Why multi-load topology designs based on orthogonal microstructures are in general non-optimal

It is well established that for a compliance constraint, the optimal topology of perforated plates under plane stress tends to that for least-weight trusses (Michell structures) as the volume fraction (i.e. the ratio material volume/available volume) approaches zero. It is shown in this note that for two loading conditions the optimal bar orientations for Michell structures are in general non-orthogonal and hence the assumption of orthogonal microstructures in multi-load plate topology optimization must lead to erroneous results.