TractLoad.f90

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SUBROUTINE tractload(R_ex,numnp, &
     interfacesfelemtract, &
     interfacesfnumelems, interfacesfnumnodes, &
     interfacesfelemconn, &
     mapnodesf,lwrbnd,uppbnd,coor)

  IMPLICIT NONE


! 1-3 for 4 node tet (i.e. 3 node triangles)
! 4-6 for 10 node tet (i.e. 6 node triangles, mid-side nodes get traction)
  INTEGER :: lwrbnd,uppbnd

  INTEGER :: interfacesfnumelems,interfacesfnumnodes
  INTEGER, DIMENSION(1:UppBnd,1:InterfaceSFNumElems) :: interfacesfelemconn
  INTEGER, DIMENSION(1:InterfaceSFNumNodes) :: mapnodesf
  REAL*8,  DIMENSION(1:3, 1:InterfaceSFNumElems) :: interfacesfelemtract
  
  INTEGER :: numnp          ! number of nodes
  
  REAL*8, DIMENSION(1:3*numnp) :: r_ex ! external force
  
  INTEGER :: nx, ny, nz
  INTEGER :: i,j,k
  
  INTEGER,DIMENSION(1:3) :: triconn
  REAL*8,DIMENSION(1:3)  :: uniftract

! mesh coordinates
  REAL*8, DIMENSION(1:3,1:numnp) :: coor

  REAL*8 :: x0p,y0p,z0p
  REAL*8 :: x1p,y1p,z1p
  REAL*8 :: x2p,y2p,z2p
  REAL*8 :: x3p,y3p,z3p

! Components sides vector

  REAL*8 :: x1x0, y1y0, z1z0
  REAL*8 :: x2x0, y2y0, z2z0
  

  REAL*8 :: xnorm, area, at
  
  at = 0.d0

  DO i = 1, interfacesfnumelems
     
!  Nodes of the Triangle ( Vertex Nodes ) 

     triconn(1:3) = interfacesfelemconn(1:3,i)

!  Uses the fact that the norm of the cross product vector
!  is the area of the parallelogram they form.  The triangle they
!  form has half that area.

     x0p = coor(1,mapnodesf(triconn(1)))
     y0p = coor(2,mapnodesf(triconn(1)))
     z0p = coor(3,mapnodesf(triconn(1)))
     
     x1p = coor(1,mapnodesf(triconn(2)))
     y1p = coor(2,mapnodesf(triconn(2)))
     z1p = coor(3,mapnodesf(triconn(2)))
     
     x2p = coor(1,mapnodesf(triconn(3)))
     y2p = coor(2,mapnodesf(triconn(3)))
     z2p = coor(3,mapnodesf(triconn(3)))

! Find vector componets of the sides

     x1x0 = x1p - x0p
     y1y0 = y1p - y0p
     z1z0 = z1p - z0p

     x2x0 = x2p - x0p
     y2y0 = y2p - y0p
     z2z0 = z2p - z0p     

!  Take the cross product

     x3p = y1y0 * z2z0  -  z1z0  *  y2y0
     y3p = z1z0 * x2x0  -  x1x0  *  z2z0
     z3p = x1x0 * y2y0  -  y1y0  *  x2x0
         
!  Computes the Euclidean norm of a vector in 3D
         
     xnorm = sqrt( x3p*x3p + y3p*y3p + z3p*z3p )
               
     area = 0.5d0*xnorm

!  Assign the load weighted equally among the 3 nodes 

     uniftract(1:3) = interfacesfelemtract(1:3,i)*area/3.d0

!  Assembly into global external load vector R_ex

     triconn(1:3) = interfacesfelemconn(lwrbnd:uppbnd,i)

     DO j = 1, 3
        nz = mapnodesf(triconn(j))*3 ! volume node
        nx = nz - 2
        ny = nz - 1
        r_ex(nx) = r_ex(nx) + uniftract(1)
        r_ex(ny) = r_ex(ny) + uniftract(2)
        r_ex(nz) = r_ex(nz) + uniftract(3)
     ENDDO
  ENDDO
  
  RETURN
END SUBROUTINE tractload