Maximize Band Gaps

SIMULIA Tosca Structure avoids problematic eigenfrequencies in dynamic problems with a special MINMAX formulation. Here, the object function $Φ$ for eigenfrequencies by TARGET= MINMAX is given:


$Φ \| α \frac{1}{f_{k} - f_{k}^{*}} \|$

By minimizing this expression, the eigenfrequencies f will be moved away from the value of $f_{k} *$ . With $α$ as a constant, the SIMULIA Tosca Structure commands are:


DRESP
 ID_NAME  = dresp_eig_1
 DEF_TYPE = SYSTEM
 TYPE     = DYN_FREQ
 LC_SET   = Modal,All,1
END_

...

DRESP
 ID_NAME  = dresp_eig_20
 DEF_TYPE = SYSTEM
 TYPE     = DYN_FREQ
 LC_SET   = Modal,All,20
END_

OBJ_FUNC
 ID_NAME =  move_dresp_eig_from_15Hz
 DRESP   = dresp_eig_1, 1.0, 15.
 ...
 DRESP   = dresp_eig_20, 1.0, 15.
 TARGET  = MINMAX
END_



Convergence of eigenvalues of a bandgap optimization (15 Hz)

The second eigenmode will be pushed away from 15.0 Hz. The weighting of the design response is 1.0.

Important: Flat structures should first have the eigenvalues maximized before doing the band-gap optimization because the optimizer must also be able to move some eigenvalues down.