OptiStruct: Can I use buckling constraints on a topology or free-size optimization?

OptiStruct: Can I use buckling constraints on a topology or free-size optimization?

There are several barriers for buckling constraints in topology optimization:
Buckling constraints are conditional, similar to stress constraints (see Can I use stress constraints with topology or free-size optimization?). Structural instability does not exist when structural parts vanish. This results in the phenomenon of singular topology, where sudden changes of the feasible design domain occur when the density of a design element approaches zero. Gradient based optimization algorithms cannot overcome this barrier. For example, structural stability might be most critical around an opening in a panel. Instead of removing material from the boundary to improve the shape of the opening, the optimization process usually tends to try to add material to the boundary to improve the stability. This prevents the finding of more meaningful topology and shape.
Although low density material might have very little impact to structural stiffness, it can significantly impact the buckling load limits; often times a small amount of lateral support can significantly improve structural stability.
Buckling modes in vanishing areas (low density zones) have no implication to the structural integrity. How to effectively filter out these buckling modes remains another challenging task for buckling constraints.
Because of the above reasons, for the time being, reasonable success can only be expected for one class of design problems — shell structures with non-zero base thickness.