
xis(6,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
xis(7,1) = 1/sqrt(3.0d0)
xis(7,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(7,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
xis(8,1) = -1/sqrt(3.0d0)
xis(8,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(8,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
xis(8,1) = -1/sqrt(3.0d0)
xis(8,2) = -(t4-t2+2*b)/((-2*b)+t2+t4)
xis(8,3) = (t3-t1-2*a)/((-2*a)+t1+t3)
!
! extrapolate from int points to node points
!
do k=1,nfield
yig(k,1)=yil(k,9)
yig(k,2)=yil(k,25)
yig(k,3)=yil(k,29)
yig(k,4)=yil(k,13)
yig(k,5)=yil(k,5)
yig(k,6)=yil(k,21)
yig(k,7)=yil(k,17)
yig(k,8)=yil(k,1)
enddo
!
do j=1,8
call shape8h(xis(j,1),xis(j,2),xis(j,3),dummy,dummy,shp,1)
do k=1,nfield
field(k,j)=0.0d0
do l=1,8
field(k,j)=field(k,j)+shp(4,l)*yig(k,l)
enddo
enddo
enddo
!
endif
!
return
end
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