Manual pages | Cast3M

$$$$ SPON     NOTICE  CHAT      11/09/12    21:18:10     7124           
                                             DATE     11/09/12

    Operateur SPON                           Voir aussi : SPO
    --------------   
    EVOL3 = SPON ('DEMA') 'SIGN' EVOL1 'SPEL' EVOL2 MOT1 

             'AMOR' LREEL1 'MOT2' LREEL2  ('COUL' COUL1)  MOT3;


    Description :
    _____________

    This operator makes it possible to calculate one or several
    non linear oscillator spectra EVOL3 depending on whether one
    or several damping and linear spectra are given.

    Contents :
    _________

   'DEMA'    :key word. If it is given the computed spectrum is
              the non linear spectrum with a ductility demand 
              equal to the given ductility. In this case the 
              ordinates of the result object are the relative
              displacement, pseudo-velocity or pseudo-acceleration
              corresponding to the yield limit.
              If 'DEMA'is not given the computed spectrum is the 
              non linear responce spectrum with a yield 
              displacement equal to the ratio between the maximum
              linear displacement (given by EVOL2) and the given
              ductility (first value of LREEL2). In this case the
              ordinates of the result are the relative displacement,
              pseudo-velocity or pseudo-acceleration defined in the 
              usual way.
   'SIGN'    : key word followed by :
    EVOL1    : object containing the signal of excitation with
               constant time step ( DT = CONSTANT !! )

   'SPEL'    : key word followed by :
    EVOL2    : object containing the linear spectrum with 
               ordinates in frequency. Il may be computed with
               the SPO operator. This is not obligatory because
               this evolution is used only to determine the yield
               limit if the key word 'DEMA' is not given or its
               value for the firsT iteration if 'DEMA 'is given.
               

    MOT1     : MOT for specifying the type of linear spectrum
              (EVOL2) :
              'DEPL' : spectrum in displacement
              'VITE' : spectrum in pseudo-velocity
              'ACCE' : spectrum in pseudo-acceleration

   'AMOR'    : key word followed by :
    LREEL1   : damping value(s) corresponding to the oscillator(s)
               and to the spectrum (spectra) given in EVOL2

   'MOT2'    : key word indicating a bilinear type non linear law :
              'TAKE' : binear Takeda 
              'CINE' : elastoplastic with kinematic hardening
              'ISOT' : elastoplastic with isotropic hardening
              'ELAS' : non linear elastic
    LREEL2   : object containing the properties of the non linear
               model 

               For the Takeda model :
               ----------------------
              5 FLOTTANTS. Order :

                       Force |
                             |    ___2_____
                             |   /      * /
                             | 1/*       /
                         7*  | /        /3
              _______*_______ /________/_________
                    /        /      *       Displ.
                  6/        /|   *
                  /        / |* 4
                -----5----/* |
                             |
                             |
             Figure: General Shape of the Force/Displacement Model 
                     

                - Ductility : quotient between the maximum
                  displacement and the yield displacement 

                - Teta : quotient between stiffness after elastic limit
                  (Rig2) and the linear stiffness (Rig1 = W**2). 
                  The stiffness after elastic limit is computed by :
                  Rig2 = W ** 2 * Teta

                - sfdp : stiffness degradation parameter. An unloading
                  branch is oriented towards a moment equal to
                  -sfdp*yield force (cf. notice of MATE) 

                - Beta : Pinching parameter.
                  The value of the torce pinp (cf. notice of MATE) is :
                  pinp = beta*yield force

                - Gama : parameter of cyclic softening. It is equal to 
                  the increase of the maximum deformation per unit of 
                  absorbed energy

               For the other models :
               ----------------------
                The two first values of the preceding model must be 
                given
         

   'COUL'    : key word followed by :
    COUL1    : requested color for the curves

    MOT3     : MOT for specifying the type of output :
              'DEPL' : spectrum in displacement
              'VITE' : spectrum in pseudo-velocity
              'ACCE' : spectrum in pseudo-acceleration 
              'EPSE' : spectrum in cumulated non linear deformation

    EVOL3    : EVOLUTION type result. Each curve of this object has
               a number of points equal to the points of EVOL2