Setting of Weighting function

Altair Forum User

Greetings,

I have a basic question about the optimization in Inspire 2017 7305.

It is possible to maximize the stiffness as well as the natural frequency of structures in Inspire,
but how can I decide the weighting function of these two objective functions?

In general, in such multi-objective optimizations, I think it is necessary to adjust a weighting function. 
Maybe it is performed automatically by Inspire, but how is it done? On which is focused more - maximization of stiffness, or maximization of natural frequency?

Thanks in advance. 

Altair Forum User

Hi Grasshopper,

you can maximize both simutaniously, but you can't manipulate the weightening function (which is set automatically). Inspire is using Altair Optistruct as a solver, which is calculating a compliance for each mode and the static compliance. Please see below an abstract from the topoOpt.out , located in the Inspire Scratch directory.

Combined Compliance Index

The combined compliance index is a method to consider multiple frequencies and static subcases (loadsteps, load cases) combined in a classical topology optimization. The index is defined as follows:

This is a global response that is defined for the whole structure.

The normalization factor, NORM, is used to normalize the contributions of compliances and eigenvalues. A typical structural compliance value is of the order of 1.0e4 to 1.0e6. However, a typical inverse eigenvalue is on the order of 1.0e-5. If NORM is not used, the linear static compliance requirements dominate the solution.

The quantity NORM is typically computed using the formula:

Where, Cmax is the highest compliance value in all subcases (loadsteps, load cases) and is the lowest eigenvalue included in the index.

In a new design problem, you may not have a close estimate for NORM. If this happens, OptiStruct automatically computes the NORM value based on compliances and eigenvalues computed in the first iteration step.

 

Abstract from topoOpt.out

ITERATION  39

Subcase:       1
--------------------------------------------------------------------------
 Label     x-force    y-force    z-force   x-moment   y-moment   z-moment
--------------------------------------------------------------------------
Sum-App.  0.000E+00  1.000E+03  0.000E+00 -2.000E+01  0.000E+00  1.870E+02
Sum-SPCF -6.333E-09 -1.000E+03  2.689E-11  2.000E+01 -6.171E-11 -1.870E+02
--------------------------------------------------------------------------
  the 2nd satisfied convergence ratio =  2.8748E-03

Objective Function (Minimize COMB ) =  1.47125E-02   % change =        -0.29
Maximum Constraint Violation %      =  0.20159E-05
Design Volume Fraction              = 3.00000E-001   Mass     = 5.61149E+000

 Subcase  Weight     Compliance    Epsilon                 Weight*Comp.
       1  1.000E+00  8.520537E-03 -2.098521E-03            8.520537E-03
                                                           ------------
Sum of Weight*Compliance                                   8.520537E-03

Note : Epsilon = Residual Strain Energy Ratio.

 Subcase Mode      Weight     Frequency      Eigenvalue    Weight/Eigen
       2     1   1.000E+00   3.823884E+02   5.772571E+06   1.732330E-07
       2     2   1.000E+00   9.579818E+02   3.623050E+07   2.760106E-08
       2     3   1.000E+00   9.707180E+02   3.720026E+07   2.688153E-08
       2     4   1.000E+00   1.466867E+03   8.494565E+07   1.177223E-08
       2     5   1.000E+00   1.667356E+03   1.097531E+08   9.111363E-09
       2     6   1.000E+00   1.821137E+03   1.309317E+08   7.637568E-09
                                                           ------------
Sum of (Weight/Eigenvalue) / Sum of Weights                4.270613E-08
Mode Normalization Factor                                  x  1.450E+05
                                                           ------------
Weighted Inverse Eigenvalues                               6.191977E-03
Weighted Compliances                                       8.520537E-03
                                                           ------------
Combined Compliance Index                                  1.471251E-02

 

Hope this helps!

 

Kind Regards,

Felix