# Setting of Weighting function

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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?

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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

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I'm sorry for my late reply...
Thank you very much for your detailed explanation.

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