Procédures | Cast3M

* TOPOCMPL  PROCEDUR  FD218221  25/12/18    21:15:04     12429          
 
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** Procedure called by TOPOOBJE for calculating:
**
** 1 - The total mechanical or thermal compliance
**     (or, more precisely, "2 * the total elastic strain energy" in
**     mechanics, or the "total thermal compliance" in thermal problems)
**
** 2 - Its volume-normalized sensitivity (w.r.t. X)
**     Defined as  ∂cpl/∂X / vol1_e = dZ/dX * q1_e / vol1_e
**     ∂cpl/∂X does not include the implicit contribution of the
**     displacement field U(X). In other words, ∂cpl/∂X is therefore
**     not the full total sensitivity with respect to the design
**     variables X.
**
** Author:
** Guenhael Le Quilliec (LaMe - Polytech Tours)
**
** Version:
** 1.0 2025/11/28 This step was previously defined multiple times in
**                TOPOSENS and is now renamed TOPOOBJE
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DEBP TOPOCMPL mod*'MMODEL' Zmat*'MCHAML' dZdY_Z*'MCHAML'
              sig/'MCHAML' eps/'MCHAML' TA/'CHPOINT' ;
 
SI (EXIS sig) ;
 
*   Mechanical compliance
*   *********************
 
*   For each element, compliance is defined as
*   "2 * the elastic strain energy density * volume of the element"
*   = Cijkl.[1/2(diUj + djUi)].[1/2(dkUl + dlUk)].vol1_e
*   = Cijkl.EPSij.EPSkl.vol1_e = EPSij.SIGij.vol1_e = (ENER output).vol1_e
    enedst = ENER mod sig eps ;
 
*   Element field of the elastic strain energy at the centroid
    ene = INTG 'ELEM' enedst mod Zmat ;
 
*   Sensitivity field with respect to Y
*   It corresponds to the elastic strain energy divided by the penalized
*   physical density (Z), then multiplied by dZ/dY
    dcpldY = ene * dZdY_Z ;
 
*   Total compliance (2 * total elastic strain energy)
*    cpl = INTG enedst mod Zmat ;
    cpl = SOMM (EXTR ene 'VALE' 'SCAL') ;
 
SINO ;
 
*   Thermal compliance
*   ******************
 
*   For each element, "thermal compliance" is defined as
*   = K.grad(T).grad(T).vol1_e = K.(grad(T))^2.vol1_e
    grdTA = GRAD mod TA ;
    lstcpn = EXTR grdTA 'COMP' ;
    grd2TA = CHAN 'TYPE' (PSCA grdTA grdTA lstcpn lstcpn) 'SCALAIRE' ;
 
*   Conductivity field: K
    enedst = grd2TA * (EXCO 'K' Zmat 'SCAL') ;
 
*   Element field of the thermal compliance at the centroid
    ene = INTG 'ELEM' enedst mod Zmat ;
 
*   In thermal mode, INTG 'ELEM' is not evaluated at 'GRAVITE' even if
*   the input fields were defined at 'GRAVITE'
*   This issue is resolved by using CHAN 'GRAVITE'
    ene = CHAN 'GRAVITE' ene mod ;
 
*   Sensitivity field with respect to Y
*   It corresponds to the thermal compliance divided by the penalized
*   physical density (Z), then multiplied by dZ/dY
    dcpldY = ene * dZdY_Z ;
 
*   Total thermal compliance
*    cpl = INTG enedst mod Zmat ;
    cpl = SOMM (EXTR ene 'VALE' 'SCAL') ;
 
FINS ;
 
FINP cpl dcpldY ;