DATE     96/09/23
    Opérateur RTENS
    ---------------                            See also :SIGM EPSI 
                                                         CALP GRAD 
                                                         POLA 

CHAM3  =  RTENS  CHAM1 MODL1 |   CHAM2   ;
                             |
                             |  ( CHAM2 )  ...

                 |   VEC1 ( VEC2 )  ;
                 |
           ...   |  'POLA'  CENTR1 ;
                 |  'SPHE'  CENTR1   AXEI1 ;
                 | 'CYLI'  CENTR1   AXEI1 ;
                 | 'TORI' ('CART')  CENTR1 AXEI1 ;
                 | 'TORI'  'CIRC'   CENTR1 AXEI1 CENTR2 ;

CHPO2  =  RTENS  CHPO1 VEC1 (VEC2)  ;

CHAM4  =  RTENS  CHAM1 MODL1  GRAD1  | ('RTAR') |  ;
                                     |   RART   |

    This operator has several functions depending on the data.


    -----------------
    | 1st  function |
    -----------------


  The RTENS operator calculates the stress or strain field in a  
 new orthonormal and direct basis, from a stress or strain field
 defined in the general basis for solid elements, in the element
 local axes (whose first vector is co-linear to the element first 
 side) for thin shells, and in the local axes ( in every point of
 integration) for thick shells.
 

    CHAM3  =  RTENS  CHAM1 MODL1 (CHAM2) VEC1 ( VEC2 )  ;


    Contents :
    _________

    CHAM1  : stress or strain initial field (MCHAML type,
             CONTRAINTES or DEFORMATIONS subtype)

    MODL1  : model object (MMODEL type)

    CHAM2  : characteristics field which contains the thickness in
             case of thick shells (MCHAML type, CARACTERISTIQUES
             subtype)

    VEC1 | : vectors used to define the orthonormal basis 
    VEC2 |   (POINT type)

    CHAM3  : stress or strain field in the new basis
             (MCHAML type, CONTRAINTES or DEFORMATIONS subtype)
             



    Note :
    ________

     The direct orthonormal basis is defined as follows :

  -  for the two-dimensional solid elements : by the VEC1 vector
     and the vector normal to VEC1 (obtained from VEC1 by a pi/2
     rotation in the trigonometric direction)
      
  -  for the three-dimensional solid elements : by the VEC1 
     vector, by the vector contained in the plane ((VEC1,VEC2) 
     and normal to VEC1, and by the vector resulting from the 
     vectorial product between VEC1 and VEC2)
     
  -  for the three-dimensional shell elements : by the vector
     resulting from the projection of VEC1 onto the shell plane
     and the vector contained in the shell plane, normal to VEC1 
     such that their vectorial product be directed according to
     the positive normal to the element if only VEC1 is supplied,
     or such that their vectorial product be oriented like VEC1 and 
     VEC2, if VEC2 is also supplied.
     
    
    -----------------
    | 2nd  function |
    -----------------

    The RTENS operator calculates the stress or strain field in the
 orthotropic basis from a stress or strain field defined in the general
 basis for orthotropic solid elements, in the element local axes
 (whose first vector is co-linear to the element first side) for the
 orthotropic thin shells and in the local axes ( in every point of
 integration) for the orthotropic thick shells.


    CHAM3  =  RTENS  CHAM1 MODL1 CHAM2     ;


    Contents :
    _________

    CHAM1  : stress or strain initial field (MCHAML type,
             CONTRAINTES or DEFORMATIONS subtype)

    MODL1  : model object (MMODEL type)


    CHAM2  : field of direction cosines for the orthotropic axes 
             with respect to the elements local bases (MCHAML type,
             CARACTERISTIQUES subtype)

    CHAM3  : stress or strain field in the orthotropic basis
             (MCHAML type, CONTRAINTES or DEFORMATIONS subtype)

             

    Note 1 :
    __________

    CHAM2 (or CHEL2) may be the mchaml of material properties
    created by the MATR (or MATE) operator since the mchaml of
    material properties contains the direction cosines for the
    orthotropic bases. The names of component standing for the 
    direction cosines of the orthotropic axes are : V1X,V1Y for the
    2D-shell and solid elements, and V1X,V1Y,V1Z,V2X,V2Y,V2Z for 
    the 3D-solid elements.


    ----------------
    | 3rd Fonction |
    ----------------

    The RTENS operator calculates the stress or strain field in a  
new orthonormal and direct local basis (well adapted to the chosen
geometry), from a stress or strain field defined in the general
basis for solid elements, in the element local axes (whose first vector 
is co-linear to the element first side) for thin shells and in the local 
axes ( in every point of integration) for thick shells.


CHAM3 = RTENS CHAM1 MODL1 (CHAM2) | 'POLA'  CENTR1 ;
                                  | 'SPHE'  CENTR1   AXEI1 ;
                                  | 'CYLI'  CENTR1   AXEI1 ;
                                  | 'TORI' ('CART')  CENTR1 AXEI1 ;
                                  | 'TORI'  'CIRC'   CENTR1 AXEI1 CENTR2 ;


    Contents :
    __________

    CHAM1  : stress or strain initial field (MCHAML type,
             CONTRAINTES or DEFORMATIONS subtype)

    MODL1  : model object (MMODEL type)

    CHAM2  : characteristics field which contains the thickness in
             case of thick shells (MCHAML type, CARACTERISTIQUES
             subtype)

    CHAM3  : stress or strain field in the new basis
             (MCHAML type, CONTRAINTES or DEFORMATIONS subtype)
             
    CENTR1 : centre of the new basis (POINT type)

    AXEI1  : point used to define the circular symmetry axis of the
             new basis : this axis contains CENTR1 and AXEI1

    CENTR2 : centre (POINT type) of a meridian circle of the torus,
             if using the option 'TORI' 'CIRC'

    'POLA' : the new basis is the usual basis of polar coordinates
             (only 2D)

    'CYLI' : the new basis is the usual basis of cylindrical
             coordinates which symmetry axis is (CENTR1,AXEI1)

    'SPHE' : the new basis is the usual basis of spheric coordinates,
             which centre is CENTR1. The coordinates axis are the
             following :
              * UR : radial axis
              * UTHETA : tangent line to the meridian (longitude,
                         north to south oriented)
              * UPHI : tangent line to the parallel (latitude, west
                       to east oriented)

    'TORI' : the new basis is one of the two possible torus basis.
             Without any secund key-word, the default option is
             'CART'
             
    'CART' : the basis is a cartesian coordinates basis in each
             meridian plan. The coordinates axis are the
             following :
              * UR : radial axis of the  usual basis of cylindrical 
                     coordinates  
              * UTHETA : corresponding orthoradial axis
              * V1 : (CENTR1,AXEI1) axis

    'CIRC' : in each meridian plan the new basis is a basis of
             polar coordinates (centered on the centre of the
             meridian circle). The coordinates axis are the
             following :
              * UTHETA : the same as 'TORI' 'CART'
              * UT : tangent line to the meridian circle
              * UN : outgoing normal line to the meridian circle        

   IMPORTANT NOTE
   ______________

      Suffixes X, Y and Z correspond respectively to the three axis of
   the new basis.
      For example : in the case of spheric coordinates, SMYZ correspond 
   to the axis UTHETA and UPHI.

     In the case of shell elements the first direction is the projection 
   of UTHETA onto the shell plane and the second one coresponds to the 
   projection onto the same plane (and orhogonalization with respect of
   UTHETA projection) of the axis (axei1 - centr1). If the axis 
   (axei1 - centr1) is normal to the element plane, the second direction
   is -UR.



    ----------------
    | 4th Function |
    ----------------

   The RTENS operator calculates the displacement field in a new 
orthonormal and direct basis, form a given displacement field in 2D
and 3D except axisymetrical and Fourier cases.
 

    CHPO2  =  RTENS  CHPO1 VEC1 (VEC2)  ;



    Contents :
    __________

    CHPO1  : initial displacement field (CHPOINT type)
             
    VEC1   : first vector of the basis (POINT type)

    VEC2   : second vector of the basis (3D only) (POINT type)

    CHPO2  : final displacement field (CHPOINT type)


    Note :
    ______

    The axisymetrical and Fourier cases are not implemented.
   
    The direct orthonormal basis is defined as follows :

  -  in 2D by the VEC1 vector and the vector normal to VEC1 (obtained
     from VEC1 by a pi/2 rotation in the trigonometric direction)
      
  -  in 3D by the VEC1 vector, by the vector contained in the plane
     ((VEC1,VEC2) and normal to VEC1, and by the vector resulting from
     the vectorial product between VEC1 and VEC2)


    ----------------
    | 5th Function |
    ----------------

   For a given field of rotation matrices, the RTENS operator
enables to rotate a stress field or a strain field or a field
of internal variables. In this later case, only the tensorial
variables are modified.
 

   CHAM4  =  RTENS  CHAM1 MODL1  GRAD1  | ('RTAR') |  ;
                                        |   RART   |



    Contents :
    __________

    CHAM1  : stress or strain initial field (MCHAML type,
             CONTRAINTES or DEFORMATIONS  or VARIABLES INTERNES
             subtype)

    MODL1  : model object (MMODEL type)


    GRAD1  : field of rotation matrices (type MCHAML, GRADIENT
             subtype)

   'RTAR'  : key-word (defect option) indicating that the product
             Rt * A * R is wanted, where R is the rotation matrix,
             Rt its transpose, and A the stress or strain tensor
             (MOT subtype)

   'RART'  : mot-clé indiquant qu'on veut le produit R * A * Rt
             (MOT subtype)

    CHAM4  : stress or strain field in the orthotropic basis
             (MCHAML type, CONTRAINTES or DEFORMATIONS or
              VARIABLES INTERNES subtype)