Setting of Weighting function
Altair EmployeeGreetings,
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.
Answers
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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-03Objective Function (Minimize COMB ) = 1.47125E-02 % change = -0.29
Maximum Constraint Violation % = 0.20159E-05
Design Volume Fraction = 3.00000E-001 Mass = 5.61149E+000Subcase Weight Compliance Epsilon Weight*Comp.
1 1.000E+00 8.520537E-03 -2.098521E-03 8.520537E-03
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Sum of Weight*Compliance 8.520537E-03Note : 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
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Sum of (Weight/Eigenvalue) / Sum of Weights 4.270613E-08
Mode Normalization Factor x 1.450E+05
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Weighted Inverse Eigenvalues 6.191977E-03
Weighted Compliances 8.520537E-03
------------
Combined Compliance Index 1.471251E-02Hope this helps!
Kind Regards,
Felix
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I'm sorry for my late reply...
Thank you very much for your detailed explanation.0