DATE     98/10/09

    Opérateur VMIS                             See also :SIGM TRES 
    --------------                                       PRIN CARA 
                                                         CALP 
       VMIS1  =  VMIS  MODL1 SIG1 ( CAR1 ) ;

    Description :
    _____________

    The VMIS operator calculates a stress which is equivalent to a
 stress field. In the solid cases (2D and 3D) it coincides
 with Von Mises' stress.

      Contents :
      __________


      MODL1 : model object  (MMODEL type)

      SIG1  : CONTRAINTES (stress) field (MCHAML type, CONTRAINTES
              subtype)

      CAR1  : field of geometrical CARACTERISTIQUES required for
              the shell, beam, and pipe elements (MCHAML type,
              CARACTERISTIQUES subtype)

      VMIS1 : generated object (MCHAML type)


    Note :
    ________

    For thin shells, the equivalent stress is calculated
 from membrane-type efforts Nij and bending moments Mij, 
 and from characteristics (cf CARA operator) depending on the
 following formula :

    Seq = ( (N / EPAIS)**2 + (6 * ALFA * M / EPAIS**2)**2 ) ** 0.5

    where     N   = ( N11**2 + N22**2 - N11*N22 + 3*N12**2 ) ** 0.5
           M   = ( M11**2 + M22**2 - M11*M22 + 3*M12**2 ) ** 0.5

    For beams, the equivalent stress is calculated from
 the forces, moments, and characteristics (cf CARA operator) depending
 on the following formula :

    Seq = ( ( EFFX / SECT )**2 + ( MOMX * DX / TORS )**2

        + ( MOMY * DY / INRY )**2 + ( MOMZ * DZ / INRZ )**2 )**0.5

   For pipe elements, the equivalent stress is calculated from
 the forces, moments, and characteristics (cf CARA operator) depending
 on the following formula :

    Seq = ( ( EFFX * CFFX / SECT )**2 + ( MOMX * CFMX / TORS )**2

        + ( MOMY * CFMY / INRY )**2 + ( MOMZ * CFMZ / INRZ )**2 )
        + ( PRES * RMOY * CFPR / EPAI )**2 )**0.5

 The inertias may be modified in relation to the flexibilities
 for the elbows.