shape10tet.f File Reference

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Functions/Subroutines
subroutine	shape10tet (xi, et, ze, xl, xsj, shp, iflag)

Function/Subroutine Documentation

shape10tet()

subroutine shape10tet	(	real*8, intent(in)	xi,
		real*8, intent(in)	et,
		real*8, intent(in)	ze,
		real*8, dimension(3,10), intent(in)	xl,
		real*8, intent(out)	xsj,
		real*8, dimension(4,10), intent(out)	shp,
		integer, intent(in)	iflag
	)

!
!     shape functions and derivatives for a 10-node quadratic
!     isoparametric tetrahedral element. 0<=xi,et,ze<=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(4,10),xs(3,3),xsi(3,3),xl(3,10),sh(3),xi,et,ze,xsj,a
!
      intent(in) xi,et,ze,xl,iflag
!
      intent(out) shp,xsj
!
!     shape functions and their glocal derivatives
!
!     shape functions
!
      a=1.d0-xi-et-ze
      shp(4, 1)=(2.d0*a-1.d0)*a
      shp(4, 2)=xi*(2.d0*xi-1.d0)
      shp(4, 3)=et*(2.d0*et-1.d0)
      shp(4, 4)=ze*(2.d0*ze-1.d0)
      shp(4, 5)=4.d0*xi*a
      shp(4, 6)=4.d0*xi*et
      shp(4, 7)=4.d0*et*a
      shp(4, 8)=4.d0*ze*a
      shp(4, 9)=4.d0*xi*ze
      shp(4,10)=4.d0*et*ze
!
      if(iflag.eq.1) return
!
!     local derivatives of the shape functions: xi-derivative
!
      shp(1, 1)=1.d0-4.d0*a
      shp(1, 2)=4.d0*xi-1.d0
      shp(1, 3)=0.d0
      shp(1, 4)=0.d0
      shp(1, 5)=4.d0*(a-xi)
      shp(1, 6)=4.d0*et
      shp(1, 7)=-4.d0*et
      shp(1, 8)=-4.d0*ze
      shp(1, 9)=4.d0*ze
      shp(1,10)=0.d0
!
!     local derivatives of the shape functions: eta-derivative
!
      shp(2, 1)=1.d0-4.d0*a
      shp(2, 2)=0.d0
      shp(2, 3)=4.d0*et-1.d0
      shp(2, 4)=0.d0
      shp(2, 5)=-4.d0*xi
      shp(2, 6)=4.d0*xi
      shp(2, 7)=4.d0*(a-et)
      shp(2, 8)=-4.d0*ze
      shp(2, 9)=0.d0
      shp(2,10)=4.d0*ze
!
!     local derivatives of the shape functions: zeta-derivative
!
      shp(3, 1)=1.d0-4.d0*a
      shp(3, 2)=0.d0
      shp(3, 3)=0.d0
      shp(3, 4)=4.d0*ze-1.d0
      shp(3, 5)=-4.d0*xi
      shp(3, 6)=0.d0
      shp(3, 7)=-4.d0*et
      shp(3, 8)=4.d0*(a-ze)
      shp(3, 9)=4.d0*xi
      shp(3,10)=4.d0*et
!
!     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=1,10
            xs(i,j)=xs(i,j)+xl(i,k)*shp(j,k)
          enddo
        enddo
      enddo
!
!     computation of the jacobian determinant
!
      xsj=xs(1,1)*(xs(2,2)*xs(3,3)-xs(2,3)*xs(3,2))
     &   -xs(1,2)*(xs(2,1)*xs(3,3)-xs(2,3)*xs(3,1))
     &   +xs(1,3)*(xs(2,1)*xs(3,2)-xs(2,2)*xs(3,1))
!
      if(iflag.eq.2) return
!
!     computation of the global derivative of the local coordinates
!     (xsi) (inversion of xs)
!
      xsi(1,1)=(xs(2,2)*xs(3,3)-xs(3,2)*xs(2,3))/xsj
      xsi(1,2)=(xs(1,3)*xs(3,2)-xs(1,2)*xs(3,3))/xsj
      xsi(1,3)=(xs(1,2)*xs(2,3)-xs(2,2)*xs(1,3))/xsj
      xsi(2,1)=(xs(2,3)*xs(3,1)-xs(2,1)*xs(3,3))/xsj
      xsi(2,2)=(xs(1,1)*xs(3,3)-xs(3,1)*xs(1,3))/xsj
      xsi(2,3)=(xs(1,3)*xs(2,1)-xs(1,1)*xs(2,3))/xsj
      xsi(3,1)=(xs(2,1)*xs(3,2)-xs(3,1)*xs(2,2))/xsj
      xsi(3,2)=(xs(1,2)*xs(3,1)-xs(1,1)*xs(3,2))/xsj
      xsi(3,3)=(xs(1,1)*xs(2,2)-xs(2,1)*xs(1,2))/xsj
!
!     computation of the global derivatives of the shape functions
!
      do k=1,10
        do j=1,3
          sh(j)=shp(1,k)*xsi(1,j)+shp(2,k)*xsi(2,j)+shp(3,k)*xsi(3,j)
        enddo
        do j=1,3
          shp(j,k)=sh(j)
        enddo
      enddo
!
      return