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$$$$ DYNE     NOTICE  CHAT      11/09/12    21:15:58     7124           
                                             DATE     11/09/12

    Operateur DYNE                           Voir aussi : VIBR PJBA
    ______________                                        PSMO   RECO   
                                                          EVOL   TRADUIRE   
                                                          BASE   CINIMOD   
                                                                                


    Description :
    ____________

    Computation of a dynamic response by means of two explicit 
    algorithms: central differences or Fu-de Vogelaere algorithm


    Syntax 1 :
    ________



    TAB1 = DYNE  |'DIFFERENCES_CENTREES'| ...
                 |'DE_VOGELAERE'|        

   ... | TAB2      | (TAB4) (TAB5) | TAB6      | N1 FLOT1 (N2) TAB8 ;
       | TAB3      |               | TAB7      |
                                   | TAB6 TAB7 |


    Syntax 2 :
    ________



    DYNE 'DE_VOGELAERE' TAB11 ;


    Description :
    ____________

    It consists in computing the solution for the following system
 of equations :
   

        ~     .
      M Q + C Q = F(Q,t) avec F(Q,t) = -K Q + Fl + Fe
                   .
      Q(0) = Q0 et Q(0) = L0

      with :

      M  : diagonal matrix of generalized masses 
      C  : modal dampings matrix
      K  : diagonal matrix of generalized stiffnesses
      Fl : vector of linkage forces 
      Fe : vector of external forces
      Q  : vector of modal contributions 
      Q0 : vector of initial modal contributions 
      L0 : vector of initial modal velocity 


    Contents :
    __________

    TAB2   : table representing a modal base or a set of modal bases
             (TABLE type)

    TAB3   : table gathering the generalized stiffness and mass 
             matrices (TABLE type). Only the diagonal part of the
             matrices are taken into account.

    TAB4   : table representing the generalized damping matrix
             (TABLE type)

    TAB5   : table gathering the linkage descriptions (TABLE type)
       
    TAB6   : table representing the evolution of applied free
             forces (TABLE type) 

    TAB7   : table providing the initial conditions (TABLE type)

    TAB8   : table defining the results requested in the TAB1 
             output table (TABLE type)

    N1     : number of steps (ENTIER type)

    FLOT1  : time step (FLOTTANT type)

    N2     : output every N2 calulation step (ENTIER type)
             by default N2 = 1 .

    TAB1   : table containing the results


    TAB11 : table specifying the computation in a similar way than
            in the 'PASAPAS' procedure (TABLE type) ;
            thus the subtype is 'PASAPAS', the other indices are : 

       'MODELE', object (MMODEL type) restricted to the 
            'ELASTIQUE' 'MODAL' material behavior, describing an
            eigen-modes basis, component name 'ALFA', and to those
            belonging to the 'LIAISON' formulation, describing the
            linkages (see MODE notice);

       'CARACTERISTIQUES', material properties (MCHAML type), 
            associated to 'MODELE';

       'CHARGEMENT', loading expressed in the eigen-modes basis, 
            conjugated component 'FALF' (CHARGEMENT type) ;

       'SORTIE', analogous to TAB8 in syntaxe 1 (TABLE type), requests
            datas for the linkages variables ;

       'DEPLACEMENTS', table (TABLE type) which indices are integers : 
          'DEPLACEMENTS' . 0 is the initial displacement field
            (CHPOINT type), component 'ALFA' ;

       'VITESSES', table (TABLE type), which indices are integers : 
          'VITESSES' . 0 is the initial velocity field (CHPOINT type),
             component 'ALFA' ;
 
       'INIT_DYNE', enables to resume a computation ('TABLE' type) 
             with the table obtained at 'REPRISE' or 'REPRISE_DYNE' ; 

       'NOMBRE_PAS', number of steps (ENTIER type) ;

       'PAS_DE_TEMPS', time increment for each step (ENTIER type);

       'PAS_DE_SORTIE', step frequency for output (ENTIER type) ;

        created or completed par DYNE operator :

       'LIAISONS', contains the results for the linkages asked by 
          the 'SORTIE' table (TABLE type) ;

       'DEPLACEMENTS', displacements at 'MODELE' points (TABLE type) ;

       'VITESSES', velocities at 'MODELE' points (TABLE type) ;

       'REPRISE_DYNE', collects data in order to resume the computation
          (TABLE type).
    

    In what follows A basis is the modal basis in which the equations 
    are uncoupled (component 'ALFA' );
    and the B basis is the basis of the nodal displacement 
    (components 'UX' , 'UY' ...)

    Description of the tables :
    __________________________

    1/ TAB2 :
      -------
        a/ case of a single base :
           TAB2.'SOUSTYPE'           : 'BASE_MODALE'
           TAB2.'MODES' = TAB21
                  TAB21 : base defined by the TRADUIRE procedure
           TAB2.'PSEUDO_MODES' = TAB22
                  TAB22 : pseudo-modes defined by the PSMO operator

        b/ case of a base composed of several bases :
           TAB2.'SOUSTYPE'           : 'ENSEMBLE_DE_BASES'
                I varying from 1 to n bases
           TAB2.I = TBA22
                  TBA22 : base defined at a/
 
        c/ in order to take into account the displacements due to 
       large rigid body rotations one must comlete the table with :
           TAB2.'MODES'.Irot.'CORPS_RIGIDE' = 'VRAI';
           TAB2.'MODES'.Irot.'CENTRE_DE_GRAVITE'= G;

        Displacements due to rigid bodies rotation :
        
        TAB2.'MODES'.Irot.'CORPS_RIGIDE' = 'VRAI';
        TAB2.'MODES'.Irot.'CENTRE_DE_GRAVITE'= G;
        Irot is the number of rotation "eigenmode", G is the center
        of gravity (POINT type).
        The coordinates of the rotation axis are the components 
        'RX','RY','RZ' of the field by element of the rotation 
        "eigenvector". The value of the rotation is automatically 
         normalised to one. An elementary basis can include only one
         rigid body rotation "mode". In the case of more than one 
         rigid bodies one must define one modal basis for each rigid 
         body.
 
 
    2/ TAB3 :
      -------
        TAB3.'SOUSTYPE' : 'RAIDEUR_ET_MASSE'
        TAB3.'RAIDEUR'  : stiffness matrix (RIGIDITE type)
        TAB3.'MASSE'    : mass matrix  (RIGIDITE type)

    3/ TAB4 :
      -------
        TAB4.'SOUSTYPE'       : 'AMORTISSEMENT'
        TAB4.'AMORTISSEMENT'  : damping matrix (RIGIDITE type)


    4/ TAB5 :
      -------
        TAB5.'SOUSTYPE'   : 'LIAISON'
        TAB5.'LIAISON_A'  : TABLE of LIAISON_A subtype, defining
                            the linkages on base A
        TAB5.'LIAISON_B'  : TABLE of LIAISON_B subtype, defining
                            the linkages on base B

        Example :
                   TLIA = TABLE 'LIAISON'   ;
                   TTLB = TABLE 'LIAISON_B' ;
                   TLIA.'LIAISON_B' = TTLB  ;
                   TTLB.1 = TL1 ;
                   TTLB.2 = TL2 ;

                   TL1 and TL2 are both tables defining linkages
                   (see section 9)
                   In the table gathering linkages ( TTLB in the
                   example ) , the tables defining linkages
                   must be found under the indices 1 to NL
                   where NL is the total number of these
                   linkages.

    5/ TAB6 :
      -------
        TAB6.'SOUSTYPE' : 'CHARGEMENT'
        TAB6.'BASE_A'   : external loading in base A (CHARGEMENT
                          type)
        TAB6.'BASE_B'   : external loading in basis B (CHARGEMENT
                          type)
        It is used to calculate (and update) the moments due to 
        forces acting on the linkage points, in the case of rigid
        body rotation. If one wants to take into account the 
        influence of these forces on the translation mouvements of
        the solid, he must define these forces as BASE_A loading too.

    6/ TAB7 :
      -------
        TAB7.'SOUSTYPE'     : 'INITIAL'

          case 1: initial values of the unknowns
        TAB7.'DEPLACEMENT'  : initial displacements (CHPOINT type)
        TAB7.'VITESSE'      : initial velocities    (CHPOINT type)
          These above CHPOINTS are given in the generalized coordinates
          basis. If the initial conditions are known in the nodal 
          coordinates basis, one may use the procedure CINIMOD. 

           or

          case 2: restart from a former calculation
        TAB7.'REPRISE'      : TABLE defining the calculation 
                              restart

  7/ TAB8 :
    -------
        TAB8.'SOUSTYPE'   : 'SORTIE'
        TAB8.'VARIABLE'   : TABLE of VARIABLE subtype, defining the
                            variables to be saved. By default the
                            displacement and velocity at output step
                            will be saved.

        The following variables can be saved :

          - the displacement at half step prior to the output step             
          - the velocity at half step prior to the output step                  
          - the acceleration at output step
          - the acceleration at half step prior to the output step
          - the work of external forces from the beginning up to
            the output step
          - the work of internal forces (stiffnes and damping and 
            linkage forces) from the beginning up to the output step

        The following strings are the indices for this table :

              'DEPLACEMENT'        |
              'VITESSE'            |  VRAI (TRUE) if this variable is
              'DEPLACEMENT_1/2'    |  requested
              'VITESSE_1/2'        |
              'ACCELERATION'   '   |  FAUX (FALSE) if it is not requested
              'ACCELERATION_1/2'   |
              'TRAVAIL_EXTERIEUR'  |
              'TRAVAIL_INTERIEUR'  |

        Example :
                   TSORT = TABLE 'SORTIE'   ;
                   TSORV = TABLE 'VARIABLE' ;
                   TSORT.'VARIABLE' = TSORV ;
                   TSORV.'VITESSE'         = FAUX ;
                   TSORV.'DEPLACEMENT_1/2' = VRAI ;
                   TSORV.'ACCELERATION'    = VRAI ;

        Nota : The computation of 'TRAVAIL_EXTERIEUR' and
               'TRAVAIL_INTERIEUR' for the linkages of '.._FLUIDE'
               type is not completed.

        TAB8.'LIAISON_A'  : TABLE of LIAISON_A subtype, defining
                            the linkages on base A to be saved.

        TAB8.'LIAISON_B'  :  TABLE of LIAISON_B subtype, defining
                            the linkages on base B to be saved.


        The index for this table is the table defining the linkage to
        be saved the value of which is VRAI (TRUE) if it is requested to
        have all the linkage internal variables.

        Example :
                   TSORT = TABLE 'SORTIE'    ;
                   TSORL = TABLE 'LIAISON_A' ;
                   TSORT.'LIAISON_A' = TSORL ;
                   TSORL.TL1 = VRAI ;
                   TSORL.TL2 = VRAI ;

                   TL1 and TL2 are both tables defining linkages       
        (see section 9)

        If its internal variables are selected, they must be given
        in a table. The names of these variables are the indices of 
        this table, and their values are VRAI (TRUE) or FAUX (FALSE).
        See section 8
        for the definition of internal variables for each type of
        linkage.
      
        Example :
                   TSORT = TABLE 'SORTIE'    ;
                   TSORL = TABLE 'LIAISON_A' ;
                   TSORT.'LIAISON_A' = TSORL ;
                   TVAR  = TABLE 'VARIABLE'    ;
                   TVAR.'FORCE_DE_CHOC' = VRAI ;
                   TVAR.'DEPLACEMENT'   = FAUX ;
                   TSORL.TL1 = TVAR ;
                   TL1 is a table which defines a linkage (see
                   section 9)

    8/ TAB1 :
      -------
        TAB1.'SOUSTYPE'        : 'RESULTAT_DYNE'
        TAB1.'TEMPS_DE_SORTIE' : list of output times
        TAB1.'REPRISE'         : TABLE containing the information
                                 for a possible restart

        Depending on output requests :
           TAB1.I
           TAB1.TL1

       TAB1.I   : TABLE containing the results of the I-th output
                  step. The indices for this table depend on the
                  requested variables, the result is a CHPOINT.
                 

                  The possibles indices are  :    'DEPLACEMENT'
                                                  'VITESSE'
                                                  'DEPLACEMENT_1/2'
                                                  'VITESSE_1/2'
                                                  'ACCELERATION'
                                                  'ACCELERATION_1/2'

       TAB1.TL1 : TABLE containing the linkage results.
                  TL1 is a table which defines a linkage.
                  The indices for this table depend on the linkage
                  internal variables. (they are the table indices).
                  The result is a LISTREEL.
                 
                  For the linkage POINT_PLAN base A, the indices are :
                                          'DEPLACEMENT'
                                          'FORCE_DE_CHOC'
                  if damping              'VITESSE_NORMALE'

                  For the linkage POINT_PLAN base B, and
                      the linkage POINT_CERCLE base B,
                  the indices are :
                                          'UX', 'UY', 'UZ', ...
                                          'FORCE_DE_CHOC'
                  if damping              'VITESSE_NORMALE'

                  For the linkage POINT_POINT base B, the indices are :
                                          'UX_POINT_A', 'UY_POINT_A', ..
                                          'UX_POINT_B', 'UY_POINT_A', ..
                                          'FORCE_DE_CHOC_POINT_A'
                                          'FORCE_DE_CHOC_POINT_B'
                  if damping              'VITESSE_NORMALE'


                  For the linkage POINT_POINT_FROTTEMENT base B,  
                                        the indices are :
                                          'UX_POINT_A', 'UY_POINT_A', ..
                                          'UX_POINT_B', 'UY_POINT_A', ..
                                          'FORCE_DE_CHOC_POINT_A'
                                          'FORCE_DE_CHOC_POINT_B'
                                          'FORCE_DE_CHOC_TANGENTIELLE         
                                          'PUISSANCE_USURE_INSTANTANEE'         
                   if damping             'VITESSE_NORMALE'


                  For the linkage POINT_CERCLE_FROTTEMENT base B, and
                      the linkage POINT_PLAN_FROTTEMENT base B, 
                                         the indices are :
                                          'UX', 'UY', 'UZ', ...
                                          'FORCE_DE_CHOC_NORMALE'
                                          'FORCE_DE_CHOC_TANGENTIELLE'
                                          'PUISSANCE_USURE_INSTANTANEE'
                   if damping             'VITESSE_NORMALE'
                  These results are available for the linkage 
                  POINT_CERCLE_MOBILE also. In this case the displacements 
                  and the velocities are the relative displacements and 
                  velocities of the point with respect to the circle.


                  For the linkage CERCLE_CERCLE_FROTTEMENT base B, and
                      the linkage CERCLE_PLAN_FROTTEMENT base B,
                                         the indices are :
                                          'UX_POINT_FIBRE_NEUTRE'
                                          'UY_POINT_FIBRE_NEUTRE'
                                          'UZ_POINT_FIBRE_NEUTRE' ...
                                          'VX_POINT_CONTACT'
                                          'VY_POINT_CONTACT'
                                          'VZ_POINT_CONTACT' ...
                                          'FORCE_DE_CHOC_NORMALE'
                                          'FORCE_DE_CHOC_TANGENTIELLE'
                                          'MX_POINT_FIBRE_NEUTRE'
                                          'MY_POINT_FIBRE_NEUTRE'
                                          'MZ_POINT_FIBRE_NEUTRE' ...
                                          'RX_POINT_FIBRE_NEUTRE'
                                          'RY_POINT_FIBRE_NEUTRE'
                                          'RZ_POINT_FIBRE_NEUTRE' ...
                                          'PUISSANCE_USURE_INSTANTANEE'
                    if damping            'VITESSE_NORMALE'

                   For the linkage PROFIL_PROFIL_INTERIEUR base B, and
                       the linkage PROFIL_PROFIL_EXTERIEUR base B,
                                         the indices are  :
                                          'UX', 'UY', 'UZ', ...
                                          'FORCE_DE_CHOC'

                   For the linkage POINT_PLAN_FLUIDE base A,
                                         the indices are  :
                                          'DEPLACEMENT'
                                          'VITESSE_NORMALE'
                                          'MASSE_AJOUTEE'
                                          'FORCE_CONVECTION'
                                          'FORCE_VISCOSITE'
                                          'FORCE_PERTE_DE_CHARGE'

                  For the linkage POINT_PLAN_FLUIDE base B,
                                          the indices are  :
                                          'UX', 'UY', 'UZ'
                                          'VITESSE_NORMALE'
                                          'ACCELERATION_NORMALE'
                                          'FORCE_INERTIE'
                                          'FORCE_CONVECTION'
                                          'FORCE_VISCOSITE'
                                          'FORCE_PERTE_DE_CHARGE'

                  For the linkage COUPLAGE_DEPLACEMENT base A,
                                         the indices are  :
                                          'DEPLACEMENT'
                                          'FORCE_DE_COUPLAGE_DEPLACEMENT

                  For the linkage COUPLAGE_VITESSE base A,
                                         the indices are  :
                                          'DEPLACEMENT'
                                          'VITESSE'
                                          'FORCE_DE_COUPLAGE_VITESSE'

                  For the linkage POLYNOMIALE base A,
                                          the index is  :
                                           'FORCE_POLYNOMIALE'

                  For the linkage POINT_POINT_DEPLACEMENT_PLASTIQUE base B,
                  the indices are :
                                          'UX_POINT_A', 'UY_POINT_A', ..
                                          'UX_POINT_B', 'UY_POINT_A', ..
                                          'FORCE_DE_CHOC_POINT_A'
                                          'FORCE_DE_CHOC_POINT_B'
                                          'DEPLACEMENT_PLASTIQUE'
                  if damping              'VITESSE_NORMALE'

                  For the linkage POINT_POINT_ROTATION_PLASTIQUE base B,
                  the indices are :
                                          'RX_POINT_A', 'RY_POINT_A', ..
                                          'RX_POINT_B', 'RY_POINT_A', ..
                                          'MOMENT_DE_CHOC_POINT_A'
                                          'MOMENT_DE_CHOC_POINT_B'
                                          'ROTATION_PLASTIQUE'
                  if damping              'VITESSE_ROTATION_AXIALE'




                  For the linkage LIGNE_LIGNE_FROTTEMENT base B,
                  the indices are :
                                          'FORCE_DE_CHOC_NORMALE'
                                          'FORCE_DE_CHOC_TANGENTIELLE'
                                          'CHPOINT_FORCE_DE_CHOC'
                All these results, except 'CHPOINT_FORCE_DE_CHOC', are
                LISTREEEL objects with ordinates which are the sum of 
                the values of all the slave noads.
                The CHPOINT_FORCE_DE_CHOC' has two components : the 
                normal and the tangential force of each node. It must 
                be explicitly declared in the output specification.


                  For the linkage LIGNE_CERCLE_FROTTEMENT base B,
                  the indices are :
                                          'FORCE_DE_CHOC_NORMALE'
                                          'FORCE_DE_CHOC_TANGENTIELLE'
                                          'CHPOINT_FORCE_DE_CHOC'
                All these results, except 'CHPOINT_FORCE_DE_CHOC', are
                LISTREEEL objects with ordinates which are the sum of 
                the values of all the slave noads.
                The CHPOINT_FORCE_DE_CHOC' has two components : the 
                normal and the tangential force of each node. It must 
                be explicitly declared in the output specification.


                 For the linkage PALIER_FLUIDE base B,
                 the indices are :
                                           'UY_ARBRE'       
                                           'UZ_ARBRE'       
                                           'VY_ARBRE'       
                                           'VZ_ARBRE'       
                                           'FY_ARBRE'       
                                           'FZ_ARBRE'       
                                           'TRAVAIL_FLUIDE'
                All these results are LISTREEEL objects with
                ordinates which are the instant values of the
                above quantities.


           For the linkages with damping, as well as the polynomial
           or hydrodynamic bearing linkages, the velocities are
           calculated in the following way :

                xvit = (xdep - xdepm1) / pdts2
                     xvit   : calculated velocity
                     xdep   : displacement at step m
                     xdepm1 : displacement at step m-1/2
                     pdts2  : time half-step


    9/ DEFINITION OF LINKAGES :
      -------------------------

    There are 20 types of linkages :
         1- linkage POINT_PLAN  A basis and B basis
         2- linkage  POINT_POINT  B basis
         3- linkage  POINT_CERCLE B basis
         4- linkage POINT_CERCLE_FROTTEMENT B basis
         5- linkage POINT_PLAN_FROTTEMENT B basis
         6- linkage  POINT_POINT_FROTTEMENT B basis                             
         7- linkage CERCLE_CERCLE_FROTTEMENT B basis
         8- linkage CERCLE_PLAN_FROTTEMENT B basis 
         9- linkage PROFIL_PROFIL_INTERIEUR B basis 
        10- linkage PROFIL_PROFIL_EXTERIEUR B basis 
        11- linkage POINT_PLAN_FLUIDE A basis and B basis
        12- linkage COUPLAGE_DEPLACEMENT A basis
        13- linkage COUPLAGE_VITESSE A basis
        14- linkage POLYNOMIALE A basis
        15- linkage POINT_CERCLE_MOBILE B basis
        16- linkage POINT_POINT_DEPLACEMENT_PLASTIQUE basis B
        17- linkage POINT_POINT_ROTATION_PLASTIQUE basis B
        18- linkage LIGNE_LIGNE_FROTTEMENT basis B
        19- linkage LIGNE_CERCLE_FROTTEMENT basis B 
        20- linkage PALIER_FLUIDE basis B


        All these linkages, except the linkages of 'PROFIL_...' 
       type and PALIER_FLUIDE type, may be taken as  conditional ones.
       This means that the linkage force is applied on
       the system only if a condition is satisfied .
        This condition is a simple assmbly of elementary
        conditions .
        These elementary conditions are of the kind
           | F  of a linkage   |  > or <  1e-20
       (The term | F  of a linkage | is equal to the square root
       of the sum of the squares of the forces acting on all the 
       points of a linkage. E.g. for the 'POINT_PLAN' B basis 
       linkage this term is equal to the contact force, whereas
       for the 'POINT_POINT' linkage it is equal to the contact 
       force multiplied by 2**.5)

       These conditions are put into action for aa linkage
     which is otherwise defined in a table TLX by :


         TLX . .... = standard definition
         TLX . TLY = vrai   ;
         TLX . TLZ  = faux  ;
           etc ...
        This means that     Ftlx will only be applied if
         |Ftly|  > 1e-20  and  |Ftlz| <1e-20  and   etc...
     It should be noted that all this applies to the fact of
     taking into account Ftlx , not to the fact of calculating it
      Only linkages of the same base may be related .
     No mutual conditionning or higher order conditionning
     are acceptable.

   1- Linkage POINT_PLAN
    -----------------------

    1.1- Linkage POINT_PLAN base A
       ------------------------------
       Impact of a point pertaining to a structure onto a fixed plane.
       In base A, a linkage is expressed on a scalar unknown.
       To express an impact POINT_PLAN (base A is the base for modal
       displacements) the user must give :
                type of linkage
                point (POINT type object)
                impact stiffness (FLOTTANT type object)
                gap (FLOTTANT type object)
                  optional :
                damping (FLOTTANT type object)


            Plane        Plane        A  structure SUPPORT point
              |           |
              |           |
              |    A      |
              |     *     |             The direction of the impact
              |     .     |             can only be given by the sign 
              |     .     |             of the gap.
              |     .positive gap
              |     .---->|
              |<----.
                negative gap


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'  =  MOT 'POINT_PLAN' ;
         TL1.'SUPPORT'       =  ...              ;
         TL1.'RAIDEUR'       =  ...              ;
         TL1.'JEU'           =  ...              ;
           with damping
         TL1.'AMORTISSEMENT' =  ...              ;


    1.2- Linkage POINT_PLAN base B
       ------------------------------
       Impact of a point pertaining to a structure onto a semi-
       infinite medium, delimited by a fixed plane.
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object)
                          normal (POINT type object)
                          stiffness impact (FLOTTANT type object)
                               or
                          elastic behaviour law (EVOLUTION type object)
                          gap (FLOTTANT type object)
                            optional :
                          damping (FLOTTANT type object)
                          yield limit (FLOTTANT type object) (in this
                          case the impact spring is considered elastic
                          perfectly plastic. In order to define an 
                          initial plastic displacement one has to 
                          include it in the gap value)
                          permanent condition (LOGIQUE type object)


                      Plane           A    structure SUPPORT point
                        |
                        |   -->     -->
                 A      |    N       N  normal perpendicular to the plane
                  *     |------>        and oriented towards the solid
                  .     |               inside.
                  .     |
                  . gap |              the gap can be negative or null
                  .<--->|



       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'  =  MOT 'POINT_PLAN' ;
         TL1.'SUPPORT'       =  ...              ;
         TL1.'NORMALE'       =  ...              ;
         TL1.'RAIDEUR'       =  ...              ;
             or
         TL1.'LOI_DE_COMPORTEMENT'  =  ...       ;
         TL1.'JEU'           =  ...              ;
           with damping
         TL1.'AMORTISSEMENT' =  ...              ;
           with plastification of impact spring
         TL1.'SEUIL_PLASTIQUE'= ...              ;
           with permanent condition
         TL1.'LIAISON_PERMANENTE' = ...          ;


    2- Linkage POINT_POINT base B
       -----------------------------
       Impact between two structures that can pertain to different
       structures.
       A table of LIAISON_ELEMENTAIRE subtype
       The data are :     type of linkage
                          first point (POINT type object)
                          second point (POINT type object)
                          normal (POINT type object)
                          impact stiffness (FLOTTANT type object)
                               or
                          elastic behaviour law (EVOLUTION type object)
                          gap (FLOTTANT type object)
                            optional :
                          damping (FLOTTANT type object)
                          permanent condition (LOGIQUE type object)


                           -->
                 Point A    N        Point B
                    * ----------->    *

                             -->
                  The normal  N  indicates the direction of the impact

       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'     ;
         TL1.'TYPE_LIAISON'  =  MOT 'POINT_POINT' ;
         TL1.'POINT_A'       =  ...               ;
         TL1.'POINT_B'       =  ...               ;
         TL1.'NORMALE'       =  ...               ;
         TL1.'RAIDEUR'       =  ...               ;
             or
         TL1.'LOI_DE_COMPORTEMENT'  =  ...       ;
         TL1.'JEU'           =  ...               ;
           with damping
         TL1.'AMORTISSEMENT' =  ...               ;
           with permanent condition
         TL1.'LIAISON_PERMANENTE' = ...          ;


    3- Linkage POINT_CERCLE base B
       ------------------------------
       Impact of a point of the structure onto a fixed circle.
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object)
                          circle offset (POINT type object)
                          normal perpendicular to the plane of the
                          circle (POINT type object)
                          circle radius (FLOTTANT type object)
                          impact stiffness (FLOTTANT type object)
                            optional :
                          damping (FLOTTANT type object)

                           Y ^
                             |
                            .|.
                         .   |   .            O   circle centre  
                       .     |     .
                             |                A   structure point 
                      .   A  *------.-->
                          *  O           X    -->
                       .           .          AO  circle offset
                         .       .
                            . .
                                              ->
                                              N  normal perpendicular
                          Z  ^                   to the plane of the 
                             |  ->               circle
                             |  N             R  circle radius
                             |
                      ...............----->
                                           X
                                R
                             ------->



       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'      ;
         TL1.'TYPE_LIAISON'  =  MOT 'POINT_CERCLE' ;
         TL1.'SUPPORT'       =  ...                ;
         TL1.'EXCENTRATION'  =  ...                ;
         TL1.'NORMALE'       =  ...                ;
         TL1.'RAIDEUR'       =  ...                ;
         TL1.'RAYON'         =  ...                ;
           with damping
         TL1.'AMORTISSEMENT' =  ...                ;


    4- Linkage POINT_CERCLE_FROTTEMENT base B
       ----------------------------------------
       Impact of a point of the structure onto a fixed circle,
       taking into account the dry friction in the contact tangent plane 
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object)
                          circle offset (POINT type object)
                          normal perpendicular to the plane of the
                          circle (POINT type object)
                          circle radius (FLOTTANT type object)
                          impact stiffness (FLOTTANT type object)
                          sliding coefficient (FLOTTANT type
                          object)
                          adherence stress coefficient (FLOTTANT type
                          object)
                          tangential stiffness (FLOTTANT type
                          object)
                          tangential damping (FLOTTANT type
                          object)
                            optional :
                          impact damping (FLOTTANT type object)

                           Y ^
                             |
                            .|.
                         .   |   .            O   circle centre  
                       .     |     .
                             |                A   point of the structure
                      .   A  *------.-->
                          *  O           X    -->
                       .           .          AO  circle offset
                         .       .
                            . .
                                              ->
                                              N  normal perpendicular to
                          Z  ^                   the plane of the 
                             |  ->               circle
                             |  N             
                             |                R  circle radius
                      ...............----->
                                           X
                                R
                             ------->

       Nota : When the initial conditions make the linkage effective
              from the very beginning of the calculation, the 
              tangential force is obtained in assuming, a priori, a
              adherence stress phase, at this very moment.


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'      ;
         TL1.'TYPE_LIAISON'             =  MOT 'POINT_CERCLE_FROTTEMENT'
         TL1.'SUPPORT'                  =  ...                ;
         TL1.'EXCENTRATION'             =  ...                ;
         TL1.'NORMALE'                  =  ...                ;
         TL1.'RAIDEUR'                  =  ...                ;
         TL1.'RAYON'                    =  ...                ;
         TL1.'COEFFICIENT_GLISSEMENT'   =  ...                ;
         TL1.'COEFFICIENT_ADHERENCE'    =  ...                ;
         TL1.'RAIDEUR_TANGENTIELLE'     =  ...                ;
         TL1.'AMORTISSEMENT_TANGENTIEL' =  ...                ;
           with dampingal 
         TL1.'AMORTISSEMENT'            =  ...                ;


    5.- Linkage POINT_PLAN_FROTTEMENT base B
      -----------------------------------------
       Impact of a point pertaining to a structure on a semi-
       infinite medium, delimited by a fixed plane.
       The data are :     type of linkage
                          point (POINT type object)
                          normal (POINT type object)
                          impact stiffness (FLOTTANT type object)
                          gap (FLOTTANT type object)
                          sliding coefficient (FLOTTANT type
                          object)
                          adherence stress coefficient (FLOTTANT type
                          object)
                          tangential stiffness (FLOTTANT type
                          object)
                          tangential damping (FLOTTANT type
                          object)
                            optional :
                          impact damping (FLOTTANT type object)


                      Plan           A  structure SUPPORT point
                        |
                        |   -->     -->
                 A      |    N       N  normal perpendicular to the 
                  *     |------>        plane and oriented towards the   
                  .     |               inside of the solid
                  .     |
                  . gap |               The gap can be negative or null
                  .<--->|

       Nota : When the initial conditions make the linkage effective
              from the very beginning of the calculation, the
              tangential force is obtained in assuming, a priori, a
              adherence stress phase at this very moment.

       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'             =  MOT 'POINT_PLAN_FROTTEMENT' ;
         TL1.'SUPPORT'                  =  ...                ;
         TL1.'NORMALE'                  =  ...                ;
         TL1.'RAIDEUR'                  =  ...                ;
         TL1.'JEU'                      =  ...                ;
         TL1.'COEFFICIENT_GLISSEMENT'   =  ...                ;
         TL1.'COEFFICIENT_ADHERENCE'    =  ...                ;
         TL1.'RAIDEUR_TANGENTIELLE'     =  ...                ;
         TL1.'AMORTISSEMENT_TANGENTIEL' =  ...                ;
           with damping
         TL1.'AMORTISSEMENT'            =  ...                ;



    6.- Linkage POINT_POINT_FROTTEMENT base B
      ----------------------------------------
       Impact of two points that can pertain to different structures.
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          first point (POINT type object)
                          second point (POINT type object)
                          normal (POINT type object)
                          impact stiffness (FLOTTANT type object)
                          gap (FLOTTANT type object)
                          sliding coefficient (FLOTTANT type
                          object)
                          adherence stress coefficient (FLOTTANT type
                          object)
                          the tangential stiffness (FLOTTANT type
                          object)
                          tangential damping (FLOTTANT type
                          object)
                            optional :
                          damping (FLOTTANT type object)


                           -->
                 Point A    N        Point B
                    * ----------->    *

                             -->
                 The normal  N  indicates the direction of the impact

       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'     ;
         TL1.'TYPE_LIAISON'  =  MOT 'POINT_POINT_FROTTEMENT';
         TL1.'POINT_A'       =  ...               ;
         TL1.'POINT_B'       =  ...               ;
         TL1.'NORMALE'       =  ...               ;
         TL1.'RAIDEUR'       =  ...               ;
         TL1.'JEU'           =  ...               ;
         TL1.'COEFFICIENT_GLISSEMENT'   =  ...                ;
         TL1.'COEFFICIENT_ADHERENCE'    =  ...                ;
         TL1.'RAIDEUR_TANGENTIELLE'     =  ...                ;
         TL1.'AMORTISSEMENT_TANGENTIEL' =  ...                ;
           with damping
         TL1.'AMORTISSEMENT' =  ...               ;

       Nota : When the initial conditions make the linkage effective
              from the very beginning of the calculation, the
              tangential force is obtained in assuming, a priori, a
              adherence stress phase at this very moment.



    7- Linkage CERCLE_CERCLE_FROTTEMENT base B
       -----------------------------------------
       Impact of a circle represented by a point A pertaining to a
       structure on a fixed circle, taking into account the dry 
       friction in the contact tangent plane. 
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object)
                          internal circle radius (support)
                          (FLOTTANT type object)
                          circle offset (POINT type object)
                          normal perpendicular to the plane of
                          circle (POINT type object)
                          external circle radius (thrust)
                               (FLOTTANT type object)
                          impact stiffness (FLOTTANT type object)
                          sliding coefficient (FLOTTANT type
                          object)
                          grip coefficient (FLOTTANT type
                          object)
                          tangential stiffness (FLOTTANT type
                          object)
                          tangential damping (FLOTTANT type
                          object)
                            optional :
                          impact damping (FLOTTANT type object)

                             Y ^
                               |
                              +|+
                           +   |   +
                         +     |     +
                       +       |       +
                      +        |        +
                     +         |         +
                    +    ...   |          +
                       .     . *---------------->
                    + .  A*   .O          +    X
                     + *     .           +
                      + P...            +
                       +    . .        +
                         +           +       ->
                           +       +
                              + +
                   -->
                   AO   circle offset

                    O   external circle centre (thrust)

                    A   internal circle centre (support)

                    P   support-thrust point of contact 

                   AP   internal circle radius (support)


                            Z  ^
                               |  ->
                               |  N
                               |
                    +++++++++++++++++++++++---->
                                               X
                                    R
                               ----------->

                   ->
                   N  normal perpendicular to the circle plane

                   R  external circle radius (thrust)


       Nota : When the initial conditions make the linkage effective
              from the very beginning of the calculation, the
              tangential force is obtained in assuming, a priori, a 
              adherence stress phase at this very moment.


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'      ;
         TL1.'TYPE_LIAISON'             = MOT 'CERCLE_CERCLE_FROTTEMENT'
         TL1.'SUPPORT'                  =  ...                ;
         TL1.'RAYON_SUPPORT'            =  ...                ;
         TL1.'EXCENTRATION'             =  ...                ;
         TL1.'NORMALE'                  =  ...                ;
         TL1.'RAIDEUR'                  =  ...                ;
         TL1.'RAYON_BUTEE'              =  ...                ;
         TL1.'COEFFICIENT_GLISSEMENT'   =  ...                ;
         TL1.'COEFFICIENT_ADHERENCE'    =  ...                ;
         TL1.'RAIDEUR_TANGENTIELLE'     =  ...                ;
         TL1.'AMORTISSEMENT_TANGENTIEL' =  ...                ;
           with damping
         TL1.'AMORTISSEMENT'            =  ...                ;


    8.- Linkage CERCLE_PLAN_FROTTEMENT base B
      -----------------------------------------
       Impact of a circle represented by a point A pertaining to a
       structure on a semi-infinite medium, delimited by a fixed plane.
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object)
                          circle radius (FLOTTANT type object)
                          normal (POINT type object)
                          impact stiffness (FLOTTANT type object)
                          gap (FLOTTANT type object)
                          sliding coefficient (FLOTTANT type
                          object)
                          adherence stress coefficient (FLOTTANT type
                          object)
                          tangential stiffness (FLOTTANT type
                          object)
                          tangential damping (FLOTTANT type
                          object)
                            optional :
                          impact damping  (FLOTTANT type object)


                                  Plane

                                    |
                           +        |   -->
                         +   + P    |    N
                        + A*  *     |------>
                         +   +.     |
                           +  .     |
                              .     |
                              .gap |
                              .<--->|

                   A  structure SUPPORT circle centre

                   P  circle-plane point of contact 

                   AP circle radius

                   ->
                   N  normal perpendicular to the plane and oriented 
                      towards the solid inside.

                   The gap can be negative or null.


       Nota : When the initial conditions make the linkage effective
              from the very beginning of the calculation, the
              tangential force is obtained in assuming, a priori, a
              adherence stress phase at this very moment.

       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'             =  MOT 'CERCLE_PLAN_FROTTEMENT';
         TL1.'SUPPORT'                  =  ...                ;
         TL1.'RAYON_SUPPORT'            =  ...                ;
         TL1.'NORMALE'                  =  ...                ;
         TL1.'RAIDEUR'                  =  ...                ;
         TL1.'JEU'                      =  ...                ;
         TL1.'COEFFICIENT_GLISSEMENT'   =  ...                ;
         TL1.'COEFFICIENT_ADHERENCE'    =  ...                ;
         TL1.'RAIDEUR_TANGENTIELLE'     =  ...                ;
         TL1.'AMORTISSEMENT_TANGENTIEL' =  ...                ;
           with damping
         TL1.'AMORTISSEMENT'            =  ...                ;


    9.- Linkage PROFIL_PROFIL_INTERIEUR base B
      -----------------------------------------
       Impact of a section represented by a point A pertaining to a
       structure on a fixed section.
       The section represented by the point A is inside the fixed
       section.
       The given normal is perpendicular to the plane composed of
       the sections.
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object)
                          mobile section (MAILLAGE type object)
                          fixed section (MAILLAGE type object)
                          normal (POINT type object)
                          impact stiffness (FLOTTANT type object)
                          stiffness exponent (FLOTTANT type object)



                    |-------------|
                    |             |<---  fixed section
                    |  +++++++++  |
                    |  +       +  |
                    |  +  A*   +<------  mobile section connected with 
                    |  +       +  |      the structure point A
                    |  +++++++++  |
                    |             |
                    |-------------|


                           ^  ->
                           |  N
                           |
                           |
                    ---+++++++++---

                   ->
                   N  normal perpendicular to the sections plane


       Nota : 1- The sections must be oriented anti clockwise
              2- In the rest position, both the mesh sections must
                 be deprived of points of intersection
              3- The normal impact force is calculated as follows :
                                        b
                         F = -K * (area)

                    area : section surface which passed through
                           the fixed section
                       K : impact stiffness supplied by the user
                       b : stiffness exponent supplied by the user


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'      =  MOT 'PROFIL_PROFIL_INTERIEUR' ;
         TL1.'SUPPORT'           =   ...        ;
         TL1.'PROFIL_MOBILE'     =   ...        ;
         TL1.'PROFIL_FIXE'       =   ...        ;
         TL1.'NORMALE'           =   ...        ;
         TL1.'RAIDEUR'           =   ...        ;
         TL1.'EXPOSANT_RAIDEUR'  =   ...        ;


   10.- Linkage PROFIL_PROFIL_EXTERIEUR base B
      -----------------------------------------
       Impact section represented by a point A pertaining to a
       structure on a fixed section.
       The section represented by the point A is outside the fixed
       section.
       The given normal is perpendicular to the plane composed of 
       the sections.
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object) 
                          mobile section (MAILLAGE type object)
                          fixed section (MAILLAGE type object)
                          normal (POINT type object)
                          impact stiffness (FLOTTANT type object)
                          stiffness exponent (FLOTTANT type object)



              |-------|
              |       |<---------   fixed section
              |       |  +++++++
              |       |  +     +
              |       |  + A*  +<---  mobile section connected with
              |       |  +     +      the structure point A
              |       |  +++++++
              |       |
              |-------|


                            ^  ->
                            |  N
                            |
                            |
              ---------  +++++++

                   ->
                   N  normal perpendicular to the sections plane


       Nota : 1- The sections must be oriented anti clockwise
              2- In the rest position, both the mesh sections must
                 be deprived of intersection points 
              3- The normal impact force is calculated as follows :
                                        b
                         F = -K * (area)

                    area : section surface which passed through
                           fixed section
                       K : impact stiffness supplied by the user
                       b : stiffness exponent supplied by the user

       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'      =  MOT 'PROFIL_PROFIL_EXTERIEUR' ;
         TL1.'SUPPORT'           =   ...        ;
         TL1.'PROFIL_MOBILE'     =   ...        ;
         TL1.'PROFIL_FIXE'       =   ...        ;
         TL1.'NORMALE'           =   ...        ;
         TL1.'RAIDEUR'           =   ...        ;
         TL1.'EXPOSANT_RAIDEUR'  =   ...        ;


   11.1- Linkage POINT_PLAN_FLUIDE base A
         ---------------------------------
       Impact of a point pertaining to a structure on a fixed plane.
       There is a film of fluid between the plane and the point.
       In base A, a linkage is expressed on a scalar unknown.
       To account for an impact PLAN_FLUIDE (base A is the base of
       real displacements) the following must be provided :
               type of linkage
               support (POINT type object)
               inertia coefficient CI (FLOTTANT type object)
               convection coefficient  CC (FLOTTANT type object)
               viscosity coefficient CV (FLOTTANT type object)
               remoteness pressure loss coefficient CPE
                              (FLOTTANT type object)
               proximity pressure loss coefficient CPR
                              (FLOTTANT type object)
               fluid gap (FLOTTANT type object)


            Plane       Plane        A  structure SUPPORT point
              |           |
              |           |
              |    A      |
              |     *     |             the impact direction can only be
              |     .     |             given by the sign of the gap
              |     .     |               
              |     . positive gap
              |     .---->|
              |<----.
                negative gap

           the velocity is calculated in the following way :
                xvit = (xdep - xdepm1) / pdts2
                     xvit   : calculated velocity
                     xdep   : displacement at step m
                     xdepm1 : displacement at step m-1/2
                     pdts2  : time half-step

          the added mass is calculated as follows and is added to
          the left-hand side terms of the following equation :
                m =  CI / | gap - xdep |
          the convection force is calculated as follows :
                              2                 2
                F = -CC * xvit  / ( gap - xdep )   if gap >0

                              2                 2
                F =  CC * xvit  / ( gap - xdep )   if gap <0
          the viscosity force is calculated as follows :
                                               3
                F = -CV * xvit / | gap - xdep |
          the pressure loss force is calculated as follows :
             if xvit > 0                                 2
                F = -CPE * xvit * |xvit| / | gap - xdep |
             if xvit < 0                                 2
                F = -CPR * xvit * |xvit| / | gap - xdep|


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'     =  MOT 'POINT_PLAN_FLUIDE' ;
         TL1.'SUPPORT'                         =    ...    ;
         TL1.'COEFFICIENT_INERTIE'             =    ...    ;
         TL1.'COEFFICIENT_CONVECTION'          =    ...    ;
         TL1.'COEFFICIENT_VISCOSITE'           =    ...    ;
         TL1.'COEFFICIENT_P_D_C_ELOIGNEMENT'   =    ...    ;
         TL1.'COEFFICIENT_P_D_C_RAPPROCHEMENT' =    ...    ;
         TL1.'JEU_FLUIDE'                      =    ...    ;


   11.2- Linkage POINT_PLAN_FLUIDE base B
         ---------------------------------
       Impact of a point pertaining to a structure on a semi-infinite
       medium, delimited by a fixed plane.
       There is a film of fluid between the plane and the point.
       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are : 
               type of linkage
               support (POINT type object)
               normal (POINT type object)
               inertia coefficient CI (FLOTTANT type object)
               convection coefficient CC (FLOTTANT type object)
               viscosity coefficient CV (FLOTTANT type object)
               remoteness pressure loss coefficient CPE
                              (FLOTTANT type object)
               proximity pressure loss coefficient CPR
                              (FLOTTANT type object)
               fluid gap (FLOTTANT type object)


                      Plan           A  structure SUPPORT point
                        |
                        |   -->     -->
                 A      |    N       N  normal perpendicular to the plane
                  *     |------>        and directed towards the solid
                  .     |               inside.
                  .     |
                  .gap |               The gap must be positive.
                  .<--->|


           the velocity is calculated as follows :
                xvit = (xdep - xdepm1) / pdts2
           the acceleration is calculated as follows :
                xacc = (xvit - xvitm1) / pdts2
                     xvit   : calculated velocity
                     xacc   : calculated acceleration
                     xdep   : displacement at step m
                     xdepm1 : displacement at step m-1/2
                     xvit   : velocity at step m
                     xvitm1 : velocity at step m-1/2
                     pdts2  : time half-step

          the force of inertia is calculated as follows :
                F = -CI * xacc / ( xdep + gap )
          the convection force is calculated as follows :
                              2                 2
                F =  CV * xvit  / ( xdep + gap )
          the viscosity force is calculated as follows :
                                               3
                F = -CC * xvit / ( xdep + gap )
          the pressure loss force is calculated as follows :
             if xvit > 0                                 2
                F = -CPE * xvit * |xvit| / ( xdep + gap )
             if xvit < 0                                 2
                F = -CPR * xvit * |xvit| / ( xdep + gap )


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'     =  MOT 'POINT_PLAN_FLUIDE' ;
         TL1.'SUPPORT'                         =    ...    ;
         TL1.'NORMALE'                         =    ...    ;
         TL1.'COEFFICIENT_INERTIE'             =    ...    ;
         TL1.'COEFFICIENT_CONVECTION'          =    ...    ;
         TL1.'COEFFICIENT_VISCOSITE'           =    ...    ;
         TL1.'COEFFICIENT_P_D_C_ELOIGNEMENT'   =    ...    ;
         TL1.'COEFFICIENT_P_D_C_RAPPROCHEMENT' =    ...    ;
         TL1.'JEU_FLUIDE'                      =    ...    ;


   12.-  Linkage COUPLAGE_DEPLACEMENT base A
         ------------------------------------
       This linkage calculates a force applied to a mode i
       proportional to the displacement stemming from a mode j.

                        Fi = coeff. * Qj

       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are : 
               type of linkage
               support (POINT type object) representing the mode
                          on which the force is applied
               origin (POINT type object) representing the mode
                          from which the force is stemming
               proportional coefficient between the force and the
                          displacement (FLOTTANT type object)


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'     =  MOT 'COUPLAGE_DEPLACEMENT' ;
         TL1.'SUPPORT'                            =    ...    ;
         TL1.'ORIGINE'                            =    ...    ;
         TL1.'COEFFICIENT'                        =    ...    ;


   13.-  Linkage COUPLAGE_VITESSE base A
         --------------------------------
       This linkage calculates a force applied to a mode i
       proportional to the velocity stemming from the mode j.
                                      .
                        Fi = coeff. * Qj

       A table of LIAISON_ELEMENTAIRE subtype must be defined
       The data are : 
               type of linkage
               support (POINT type object) representing the mode
                          on which the force is applied
               origin  (POINT type object) representing the mode 
                          from which the force is stemming
               proportional coefficient between the force and
                          the velocity (FLOTTANT type object)

      The velocity is calculated as follows :
                xvit = (xdep - xdepm1) / pdts2
      where :   xvit  is the calculated velocity
                xdep is the displacement at step m
                xdepm1 is the displacement at step  m-1/2
                pdts2 is the time half-step


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'    ;
         TL1.'TYPE_LIAISON'     =  MOT 'COUPLAGE_VITESSE' ;
         TL1.'SUPPORT'                            =    ...    ;
         TL1.'ORIGINE'                            =    ...    ;
         TL1.'COEFFICIENT'                        =    ...    ;

     14.- Linkage POLYNOMIALE base A
          ---------------------------
        This linkage calculates a force applied to a mode i, composed of
        a set of contributions stemming from other modes (modes j) :

                       b           .c       '        d          .e       '
        f   =  a   [  Q  (t - T )  Q  (t - T ) ]  [ Q  (t - T ) Q  (t - T ) ] ..
         i      i      j       j    j       j        k       k   k       k
        
        with : Q  = < q - J > si J  >= 0     <.> being the positive part of .
                j      j   d      d
                  = < J - q > si J  < 0
                       d   j      d
               .      .
               Q  = < q - J > si J  >= 0     <.> being the positive part of .
                j      j   v      v
                          .
                  = < J - q > si J  < 0
                       v   j      v

        A table of LIAISON_ELEMENTAIRE subtype must be specified.
        The data are :
                - type of linkage : POLYNOMIALE
                - support (POINT type object) representing the mode i on
                  which the linkage is applied
                - a coefficient (FLOTTANT type object)
        and for each modal contribution, a table of CONTRIBUTION subtype
        referred to in the previous table, at the index of the starting point 
        of the j mode containing :
                - displacement exponent (FLOTTANT type object)
                - displacement term of delay (FLOTTANT type object)
                - velocity exponent (FLOTTANT type object)
                - velocity term of delay (FLOTTANT type object)
                - gap connected with the displacement
                  (FLOTTANT type object)
                - gap connected with the velocity 
                  (FLOTTANT type object)

        Notes : one of the origin modes j may be the supporting mode i.
        The indices of the table of CONTRIBUTION subtype are optional,
        the corresponding values are set to zero by default.
      
        Example of a set of data :
        
        TL1 = TABLE 'LIAISON_ELEMENTAIRE' ;
        TL1.'TYPE_LIAISON' = MOT 'POLYNOMIALE' ;
        TL1.'SUPPORT'      = ... ;   <--- supporting point 
        TL1.'COEFFICIENT'  = ... ;
        TL2 = TABLE 'CONTRIBUTION' ;
        TL1.Pj             = TL2 ;   <--- point of origin
        TL2.'EXPOSANT_DEPLACEMENT' = ... ;
        TL2.'RETARD_DEPLACEMENT'   = ... ;
        TL2.'EXPOSANT VITESSE'     = ... ;
        TL2.'RETARD_VITESSE'       = ... ;
        TL2.'JEU_DEPLACEMENT'      = ... ;
        TL2.'JEU_VITESSE'          = ... ;  

    15- Linkage POINT_CERCLE_FROTTEMENT base B
       ----------------------------------------
       Impact of a point of the structure onto a mobile circle,
       taking into account the dry friction in the contact tangent plane
       We do not take into account the rotation of the circle in its plane
       for the calculation of the relative displacements and velocities. 
       The moment of the contact force with respect to the axis of the 
       circle is also neglected.

       A table of LIAISON_ELEMENTAIRE subtype must be specified.
       The data are :     type of linkage
                          point (POINT type object)
                          circle center (POINT type object)
                          normal perpendicular to the plane of the
                          circle (POINT type object)
                          circle radius (FLOTTANT type object)
                          impact stiffness (FLOTTANT type object)
                          sliding coefficient (FLOTTANT type
                          object)
                          adherence stress coefficient (FLOTTANT type
                          object)
                          tangential stiffness (FLOTTANT type
                          object)
                          tangential damping (FLOTTANT type
                          object)
                            optional :
                          impact damping (FLOTTANT type object)

                           Y ^
                             |
                            .|.
                         .   |   .            O   circle centre  
                       .     |     .
                             |                A   point of the structure
                      .   A  *------.-->
                          *  O           X    
                       .           .          
                         .       .
                            . .
                                              ->
                                              N  normal perpendicular to
                          Z  ^                   the plane of the 
                             |  ->               circle
                             |  N             
                             |                R  circle radius
                      ...............----->
                                           X
                                R
                             ------->

       Nota : When the initial conditions make the linkage effective
              from the very beginning of the calculation, the 
              tangential force is obtained in assuming, a priori, a
              adherence stress phase, at this very moment.


       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'      ;
         TL1.'TYPE_LIAISON'             =  MOT 'POINT_CERCLE_MOBILE'
         TL1.'POINT'                    =  ...                ;
         TL1.'CERCLE'                   =  ...                ;
         TL1.'NORMALE'                  =  ...                ;
         TL1.'RAIDEUR'                  =  ...                ;
         TL1.'RAYON'                    =  ...                ;
         TL1.'COEFFICIENT_GLISSEMENT'   =  ...                ;
         TL1.'COEFFICIENT_ADHERENCE'    =  ...                ;
         TL1.'RAIDEUR_TANGENTIELLE'     =  ...                ;
         TL1.'AMORTISSEMENT_TANGENTIEL' =  ...                ;
           with damping
         TL1.'AMORTISSEMENT'            =  ...                ;  


    16- Linkage POINT_POINT_DEPLACEMENT_PLASTIQUE base B
       -------------------------------------------------
       elastoplastic impact between two points that can pertain to different
       structures.
       A table of LIAISON_ELEMENTAIRE subtype
       The data are :     type of linkage
                          first point (POINT type object)
                          second point (POINT type object)
                          normal (POINT type object)
                          behaviour law (EVOLUTION type object)
                          gap (FLOTTANT type object)
                            optional :
                          damping (FLOTTANT type object)



                           -->
                 Point A    N       Point B
                    * ---------------->*

                             -->
                  The normal  N  indicates the direction of the impact

       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'     ;
         TL1.'TYPE_LIAISON'        =  MOT 'POINT_POINT_DEPLACEMENT_PLASTIQUE' ;
         TL1.'POINT_A'             =  ...               ;
         TL1.'POINT_B'             =  ...               ;
         TL1.'NORMALE'             =  ...               ;
         TL1.'LOI_DE_COMPORTEMENT' =  ...               ;
         TL1.'JEU'                 =  ...               ;
           with damping
         TL1.'AMORTISSEMENT'       =  ...               ;


       Nota : The behaviour law describes the law force-displacement :
              - The first point of the law must be the origin : (f=0 ; X=0)
              - the second point must be the elastic limit point :
                (F=Yield force ; X=Yield displacement)
              - the other points describe the plastic part of the law.

    17- Linkage POINT_POINT_ROTATION_PLASTIQUE base B
       ----------------------------------------------
       It is a linkage in rotation between two points that can pertain to differ
       structures.
       A table of LIAISON_ELEMENTAIRE subtype
       The data are :     type of linkage
                          first point (POINT type object)
                          second point (POINT type object)
                          rotation axis (POINT type object)
                          elastoplastique/elastic behaviour law
                          between the tow points (EVOLUTION type object)
                          gap (FLOTTANT type object)
                            optional :
                          damping (FLOTTANT type object) 
                          permanent condition (LOGIQUE type object)
                          hardening model (MOT type object)    
                          elastic behavior (LOGIQUE type object)                

                                     /
                                    /                           
                              _____/_                            
                             |  __/  |                       
                   point A   * |_/|  *  Point B                         
                             |__/_|  |                       
                               /                           
                              /                                                 
                             / rotation axis 
                              

          rotation axis indicates the direction (rotation) of the impact

        Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'     ;
         TL1.'TYPE_LIAISON'        =  MOT 'POINT_POINT_ROTATION_PLASTIQUE' ;
         TL1.'POINT_A'             =  ...               ;
         TL1.'POINT_B'             =  ...               ;
         TL1.'AXE_ROTATION'        =  ...               ;
         TL1.'LOI_DE_COMPORTEMENT' =  ...               ;
         TL1.'JEU'                 =  ...               ;
           with damping
         TL1.'AMORTISSEMENT'       =  ...               ;
           with permanent condition
         TL1.'LIAISON_PERMANENTE'  =  ...               ;
           with hardening model
         TL1.'ECROUISSAGE'         = 'ISOTROPE' or 'CINEMATIQUE';
           with elastic behavior
         TL1.'COMPORTEMENT_ELASTIQUE' = ...             ;


       Nota : The behaviour law describes the law moment-rotation (if non elasti
              - The first point of the law must be the origin : (M=0 ; R=0)
              - the second point must be the elastic limit point :
                (M=Yield moment ; R=Yield rotation)
              - the other points describe the plastic part of the law.
 


    18- Linkage LIGNE_LIGNE_FROTTEMENT basis B
       -------------------------------------------------
       Impact of two lines 
       A table of LIAISON_ELEMENTAIRE subtype must be specified

       The data are     : type of linkage
                          the master line(MAILLAGE type)
                          the slave line (MAILLAGE or POINT type)
                          the sliding coefficient (FLOTTANT type)
                          the sticking coefficient (FLOTTANT type)
                          the tangentiel stiffness (FLOTTANT type)
                          the tangentiel damping  (FLOTTANT type)
                          the impact stifness (CHPOINT type)
                          the normal to the contact plane 
                                     (optional in 2D, POINT type)
                            optional :
                          the impact stiffness (CHPOINT type)
                          the research indicator (MOT type)
                          the symmetry indicator (MOT type)
        
           *---*                 *------*
               |                /        \
               *--*  --->      *  slave   *        
           master |            |  line    |
           line   *            *          *
                  |       <---  \        /
               *--*              *------*
               |
           *---*
         
         
       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'     ;
         TL1.'TYPE_LIAISON'        =  MOT 'LIGNE_LIGNE_FROTTEMENT' ;
         TL1.'LIGNE_MAITRE'            =  ...               ;
         TL1.'LIGNE_ESCLAVE'           =  ...               ;
         TL1.'NORMALE'                 =  ...               ;   
         TL1.'COEFFICIENT_GLISSEMENT'  =  ...               ;
         TL1.'COEFFICIENT_ADHERENCE '  =  ...               ;
         TL1.'RAIDEUR_TANGENTIELLE'    =  ...               ;
         TL1.'AMORTISSEMENT_TANGENTIEL'=  ...               ;
         TL1.'RAIDEURS'                =  ...               ;
         TL1.'SYMETRIE'                =  ...               ;
         TL1.'RECHERCHE'               =  ...               ;
           avec l'amortissement
         TL1.'AMORTISSEMENTS'          =  ...               ;
        

          The no-penetration area lies at the left with respect to the 
        orientation of the line meshes, if the normal is oriented 
        outwords the assumed contact plane. The line elements are of
        SEG2 type and the slave line can be restricted to one point.
        The penetration of the slave nodes in the master surface is tested.
          In orde to inverse the roles specify :
        TL1.'SYMETRIE'='GLOBALE' ou 'LOCALE'. In the case of the word
        'LOCALE' the roles are inversed only for those master noads which
        were activated during the first pass.
          The research of the impacting noads and segments can be optimized
        by specifying TL1.'RECHERCHE'='LOCALE'. A global research is done
        if TL1.'RECHERCHE'='GLOBALE' is specified.
          The stiffness and damping fields by element are defined in all
        the noads of the meshes (master and slave). The contact force on 
        a slave noad is calculated with the stiffness and damping values
        of this noad.
          For the moment, only the Oden model, described at the end of the
        manual,is available for the friction. The values of the tangential
        stiffness and damping have to be defined consequently.
       


    19- Linkage LIGNE_CERCLE_FROTTEMENT basis B
       -------------------------------------------------

       Impact of a line between a set of circles with the same normal and 
       radius or with a  cylinder of constant radius.
       A table of LIAISON_ELEMENTAIRE subtype must be specified

       The data are     : type of linkage
                          the master line(MAILLAGE type)
                          the slave line (MAILLAGE or POINT type)
                          the sliding coefficient (FLOTTANT type)
                          the sticking coefficient (FLOTTANT type)
                          the tangentiel stiffness (FLOTTANT type)
                          the tangentiel damping  (FLOTTANT type)
                          the 
                          the impact stifness (CHPOINT type)
                          the normal to the circles or cylinder
                          (POINT type)
                          the radius of the circles or cylinder.
                          (FLOTTANT type)         
                            optional :
                          the impact stiffness (CHPOINT type)
                          the research indicator (MOT type)
                          the inversion indicator (MOT type)
                          the ACTNOR indicator which indicates whether 
                          you want to recalculate the normal to the contact
                          plan at each time step.
        
       
       
       As a master line, we define the line the circles will shock against.The
       slave line is the line conataining the centers of the circles.
       To calculate a linkage line-circles, we need to enter the champoints of
       stiffness and damping for the circles.
       
       But in the case of a linkage line-cylinder, the shocking nodes are the li
       ones. the line is still defined as the master line and the cylinder axe a
       the slave one, but the inversion indicator must be given the value 'VRAI'
       The champoints needed for the calculus are the champoints for line nodes.

      
            |      |      |    |                           --------------
            |      |      |   \|/                          |            |
         ---*------*------*----                      ------|------------|-----li
            |      |      |     line           or          --------------
            |      |      |                                   cylinder
                circles
         
       Example of a set of data :

         TL1  =  TABLE  'LIAISON_ELEMENTAIRE'     ;
         TL1.'TYPE_LIAISON'            =  mot 'LIGNE_CERCLE_FROTTEMENT' ;
         TL1.'LIGNE_MAITRE'            =  ...               ;
         TL1.'LIGNE_ESCLAVE'           =  ...               ;
         TL1.'NORMALE'                 =  ...               ;
         TL1.'RAYON'                   =  ...               ;   
         TL1.'COEFFICIENT_GLISSEMENT'  =  ...               ;
         TL1.'COEFFICIENT_ADHERENCE '  =  ...               ;
         TL1.'RAIDEUR_TANGENTIELLE'    =  ...               ;
         TL1.'AMORTISSEMENT_TANGENTIEL'=  ...               ;
         TL1.'RAIDEURS'                =  ...               ;
         TL1.'SYMETRIE'                =  ...               ;
         TL1.'RECHERCHE'               =  ...               ;
         TL1.'ACTNOR'                  =  ...               ;
           with damping
         TL1.'AMORTISSEMENTS'          =  ...               ;
        

        The line elements are ofSEG2 type and the slave line can be restricted
        to one point.
        The research of the impacting noads and segments can be optimized
        by specifying TL1.'RECHERCHE'='LOCALE'. A global research is done
        if TL1.'RECHERCHE'='GLOBALE' is specified.
        The ACTNOR indicator must be given the value VRAI ou FAUX.
        The stiffness and damping CHPOINTS are defined for the shocking nodes.
        The contact force on a node is calculated with the stiffness 
        and damping values of this node.
        Currently, only the Oden model, described at the end of the
        manual,is available for the friction. The values of the tangential
        stiffness and damping have to be defined consequently.

    20- Linkage PALIER_FLUIDE basis B
       -------------------------------------

       This linkage calculate the forces generated by the fluid film
       on the shaft rotating in the hydrodynamic bearing.
       The bearings are short cylindric bearings or lobes bearings.
       The model used for forces calculation is the 'Rhodes et Li'
       model (one dimension model based on a parabolic profile of the
       pressure field).

       The bearing geometry, the fluid film caracteristics and the shaft
       whirl speed are defined in a LIAISON_ELEMENTAIRE subtyped table :

       The data are     : type of linkage
                          type of model (only RODELI is available)
                          support (POINT type object)
                          fluid viscosity (FLOTTANT type object)
                          fluid density (FLOTTANT type object)
                          bearing length (FLOTTANT type object)
                          shaft radius (FLOTTANT type object)
                          shaft whirl speed (FLOTTANT type object)
                          table of bearing geometry (TABLE type object)
                           - number of lobes
                           - admission pressure
                           - convergence criteria (FLOTTANT type object)
                             a value of 0.005 means the relative error
                             on pressure calculation migth be lower than
                             0.5% 
                           - table of lobe geometry
                             - radial gap (FLOTTANT type object)
                             - preload (FLOTTANT type object)
                             - asymetry angle (FLOTTANT type object)
                             - begining angle of the loble (FLOTTANT
                                    type object)
                             - amplitude angle of the loble (FLOTTANT
                                    type object)
                             - number of nodes for the EF calculation of
                               the pressure field (FLOTTANT type object)
                             - surrelaxation coefficient, used for the
                               numerical resolution method (FLOTTANT
                                  type object)
                           
       Nota : The rotating shaft axis is considered to be the Ox, the
              refering axe for the definition of all the angles is
              considered to be the Oy axis.
              A common value of the surrelaxation coeeficient is 1.715

              This linkage works only with the option DE_VOGELAERE

       Example of a set of data :

          TL1 = TABLE LIAISON_ELEMENTAIRE;
          TL1 . 'TYPE_LIAISON'  = MOT 'PALIER_FLUIDE';
          TL1 . 'MODELE_PALIER' = MOT 'RODELI';
          TL1 . 'POINT_SUPPORT' = Point1 ;
          TL1 . 'VISCOSITE_FLUIDE' = Flottant1 ;
          TL1 . 'RHO_FLUIDE' = Flottant2 ;
          TL1 . 'LONGUEUR_PALIER' = Flottant3 ;
          TL1 . 'RAYON_ARBRE' = Flottant4 ;
          TL1 . 'VITESSE_ARBRE' = Flottant5 ;
          TL1 . 'GEOMETRIE_PALIER' = TABLE1 ;

          TABLE1 . 'NOMBRE_LOBES' = Entier1 ;
          TABLE1 . 'PRESSION_ADMISSION' = Flottant6 ;
          TABLE1 . 'CRITERE_ARRET' = Flottant7 ;
          TABLE1 . 1 = TABLE1_1 ;
          TABLE1 . 2 = TABLE1_2 ;
          TABLE1 . ...
          TABLE1 . n = TABLE1_n ; (n = Number of lobes)

          TABLE1_1 . 'JEU_USINAGE' = Flot11a ;
          TABLE1_1 . 'ASYMETRIE'   = Flot11b ;
          TABLE1_1 . 'PRECHARGE'   = Flot11c ;
          TABLE1_1 . 'ANGLE_DEBUT' = Flot11d ;
          TABLE1_1 . 'AMPL_ANGLE'  = Flot11e ;
          TABLE1_1 . 'NB_MAILLES'  = Entier11 ;
          TABLE1_1 . 'COEF_SUR'    = Flot11f ;

                 
  Notes :
  ________

  * All the TABLES must be subtyped.

  * The base A is the base on which the equations are uncoupled,
    the base B is another base on which, for instance, the linkages 
    can be expressed.
  
  * For the friction-linkages, the Antunez and al's model (Journal of 
    Fluids and  Structures 1990 , vol 4 pp. 287-304 )is used for
    the dry friction. However, the user may use the Oden model by 
    regularizing the friction force for low velocities. In this case, 
    just give a negative value for TL1.'RAIDEUR_TANGENTIELLE' and the 
    regularizing velocity epsi (positive) for TL1.'AMORTISSEMENT_TANGENTIEL'.
    If vitt is the relative tangential velocity, fn is the normal force 
    and mg the sliding coefficient. The friction force is :
    
   
    ff = -mg*|fn| * (2 - (|vitt|/epsi) ) * (vitt/epsi)   if |vitt| < epsi
    ff = -mg*|fn| * (vitt/|vitt|)                       if |vitt| >= epsi
    
    The value for TL1.'COEFFCIENT_ADHERENCE' does not come up when this 
    friction model is used.
 
  * The user may check that the subprograms are running all right, 
    by means of "OPTION IMPI 333 ;".

  * The time spent within the subprograms can be counted by means of
    "OPTION IMPI 444 ;".



 
 
 
 
 
 
 
 
 
 
 

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