Functions/Subroutines
subroutine	shape20h (xi, et, ze, xl, xsj, shp, iflag)
Function/Subroutine Documentation

◆ shape20h()

subroutine shape20h	(	real*8, intent(in)	xi,
		real*8, intent(in)	et,
		real*8, intent(in)	ze,
		real*8, dimension(3,20), intent(in)	xl,
		real*8, intent(out)	xsj,
		real*8, dimension(4,20), intent(out)	shp,
		integer, intent(in)	iflag
	)
 !
 !     shape functions and derivatives for a 20-node quadratic
 !     isoparametric brick element. -1<=xi,et,ze<=1
 !
 !     iflag=1: calculate only the value of the shape functions
 !     iflag=2: calculate the value of the shape functions and
 !              the Jacobian determinant
 !     iflag=3: calculate the value of the shape functions, the
 !              value of their derivatives w.r.t. the global
 !              coordinates and the Jacobian determinant
 !
       implicit none
 !
       integer i,j,k,iflag
 !
       real*8 shp(4,20),xs(3,3),xsi(3,3),xl(3,20),shpe(4,20),dd,
      &  dd1,dd2,dd3
 !
       real*8 xi,et,ze,xsj,omg,omh,omr,opg,oph,opr,
      &  tpgphpr,tmgphpr,tmgmhpr,tpgmhpr,tpgphmr,tmgphmr,tmgmhmr,tpgmhmr,
      &  omgopg,omhoph,omropr,omgmopg,omhmoph,omrmopr
 !
       intent(in) xi,et,ze,xl,iflag
 !
       intent(out) shp,xsj
 !
 !     shape functions and their glocal derivatives
 !
       omg=1.d0-xi
       omh=1.d0-et
       omr=1.d0-ze
       opg=1.d0+xi
       oph=1.d0+et
       opr=1.d0+ze
       tpgphpr=opg+oph+ze
       tmgphpr=omg+oph+ze
       tmgmhpr=omg+omh+ze
       tpgmhpr=opg+omh+ze
       tpgphmr=opg+oph-ze
       tmgphmr=omg+oph-ze
       tmgmhmr=omg+omh-ze
       tpgmhmr=opg+omh-ze
       omgopg=omg*opg/4.d0
       omhoph=omh*oph/4.d0
       omropr=omr*opr/4.d0
       omgmopg=(omg-opg)/4.d0
       omhmoph=(omh-oph)/4.d0
       omrmopr=(omr-opr)/4.d0
 !
 !     shape functions
 !
       shp(4, 1)=-omg*omh*omr*tpgphpr/8.d0
       shp(4, 2)=-opg*omh*omr*tmgphpr/8.d0
       shp(4, 3)=-opg*oph*omr*tmgmhpr/8.d0
       shp(4, 4)=-omg*oph*omr*tpgmhpr/8.d0
       shp(4, 5)=-omg*omh*opr*tpgphmr/8.d0
       shp(4, 6)=-opg*omh*opr*tmgphmr/8.d0
       shp(4, 7)=-opg*oph*opr*tmgmhmr/8.d0
       shp(4, 8)=-omg*oph*opr*tpgmhmr/8.d0
       shp(4, 9)=omgopg*omh*omr
       shp(4,10)=omhoph*opg*omr
       shp(4,11)=omgopg*oph*omr
       shp(4,12)=omhoph*omg*omr
       shp(4,13)=omgopg*omh*opr
       shp(4,14)=omhoph*opg*opr
       shp(4,15)=omgopg*oph*opr
       shp(4,16)=omhoph*omg*opr
       shp(4,17)=omropr*omg*omh
       shp(4,18)=omropr*opg*omh
       shp(4,19)=omropr*opg*oph
       shp(4,20)=omropr*omg*oph
 !
       if(iflag.eq.1) return
 !
 !     local derivatives of the shape functions: xi-derivative
 !
       shpe(1, 1)=omh*omr*(tpgphpr-omg)/8.d0
       shpe(1, 2)=(opg-tmgphpr)*omh*omr/8.d0
       shpe(1, 3)=(opg-tmgmhpr)*oph*omr/8.d0
       shpe(1, 4)=oph*omr*(tpgmhpr-omg)/8.d0
       shpe(1, 5)=omh*opr*(tpgphmr-omg)/8.d0
       shpe(1, 6)=(opg-tmgphmr)*omh*opr/8.d0
       shpe(1, 7)=(opg-tmgmhmr)*oph*opr/8.d0
       shpe(1, 8)=oph*opr*(tpgmhmr-omg)/8.d0
       shpe(1, 9)=omgmopg*omh*omr
       shpe(1,10)=omhoph*omr
       shpe(1,11)=omgmopg*oph*omr
       shpe(1,12)=-omhoph*omr
       shpe(1,13)=omgmopg*omh*opr
       shpe(1,14)=omhoph*opr
       shpe(1,15)=omgmopg*oph*opr
       shpe(1,16)=-omhoph*opr
       shpe(1,17)=-omropr*omh
       shpe(1,18)=omropr*omh
       shpe(1,19)=omropr*oph
       shpe(1,20)=-omropr*oph
 !
 !     local derivatives of the shape functions: eta-derivative
 !
       shpe(2, 1)=omg*omr*(tpgphpr-omh)/8.d0
       shpe(2, 2)=opg*omr*(tmgphpr-omh)/8.d0
       shpe(2, 3)=opg*(oph-tmgmhpr)*omr/8.d0
       shpe(2, 4)=omg*(oph-tpgmhpr)*omr/8.d0
       shpe(2, 5)=omg*opr*(tpgphmr-omh)/8.d0
       shpe(2, 6)=opg*opr*(tmgphmr-omh)/8.d0
       shpe(2, 7)=opg*(oph-tmgmhmr)*opr/8.d0
       shpe(2, 8)=omg*(oph-tpgmhmr)*opr/8.d0
       shpe(2, 9)=-omgopg*omr
       shpe(2,10)=omhmoph*opg*omr
       shpe(2,11)=omgopg*omr
       shpe(2,12)=omhmoph*omg*omr
       shpe(2,13)=-omgopg*opr
       shpe(2,14)=omhmoph*opg*opr
       shpe(2,15)=omgopg*opr
       shpe(2,16)=omhmoph*omg*opr
       shpe(2,17)=-omropr*omg
       shpe(2,18)=-omropr*opg
       shpe(2,19)=omropr*opg
       shpe(2,20)=omropr*omg
 !
 !     local derivatives of the shape functions: zeta-derivative
 !
       shpe(3, 1)=omg*omh*(tpgphpr-omr)/8.d0
       shpe(3, 2)=opg*omh*(tmgphpr-omr)/8.d0
       shpe(3, 3)=opg*oph*(tmgmhpr-omr)/8.d0
       shpe(3, 4)=omg*oph*(tpgmhpr-omr)/8.d0
       shpe(3, 5)=omg*omh*(opr-tpgphmr)/8.d0
       shpe(3, 6)=opg*omh*(opr-tmgphmr)/8.d0
       shpe(3, 7)=opg*oph*(opr-tmgmhmr)/8.d0
       shpe(3, 8)=omg*oph*(opr-tpgmhmr)/8.d0
       shpe(3, 9)=-omgopg*omh
       shpe(3,10)=-omhoph*opg
       shpe(3,11)=-omgopg*oph
       shpe(3,12)=-omhoph*omg
       shpe(3,13)=omgopg*omh
       shpe(3,14)=omhoph*opg
       shpe(3,15)=omgopg*oph
       shpe(3,16)=omhoph*omg
       shpe(3,17)=omrmopr*omg*omh
       shpe(3,18)=omrmopr*opg*omh
       shpe(3,19)=omrmopr*opg*oph
       shpe(3,20)=omrmopr*omg*oph
 !
 !     computation of the local derivative of the global coordinates
 !     (xs)
 !
       do i=1,3
         do j=1,3
           xs(i,j)=0.d0
           do k=1,20
             xs(i,j)=xs(i,j)+xl(i,k)*shpe(j,k)
           enddo
         enddo
       enddo
 !
 !     computation of the jacobian determinant
 !
       dd1=xs(2,2)*xs(3,3)-xs(2,3)*xs(3,2)
       dd2=xs(2,3)*xs(3,1)-xs(2,1)*xs(3,3)
       dd3=xs(2,1)*xs(3,2)-xs(2,2)*xs(3,1)
       xsj=xs(1,1)*dd1+xs(1,2)*dd2+xs(1,3)*dd3
 !
       if(iflag.eq.2) return
 !
       dd=1.d0/xsj
 !
 !     computation of the global derivative of the local coordinates
 !     (xsi) (inversion of xs)
 !
       xsi(1,1)=dd1*dd
       xsi(1,2)=(xs(1,3)*xs(3,2)-xs(1,2)*xs(3,3))*dd
       xsi(1,3)=(xs(1,2)*xs(2,3)-xs(2,2)*xs(1,3))*dd
       xsi(2,1)=dd2*dd
       xsi(2,2)=(xs(1,1)*xs(3,3)-xs(3,1)*xs(1,3))*dd
       xsi(2,3)=(xs(1,3)*xs(2,1)-xs(1,1)*xs(2,3))*dd
       xsi(3,1)=dd3*dd
       xsi(3,2)=(xs(1,2)*xs(3,1)-xs(1,1)*xs(3,2))*dd
       xsi(3,3)=(xs(1,1)*xs(2,2)-xs(2,1)*xs(1,2))*dd
 !
 !     computation of the global derivatives of the shape functions
 !
       do k=1,20
         do j=1,3
           shp(j,k)=shpe(1,k)*xsi(1,j)+shpe(2,k)*xsi(2,j)
      &          +shpe(3,k)*xsi(3,j)
         enddo
       enddo
 c      do k=1,20
 c        do j=1,3
 c          shp(j,k)=shpe(j,k)
 c        enddo
 c      enddo
 !
       return
Functions/Subroutines

Function/Subroutine Documentation

◆ shape20h()
