!-------------------------------------------------------------------------------

!                      Code_Saturne version 2.0.4n!                      --------------------------

!     This file is part of the Code_Saturne Kernel, element of the
!     Code_Saturne CFD tool.

!     Copyright (C) 1998-2008 EDF S.A., France

!     contact: saturne-support@edf.fr

!     The Code_Saturne Kernel 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; either version 2 of
!     the License, or (at your option) any later version.

!     The Code_Saturne Kernel 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 the Code_Saturne Kernel; if not, write to the
!     Free Software Foundation, Inc.,
!     51 Franklin St, Fifth Floor,
!     Boston, MA  02110-1301  USA

!-------------------------------------------------------------------------------
! Purpose :
! ---------
!     User subroutine dedicated to Fluid - Structure internal coupling

! --- Definition and management of internal Fluid Structure coupled calculations,
!     using a simplified solid modeling (linear "mass, friction and spring" modeling).

!     Here are 2 differents subroutines that need to be filled :

!  -   USSTR1 : Called at the beginning of the calculation. It enables one to define
!               internal structures and corresponding initial conditions (initial
!               displacement and velocity).

!  -   USSTR2 : Called at each time step of the calculation. Here one defines
!               structural parameters (considered to be potentially time dependent),
!               i.e. Mass, Friction, Stiffness and Fluid Stresses.

! --- Boundary faces identification
!     =============================

! Boundary faces may be identified using the 'getfbr' subroutine.
! The syntax of this subroutine is described in the 'usclim' subroutine,
! but a more thorough description can be found in the user guide.


!-------------------------------------------------------------------------------
subroutine usstr1 &
!================

 ( idbia0 , idbra0 ,                                              &
   ndim   , ncelet , ncel   , nfac   , nfabor , nfml   , nprfml , &
   nnod   , lndfac , lndfbr , ncelbr ,                            &
   nideve , nrdeve , nituse , nrtuse ,                            &
   ifacel , ifabor , ifmfbr , ifmcel , iprfml , maxelt , lstelt , &
   ipnfac , nodfac , ipnfbr , nodfbr , idfstr ,                   &
   idevel , ituser , ia     ,                                     &
   aexxst , bexxst , cfopre ,                                     &
   xyzcen , surfac , surfbo , cdgfac , cdgfbo , xyznod , volume , &
   xstr0  , vstr0  , xstreq ,                                     &
   rdevel , rtuser , ra     )



!===============================================================================
! Purpose :
! ---------

! --- Definition of internal structures and corresponding initial conditions
!     (initial displacement and velocity )

!-------------------------------------------------------------------------------
! Arguments
!__________________.____._____.________________________________________________.
! name             !type!mode ! role                                           !
!__________________!____!_____!________________________________________________!
! idbia0           ! i  ! <-- ! number of first free position in ia            !
! idbra0           ! i  ! <-- ! number of first free position in ra            !
! ndim             ! i  ! <-- ! spatial dimension                              !
! ncelet           ! i  ! <-- ! number of extended (real + ghost) cells        !
! ncel             ! i  ! <-- ! number of cells                                !
! nfac             ! i  ! <-- ! number of interior faces                       !
! nfabor           ! i  ! <-- ! number of boundary faces                       !
! nfml             ! i  ! <-- ! number of families (group classes)             !
! nprfml           ! i  ! <-- ! number of properties per family (group class)  !
! nnod             ! i  ! <-- ! number of vertices                             !
! lndfac           ! i  ! <-- ! size of nodfac indexed array                   !
! lndfbr           ! i  ! <-- ! size of nodfbr indexed array                   !
! ncelbr           ! i  ! <-- ! number of cells with faces on boundary         !
! nideve, nrdeve   ! i  ! <-- ! sizes of idevel and rdevel arrays              !
! nituse, nrtuse   ! i  ! <-- ! sizes of ituser and rtuser arrays              !
! ifacel(2, nfac)  ! ia ! <-- ! interior faces -> cells connectivity           !
! ifabor(nfabor)   ! ia ! <-- ! boundary faces -> cells connectivity           !
! ifmfbr(nfabor)   ! ia ! <-- ! boundary face family numbers                   !
! ifmcel(ncelet)   ! ia ! <-- ! cell family numbers                            !
! iprfml           ! ia ! <-- ! property numbers per family                    !
!  (nfml, nprfml)  !    !     !                                                !
! maxelt           ! i  ! <-- ! max number of cells and faces (int/boundary)   !
! lstelt(maxelt)   ! ia ! --- ! work array                                     !
! ipnfac(nfac+1)   ! ia ! <-- ! interior faces -> vertices index (optional)    !
! nodfac(lndfac)   ! ia ! <-- ! interior faces -> vertices list (optional)     !
! ipnfbr(nfabor+1) ! ia ! <-- ! boundary faces -> vertices index (optional)    !
! nodfbr(lndfbr)   ! ia ! <-- ! boundary faces -> vertices list (optional)     !
! idfstr(nfabor)   ! ia ! <-- ! boundary faces -> structure definition         !
! idevel(nideve)   ! ia ! <-> ! integer work array for temporary development   !
! ituser(nituse)   ! ia ! <-> ! user-reserved integer work array               !
! ia(*)            ! ia ! --- ! main integer work array                        !
! aexxst,bexxst    ! r  ! <-- ! prediction coefficients of structural data     !
! cfopre           ! r  ! <-- ! prediction coefficients of fluid forces        !
! xyzcen           ! ra ! <-- ! cell centers                                   !
!  (ndim, ncelet)  !    !     !                                                !
! surfac           ! ra ! <-- ! interior faces surface vectors                 !
!  (ndim, nfac)    !    !     !                                                !
! surfbo           ! ra ! <-- ! boundary faces surface vectors                 !
!  (ndim, nfabor)  !    !     !                                                !
! cdgfac           ! ra ! <-- ! interior faces centers of gravity              !
!  (ndim, nfac)    !    !     !                                                !
! cdgfbo           ! ra ! <-- ! boundary faces centers of gravity              !
!  (ndim, nfabor)  !    !     !                                                !
! xyznod           ! ra ! <-- ! vertex coordinates (optional)                  !
!  (ndim, nnod)    !    !     !                                                !
! volume(ncelet)   ! ra ! <-- ! cell volumes                                   !
! xstr0(ndim,      ! ra ! <-- ! initial displacement of internal structures    !
!       nbstru)    !    !     !                                                !
! vstr0(ndim,      ! ra ! <-- ! initial velocity of internal structures        !
!       nbstru)    !    !     !                                                !
! xstreq(ndim,     ! ra ! <-- ! displacement of initial mesh compared to       !
!       nbstru)    !    !     ! the structures position at equilibrium         !
! rdevel(nrdeve)   ! ra ! <-> ! real work array for temporary development      !
! rtuser(nrtuse)   ! ra ! <-> ! user-reserved real work array                  !
! ra(*)            ! ra ! --- ! main real work array                           !
!__________________!____!_____!________________________________________________!

!     Type: i (integer), r (real), s (string), a (array), l (logical),
!           and composite types (ex: ra real array)
!     mode: <-- input, --> output, <-> modifies data, --- work array
!===============================================================================

implicit none

!===============================================================================
! Common blocks
!===============================================================================

include "paramx.h"
include "cstnum.h"
include "optcal.h"
include "entsor.h"
include "pointe.h"
include "albase.h"
include "period.h"
include "parall.h"

!===============================================================================

! Arguments

integer          idbia0 , idbra0
integer          ndim   , ncelet , ncel   , nfac   , nfabor
integer          nfml   , nprfml
integer          nnod   , lndfac , lndfbr , ncelbr
integer          nbstru
integer          nideve , nrdeve , nituse , nrtuse

integer          ifacel(2,nfac) , ifabor(nfabor)
integer          ifmfbr(nfabor) , ifmcel(ncelet)
integer          iprfml(nfml,nprfml)
integer          maxelt, lstelt(maxelt)
integer          ipnfac(nfac+1), nodfac(lndfac)
integer          ipnfbr(nfabor+1), nodfbr(lndfbr)
integer          idfstr(nfabor)
integer          idevel(nideve), ituser(nituse)
integer          ia(*)

double precision aexxst, bexxst, cfopre
double precision xyzcen(ndim,ncelet)
double precision surfac(ndim,nfac), surfbo(ndim,nfabor)
double precision cdgfac(ndim,nfac), cdgfbo(ndim,nfabor)
double precision xyznod(ndim,nnod), volume(ncelet)
double precision xstr0(3,nstrmx), xstreq(3,nstrmx)
double precision vstr0(3,nstrmx)
double precision rdevel(nrdeve), rtuser(nrtuse), ra(*)

! Local variables

integer          idebia, idebra
integer          ifac
integer          ilelt, nlelt

!===============================================================================


!===============================================================================
! 1.  Initialization

!===============================================================================

idebia = idbia0
idebra = idbra0

!===============================================================================
! 2.  Definition of internal structures
!===============================================================================

!    Here one fills array IDFSTR(NFABOR)
!    For each boundary face IFAC, IDFSTR(IFAC) is the number of the structure
!    the face belongs to (if IDFSTR(IFAC) = 0, the face IFAC doesn't
!    belong to any structure.)
!    When using internal coupling, structure number necessarily
!    needs to be positive (as shown in following examples).

!    The number of "internal" structures is automatically defined with the
!    maximum value of IDFSTR table, meaning that
!    internal structure numbers must be defined sequentially with positive values,
!    beginning with integer value '1'.


!    In following example, boundary faces with color 4 belong to internal structure '1'.
!    Boundary faces with color 2 belong to internal structure '2'.
!    The total number of internal structures equals 2.

!    Boundary faces identification
!    =============================

!    Boundary faces may be identified using the 'getfbr' subroutine.
!    The syntax of this subroutine is described in the 'usclim' subroutine,
!    but a more thorough description can be found in the user guide.


CALL GETFBR('4',NLELT,LSTELT)
!==========

do ilelt = 1, nlelt

  ifac = lstelt(ilelt)

  idfstr(ifac) = 1

enddo

CALL GETFBR('6',NLELT,LSTELT)
!==========

do ilelt = 1, nlelt

  ifac = lstelt(ilelt)

  idfstr(ifac) = 2

enddo

! --- For each internal structure one can here define :
!     - an initial velocity VSTR0
!     - an initial displacement XSTR0 (i.e. XSTR0 is the value of the displacement XSTR
!       compared to the initial mesh at time t = 0)
!     - a displacement compared to equilibrium XSTREQ (i.e. XSTREQ is the initial displacement
!       of the internal structure compared to its position at equilibrium; at each
!       time step t and for a displacement XSTR(t) associated internal structure will be
!       subjected to a force -k*(XSTR(t)+XSTREQ) due to the spring).

! --- Note that XSTR0, XSTREQ and VSTR0 arrays are initialized at the beginning of the calculations
!     to the value of 0.

! --- When starting a calculation using ALE, or re-starting a calculation with ALE basing
!     on a first calculation without ALE, an initial iteration 0 is automatically calculated
!     in order to take initial arrays XSTR0, VSTR0 and XSTREQ into account. In another case
!     add the following expression 'italin=1' in subroutine 'usalin', so that the code can
!     deal with arrays XSTR0, VSTR0 or XSTREQ.

! --- In the following example :
!     - internal structure '1' has got an initial displacement XSTR0 = 2 (m) in 'y' direction and
!     a displacement compared to equilibrium XSTREQ = 1 (m) in 'y' direction, too.
!     - Initial velocity in 'z' direction of structure '2' equals VSTR0=-0.5 (m/s).

xstr0(2,1)  = 2.d0
xstreq(2,1) = 1.d0
vstr0(3,2)  =-0.5d0

! --- Here one can modify the values of the prediction coefficients for
!     displacements anf fluid forces in internal FSI coupled algorithm.
!
!     the use of these coefficients is reminded here :
!       - predicted displacement = X(n) + aexxst * DT * X'(n)
!                                       + bexxst * DT * (X'(n)-X'(n-1))
!             X(n) stands for the displacement at iteration 'n'
!             X'(n) and X'(n-1) represent internal structure velocity respectively
!              at iteration 'n' and 'n-1'.
!       - fluid force sent to structure internal solver = CFOPRE * F(n)
!                                                        + (1.D0-CFOPRE) * F(n-1)
!             F(n) and F(n-1) stand for fluid force acting on the structure respectively
!              at iteration 'n' and 'n-1'.

aexxst =  0.5d0
bexxst =  0.0d0
cfopre =  2.d0

! --- Activation of structural history output (i.e. displacement, structural velocity,
!     structural acceleration anf fluid force)
!     (ihistr=0, not activated ; ihistr=1, activated)
!     The value of structural history output step is the same as the one for standard
!     variables ('NTHIST').
ihistr = 1
!
return

end subroutine


!===============================================================================


subroutine usstr2 &
!================

 ( idbia0 , idbra0 ,                                              &
   ndim   , ncelet , ncel   , nfac   , nfabor , nfml   , nprfml , &
   nnod   , lndfac , lndfbr , ncelbr , nbstru ,                   &
   nideve , nrdeve , nituse , nrtuse ,                            &
   ifacel , ifabor , ifmfbr , ifmcel , iprfml ,                   &
   ipnfac , nodfac , ipnfbr , nodfbr , idfstr ,                   &
   idevel , ituser , ia     ,                                     &
   xyzcen , surfac , surfbo , cdgfac , cdgfbo , xyznod , volume , &
   dtcel  ,                                                       &
   xmstru , xcstru , xkstru , xstreq , xstr   , vstr   , forstr , &
   dtstr  ,                                                       &
   rdevel , rtuser ,                                              &
   ra     )



!===============================================================================
! Purpose :
! ---------

! --- Definition of structural parameters in case of Fluid Structure internal coupling :
!                 Mass, Friction, Stiffness anf Fluid Stresses.
!
!-------------------------------------------------------------------------------
! Arguments
!__________________.____._____.________________________________________________.
! name             !type!mode ! role                                           !
!__________________!____!_____!________________________________________________!
! idbia0           ! i  ! <-- ! number of first free position in ia            !
! idbra0           ! i  ! <-- ! number of first free position in ra            !
! ndim             ! i  ! <-- ! spatial dimension                              !
! ncelet           ! i  ! <-- ! number of extended (real + ghost) cells        !
! ncel             ! i  ! <-- ! number of cells                                !
! nfac             ! i  ! <-- ! number of interior faces                       !
! nfabor           ! i  ! <-- ! number of boundary faces                       !
! nfml             ! i  ! <-- ! number of families (group classes)             !
! nprfml           ! i  ! <-- ! number of properties per family (group class)  !
! nnod             ! i  ! <-- ! number of vertices                             !
! lndfac           ! i  ! <-- ! size of nodfac indexed array                   !
! lndfbr           ! i  ! <-- ! size of nodfbr indexed array                   !
! ncelbr           ! i  ! <-- ! number of cells with faces on boundary         !
! nbstru           ! e  ! <-- ! nombre de structures definies                  !
! nvar             ! i  ! <-- ! total number of variables                      !
! nscal            ! i  ! <-- ! total number of scalars                        !
! nphas            ! i  ! <-- ! number of phases                               !
! nideve, nrdeve   ! i  ! <-- ! sizes of idevel and rdevel arrays              !
! nituse, nrtuse   ! i  ! <-- ! sizes of ituser and rtuser arrays              !
! ifacel(2, nfac)  ! ia ! <-- ! interior faces -> cells connectivity           !
! ifabor(nfabor)   ! ia ! <-- ! boundary faces -> cells connectivity           !
! ifmfbr(nfabor)   ! ia ! <-- ! boundary face family numbers                   !
! ifmcel(ncelet)   ! ia ! <-- ! cell family numbers                            !
! iprfml           ! ia ! <-- ! property numbers per family                    !
!  (nfml, nprfml)  !    !     !                                                !
! ipnfac           ! te ! <-- ! position du premier noeud de chaque            !
!   (nfac+1)       !    !     !  face interne dans nodfac (optionnel)          !
! nodfac           ! te ! <-- ! connectivite faces internes/noeuds             !
!   (lndfac)       !    !     !  (optionnel)                                   !
! ipnfbr           ! te ! <-- ! position du premier noeud de chaque            !
!   (nfabor+1)     !    !     !  face de bord dans nodfbr (optionnel)          !
! nodfbr           ! te ! <-- ! connectivite faces de bord/noeuds              !
!   (lndfbr)       !    !     !  (optionnel)                                   !
! idfstr(nfabor    ! te ! <-- ! definition des structures                      !
! idevel(nideve)   ! ia ! <-> ! integer work array for temporary development   !
! ituser(nituse)   ! ia ! <-> ! user-reserved integer work array               !
! ia(*)            ! ia ! --- ! main integer work array                        !
! xyzcen           ! ra ! <-- ! cell centers                                   !
!  (ndim, ncelet)  !    !     !                                                !
! surfac           ! ra ! <-- ! interior faces surface vectors                 !
!  (ndim, nfac)    !    !     !                                                !
! surfbo           ! ra ! <-- ! boundary faces surface vectors                 !
!  (ndim, nfabor)  !    !     !                                                !
! cdgfac           ! ra ! <-- ! interior faces centers of gravity              !
!  (ndim, nfac)    !    !     !                                                !
! cdgfbo           ! ra ! <-- ! boundary faces centers of gravity              !
!  (ndim, nfabor)  !    !     !                                                !
! xyznod           ! ra ! <-- ! vertex coordinates (optional)                  !
!  (ndim, nnod)    !    !     !                                                !
! volume(ncelet)   ! ra ! <-- ! cell volumes                                   !
! dtcel(ncelet)    ! ra ! <-- ! time step (per cell)                           !
! xmstru(ndim,     ! ra ! --> ! matrix of structural mass                      !
!  ndim,nbstru)    !    !     !                                                !
! xcstru(ndim,     ! ra ! --> ! matrix of structural friction                   !
!  ndim,nbstru)    !    !     !                                                !
! xkstru(ndim,     ! ra ! --> ! matrix of structural stiffness                 !
!  ndim,nbstru)    !    !     !                                                !
! xstreq(ndim,     ! ra ! <-- ! displacement of initial mesh compared to       !
!       nbstru)    !    !     ! the structures position at equilibrium         !
! xstr(ndim,       ! ra ! <-- ! structural displacement                        !
!       nbstru)    !    !     !                                                !
! vstr(ndim,       ! ra ! <-- ! structural velocity                            !
!       nbstru)    !    !     !                                                !
! forstr(ndim      ! ra ! <-- ! forces acting on structures (take forces       !
!       nbstru)    !    !     !         due to fluid effects into account   )  !
! dtstr(nbstru)    ! ra ! --> ! structural time step                           !
! rdevel(nrdeve)   ! ra ! <-> ! real work array for temporary development      !
! rtuser(nrtuse)   ! ra ! <-> ! user-reserved real work array                  !
! ra(*)            ! ra ! --- ! main real work array                           !
!__________________!____!_____!________________________________________________!

!     Type: i (integer), r (real), s (string), a (array), l (logical),
!           and composite types (ex: ra real array)
!     mode: <-- input, --> output, <-> modifies data, --- work array
!===============================================================================

implicit none

!===============================================================================
! Common blocks
!===============================================================================

include "paramx.h"
include "cstnum.h"
include "optcal.h"
include "pointe.h"
include "albase.h"
include "period.h"
include "parall.h"

!===============================================================================

! Arguments

integer          idbia0 , idbra0
integer          ndim   , ncelet , ncel   , nfac   , nfabor
integer          nfml   , nprfml
integer          nnod   , lndfac , lndfbr , ncelbr
integer          nbstru
integer          nideve , nrdeve , nituse , nrtuse

integer          ifacel(2,nfac) , ifabor(nfabor)
integer          ifmfbr(nfabor) , ifmcel(ncelet)
integer          iprfml(nfml,nprfml)
integer          ipnfac(nfac+1), nodfac(lndfac)
integer          ipnfbr(nfabor+1), nodfbr(lndfbr)
integer          idfstr(nfabor)
integer          idevel(nideve), ituser(nituse)
integer          ia(*)

double precision xyzcen(ndim,ncelet)
double precision surfac(ndim,nfac), surfbo(ndim,nfabor)
double precision cdgfac(ndim,nfac), cdgfbo(ndim,nfabor)
double precision xyznod(ndim,nnod), volume(ncelet)
double precision dtcel(ncelet)
double precision xmstru(3,3,nstrmx)
double precision xcstru(3,3,nstrmx)
double precision xkstru(3,3,nstrmx)
double precision xstreq(3,nstrmx)
double precision xstr(3,nstrmx)
double precision vstr(3,nstrmx)
double precision forstr(3,nstrmx)
double precision dtstr(nstrmx)
double precision rdevel(nrdeve), rtuser(nrtuse), ra(*)

! VARIABLES LOCALES

integer          idebia, idebra
integer          ii, jj, istr
double precision theta, sint, cost, xm, xc, xk, fx, fy

!===============================================================================


!===============================================================================
! 1.  INITIALIZATION

!===============================================================================

idebia = idbia0
idebra = idbra0

!===============================================================================
! 2.  Structural parameters (subroutine usstr2 is called at each time step
!                            of the calculation)
!===============================================================================

! --- For each internal structure one defines here :
!     - its Mass                  (XMSTRU)
!     - its Friction coefficient C (XCSTRU)
!     - its Stiffness K           (XKSTRU)

!     FORSTR array gives fluid stresses acting on each internal structure. Moreover
!     it's possible to take external forces (gravity for example )into account, too.

!     XSTR array indicates the displacement of the structure compared to its position
!     in initial mesh.

!     XSTR0 array gives the displacement of the structures in initial mesh compared to
!     structural equilibrium.

!     VSTR array stands for structural velocity.

!     XSTR, XSTR0, and VSTR arrays are DATA tables that can be used to define arrays
!     Mass, Friction and Stiffness. THOSE ARE NOT TO BE MODIFIED.

!     The 3D structural equation that is solved is the following one :

!       M.X'' + C.X' + K.(X+X0) = F   (1)
!       = -     = -    =  - --    -

!       X stands for the structural displacement compared to initil mesh postition (XSTR)
!       -
!       X0 represents the displacement of the structure in initial mesh compared to equilibrium
!       --

!       Note that M, C and K are 3x3 matrices.
!                 =  =     =
!       Equation (1) is solved using a Newmark HHT algorithm.
!       Note that the time step used to solve this equation (DTSTR) can be different from the one of fluid
!       calculations. USER is free to define DTSTR array. At the beginning of the calculation DTSTR is
!       initialized to the value of DTCEL (Fluid time step).
!

! --- Matrices XMSTRU, XCSTRU and XKSTRU are initialized to the value of 0.
do istr = 1, nbstru

  do ii = 1, 3
    do jj = 1, 3
      xmstru(ii,jj,istr) = 0.d0
      xcstru(ii,jj,istr) = 0.d0
      xkstru(ii,jj,istr) = 0.d0
    enddo
  enddo

enddo

! --- Example 1): In following example structure '1' is defined as an isotropic system (i.e. matrices
!     M, C and K are diagonal) : mass equals 5 kg, stiffness equals 2 N/m and friction
!     =  =     =
!     coefficient equals 3 kg.s .

do ii = 1, 3
  xmstru(ii,ii,1) = 5.d0
  xcstru(ii,ii,1) = 2.d0
  xkstru(ii,ii,1) = 3.d0
enddo

! --- Example 2): In this example structure '2' is subjected to the following movement :
!               - In plane xOy the movement is locally defined along an axis (OX). Structural parameters
!                 in X direction are called xm, xc and xk. The angle of inclination between global (Ox) axis
!                 and local (OX) axis is called THETA. Movement in local (OY) direction is imposed to be rigid.
!               - In 'z' direction the movement is modeled to be oscillating and harmonic (meaning that
!                 there is no friction). Mass equals 1. kg and stiffness equals 1. N/m. Fluid stresses in that direction
!                 are taken into account. Moreover the structure is also subjected to an external oscillating
!                 force Fz_ext = 3 * cos(4*t).


!                 This leads to the following local equations :
!                 xm.X'' + xc.X' + xk.X = FX
!                                     Y = 0
!                    Z''         +    Z = FZ + 3.cos(4.t)

theta = pi/6.d0
cost = cos(theta)
sint = sin(theta)

!               FX, FY, and FZ stand for the local fluid forces components. They are defined as follows, using gobal
!               components of fluid forces Fx, Fy and Fz .
!               FX =  COST*Fx + SINT*Fy
!               FY = -SINT*Fx + COST*Fy
!               FZ = Fz

!               After changing of basis, the problem can be described as follows, using global coordinates:

xm = 1.d0
xc = 3.d-1
xk = 2.d0
fx = forstr(1,2)
fy = forstr(2,2)

xmstru(1,1,2) = xm*cost**2
xmstru(1,2,2) = xm*cost*sint
xmstru(2,1,2) = xm*cost*sint
xmstru(2,2,2) = xm*sint**2
xmstru(3,3,2) = 1.d0

xcstru(1,1,2) = xc*cost**2
xcstru(1,2,2) = xc*cost*sint
xcstru(2,1,2) = xc*cost*sint
xcstru(2,2,2) = xc*sint**2

xkstru(1,1,2) = (xk-1.d0)*cost**2 + 1.d0
xkstru(1,2,2) = (xk-1.d0)*cost*sint
xkstru(2,1,2) = (xk-1.d0)*cost*sint
xkstru(2,2,2) = (xk-1.d0)*sint**2 + 1.d0
xkstru(3,3,2) = 1.d0

forstr(1,2) = fx*cost**2   + fy*sint*cost
forstr(2,2) = fx*sint*cost + fy*sint**2
forstr(3,2) = forstr(3,2) + 3.d0*cos(4.d0*ttcabs)

do istr = 1, nbstru
  dtstr(istr) = dtcel(1)
enddo


return

